mathic

Mathic is a C++ library of fast data structures designed for use in Groebner basis computation. This includes data structures for ordering S-pairs, performing divisor queries and ordering polynomial terms during polynomial reduction.

With Mathic you get to use highly optimized code with little effort so that you can focus more of your time on whatever part of your Groebner basis implementation that you are interested in. The data structures use templates to allow you to use them with whatever representation of monomials/terms and coefficients that your code uses. In fact the only places where Mathic defines its own monomials/terms is in the test code and example code. Currently only dense representations of terms/monomials are suitable since Mathic will frequently ask "what is the exponent of variable number x in this term/monomial?".

The paper "Practical Grobner Basis Computation" describes the data structures from a high level. It was presented at ISSAC 2012 and is available at http://arxiv.org/abs/1206.6940

The following copyright and license notice applies to all of the files in mathic.

Copyright 2012 2013 Bjarke Hammersholt Roune (http://www.broune.com) and Michael Stillman

Mathic is licensed for use under the terms of GNU Lesser General Public License version 2.0, and under any later version; the option is yours. See the files lgpl-*.txt in this directory.

Building and using the CMake package

This build requires CMake 3.18 or newer and a C++17 compiler.

cmake -S . -B build-dir -GNinja -DCMAKE_BUILD_TYPE=Release \
  -DBUILD_SHARED_LIBS=ON -DCMAKE_INSTALL_PREFIX=/your/install/prefix
cmake --build build-dir
ctest --test-dir build-dir --output-on-failure
cmake --install build-dir

BUILD_TESTING=OFF disables the GoogleTest dependency and unit tests. Both shared and static installations provide headers, pkg-config metadata, and a relocatable CMake package under the platform's library directory:

find_package(mathic 1.5 CONFIG REQUIRED)
target_link_libraries(my_program PRIVATE mathic::mathic)

The target supplies C++17, include paths and transitive dependencies. Dependency CMake configs are preferred; pkg-config metadata is supported for existing system installations. Older Homebrew CMake bottles may lack both metadata formats; build the dependency with its released Autotools build, or install a CMake package that supplies the config. Bare header/library discovery is insufficient to propagate dependencies' ABI flags. The dependency find modules are shipped with the config. Use a quoted semicolon-separated -DCMAKE_PREFIX_PATH='/prefix/one;/prefix/two' for nonstandard prefixes; the Unix environment variable uses colons instead.

The installed package exports MATHIC_DEBUG if the library was built in Debug mode, even when the consumer uses Release. It inherits dependencies' own ABI flags instead of forcing their Debug layouts. pkg-config --cflags mathic also reports the installed library's Debug flag; pkg-config consumers should select C++17 or later explicitly.