libsemigroups
is a C++14 library containing implementations of several
algorithms for computing finite, and finitely presented, semigroups and
monoids. Namely:
- the Froidure-Pin algorithm for computing finite semigroups;
- the Todd-Coxeter algorithm for finitely presented semigroups and monoids; see also this paper;
- the Knuth-Bendix algorithm for finitely presented semigroups and monoids;
- the Schreier-Sims algorithm for permutation groups;
- a preliminary implementation of the Konieczny and Lallement-McFadden algorithm for computing finite semigroups which act on sets;
- an implementation of the Radoszewski-Rytter algorithm for testing equivalence of words in free bands;
- an implementation of the algorithm for solving the word problem for small overlap monoids, and for computing normal forms in such monoids; see Kambites, Kambites, and Mitchell-Tsalakou
- a version of Sims low index subgroup algorithm for computing one-sided congruences of a semigroup or monoid.
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
, and
libsemigroups::SchreierSims
.
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.
See the documentation https://libsemigroups.readthedocs.io/en/latest/
Installation instructions are here https://libsemigroups.readthedocs.io/en/latest/install.html
If you find any problems with libsemigroups
, or have any suggestions for
features that you'd like to see, please use the issue tracker.
- R. Cirpons contributed to
IsObviouslyInfinite
, to integratingeigen
, contributed an implementation of the Radoszewski-Rytter algorithm for testing equivalence of words in free bands; and the intersection of permutation groups inSchreierSims
. - F. Hivert contributed many helpful ideas to
libsemigroups
, an allocator implementation (to be included in a future version), andHPCombi
. - J. James contributed some bugfixes.
- J. Jonušas contributed to the implementation of the Froidure-Pin algorithm.
- D. V. Pasechnik contributed to the build system.
- F. Smith contributed the implementation of the Konieczny and Lallement-McFadden algorithm, to the Todd-Coxeter implementation, and to BMat8s.
- N. Thiery contributed to the build system, packaging
libsemigroups
via conda, the python bindings and many helpful conversations and suggestions. - M. Torpey contributed to the congruences code in the v0.0.1 to v0.6.7.
- M. Tsalakou contributed to the Knuth-Bendix implementation, related algorithms for the class ActionDigraph, to the implementation of the Kambites class, and to the Sims1 class.
We acknowledge financial support from the OpenDreamKit Horizon 2020 European Research Infrastructures project (#676541) (primarily for the python bindings).
We thank the Carnegie Trust for the Universities of Scotland for funding the PhD scholarship of J. Jonušas when he worked on this project.
We thank the Engineering and Physical Sciences Research Council (EPSRC) for funding the PhD scholarships of M. Torpey and F. Smith when they worked on this project (EP/M506631/1, EP/N509759/1).