sym2: Small C++ library for computer algebra

This small library intends to provide a simple approach to symbolic algebra and good runtime performance. In contrast to fully-fledged computer algebra systems or libraries (e.g. maxima, GiNaC, sympy), only basic features are/will be implemented, e.g. automatic simplification, normalization, and expansion, trigonometric and logarithmiic functions, or arbitrary precision integers. Most algorithms are/will follow the techniques outlined in Cohen, Computer Algebra and Symbolic Computation [2003].

This library is under development and highly unusable at this point. Primary target platforms are 64bit Linux, BSD and MacOS. The code is MIT licensed, with a small Apache-2.0 exception. See LICENSE for more details.

Planned features

• Automatic simplification: a + b + 2*a = 3*a + b
• Expression expansion: (a + b)^2 = a^2 + 2*a*b + b^2
• Substitute (sub-)expressions 3*a + b = 6 + b for a = 2
• Trigonometric functions: sin(pi/4) = 1/sqrt(2) or sin^2(a) + cos^2(a) = 1
• Expression normalization via generalized gcd: a/b + 1/(5*b) = 1/5*(1 + 5*a)/b
• Differentiation: d/da 2*a^4 = 8*a^3
• Multiprecision integer arithmetic (not for floating point numbers)

Getting started

The build configuration is written in CMake, 3rd party dependencies are managed with conan. These dependencies are built using the conan recipes in lib/. Important: the expected compiler is gcc-12, together with libstdc++; expect build failures for any other toolchain. There is no such thing as a release yet, so the following sets up a default development/debug build with all existing targets and UBSan/ASan enabled, for use with ninja and ccache:

git clone https://github.com/lubgr/sym2.git
cd sym2

conan create lib/benchmark
conan create lib/boost-headers
conan create lib/chibi-scheme
conan create lib/cmake-coverage
conan create lib/doctest
conan create lib/ginac

mkdir build-debug
cd !$

conan install ..
cmake --preset default ..
ninja
ctest

For more options like release builds, coverage, building subsets (no benchmarks, no bindings, etc.), checkout the toplevel CMakeLists.txt or CMakePresets.json.

Notes

See the notes on the implementation for details on the design of internal data structures or notes on testing for the scripting interface.

Design-wise, the library is not intended to be extensible through subclasses that implement an interface for expressions. Instead, the expression types are fixed (symbol, integer, rational number, floating point number, complex number, sum, product, power, unary, function, binary function), and it is assumed that the existing types are sufficient to solve the users' needs. If that is not the case, you are probably looking for a different tool.