# libsemigroups - Version 2.5.1¶

## C++ library for semigroups and monoids¶

### What is libsemigroups?¶

libsemigroups is a C++14 library containing implementations of several algorithms for computing finite, and finitely presented, semigroups and monoids. Namely:

libsemigroups is partly based on Algorithms for computing finite semigroups, Expository Slides, and Semigroupe 2.01 by Jean-Eric Pin.

libsemigroups is used in the Semigroups package for GAP, and it is possible to use libsemigroups directly in Python 3 via the package libsemigroups_pybind11. The development version of libsemigroups is available on github, and some related projects are here.

The main classes in libsemigroups are named after the algorithms they implement; see, for example, libsemigroups::FroidurePin, libsemigroups::Konieczny, libsemigroups::congruence::ToddCoxeter, libsemigroups::fpsemigroup::Kambites, libsemigroups::fpsemigroup::KnuthBendix, libsemigroups::SchreierSims, libsemigroups::Sims1, or libsemigroups::Stephen.

The implementations in libsemigroups::FroidurePin, libsemigroups::Konieczny, and libsemigroups::SchreierSims are generic and easily adapted to user-defined types.

libsemigroups uses: HPCombi which uses the SSE and AVX instruction sets for very fast manipulation of transformations, partial permutations, permutations, and boolean matrices of small size; catch for tests; fmt for reporting; and eigen for some linear algebra computations.

Installation and changelog

Bibliography

Further info