This is a C++14 header-only library for symmetry-optimized tensor computation and type checking.

Tensor contraction formulas can be written using Einstein index notation:

• Repeated index names are contracted.
• Index type checking ensures that incorrect formulas are caught at compile time.
• See tests for examples.

Each tensor index has a type corresponding to a space with a basis and units (e.g. meters, inverse-seconds):

• Only dual spaces can be contracted.
• The type checker will detect incompatible index contractions.
• Space types are derived according to tensor constructions.

Contracted tensor products are lazy-evaluated:

• Intermediate terms that will not be used in the final contraction are not computed.
• Index re-use in a tensor contraction expression will result in a compiler error.

Tensors with symmetries are represented using only independent components:

• Representations are implemented for fully symmetric or anti-symmetric index groups.
• Efficient multivariable polynomials are supported.
• The representation uses a single index with a distinct type.

Memory mapping to Eigen is supported for efficient matrix operations and decompositions.

Planned:

• Young Tableaux independent component specification.
• Overlapping symmetries (e.g. for Riemann curvature tensor).
• Optimal contraction ordering (like optimal rectangular matrix associative ordering).

• Git (https://git-scm.com)
• CMake (https://cmake.org)

• Variadic Meta Programming (https://github.com/Reification/VariadicMetaProgramming)
• UnitTest++ (https://github.com/unittest-cpp/unittest-cpp)
• Doxygen Filter for CMake (https://github.com/saschazelzer/CMakeDoxygenFilter)
• Conditional Sources and Verbose Message for CMake (https://github.com/wal-rus/cmake-modules)

• Eigen (http://eigen.tuxfamily.org/index.php?title=Main_Page)

• Doxygen (http://www.stack.nl/~dimitri/doxygen/)
• MathJax (https://www.mathjax.org)

Derived from EmptyCPP project template (https://github.com/GabrielHare/EmptyCPP)

cmake -G "Unix Makefiles" -B builds/Clang -S . -DBUILD_TESTS=ON \
  -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++
cmake --build builds/Clang --target tests

cmake -G Xcode -B builds/XCode2025 -S . -DBUILD_TESTS=ON
cmake --build builds/XCode2025 --target tests --config Release

cmake -G "Visual Studio 17 2022" -B builds/VS2022 -S . -DBUILD_TESTS=ON -A x64
cmake --build builds/VS2022 --target tests --config Release