4.0.0
28 February 2022
James Mitchell
Email: jdm3@st-andrews.ac.uk
Homepage: https://jdbm.me
Address:
Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
The Semigroups package is a GAP package for semigroups, and monoids. There are particularly efficient methods for finitely presented semigroups and monoids, and for semigroups and monoids consisting of transformations, partial permutations, bipartitions, partitioned binary relations, subsemigroups of regular Rees 0-matrix semigroups, and matrices of various semirings including boolean matrices, matrices over finite fields, and certain tropical matrices. Semigroups contains efficient methods for creating semigroups, monoids, and inverse semigroups and monoids, calculating their Green's structure, ideals, size, elements, group of units, small generating sets, testing membership, finding the inverses of a regular element, factorizing elements over the generators, and so on. It is possible to test if a semigroup satisfies a particular property, such as if it is regular, simple, inverse, completely regular, and a large number of further properties. There are methods for finding presentations for a semigroup, the congruences of a semigroup, the maximal subsemigroups of a finite semigroup, smaller degree partial permutation representations, and the character tables of inverse semigroups. There are functions for producing pictures of the Green's structure of a semigroup, and for drawing graphical representations of certain types of elements.
© by J. D. Mitchell et al.
Semigroups is free software; you can redistribute it and/or modify it, under the terms of the GNU General Public License, version 3 of the License, or (at your option) any later, version.
I would like to thank:
who contributed methods for checking finiteness of semigroups of matrices of the max-plus and min-plus semirings.
who contributed to the function DotString (16.1-1).
who contributed to the part of the package relating to bipartitions. I would like to thank the University of Western Sydney for their support of the development of this part of the package.
who contributed many of the standard examples of bipartition semigroups.
Max Horn contributed many patches and fixes, in particular, to the kernel module.
Chris Jefferson contributed several patches and fixes to the build system.
Julius Jonušas contributed the part of the package relating to free inverse semigroups, free bands, and contributed to the code for ideals.
Zak Mesyan contributed to the code for graph inverse semigroups; see Section 7.10.
Dima Pasechnik contributed to the build system of the kernel module.
Markus Pfeiffer contributed the majority of the code relating to semigroups of matrices over finite fields.
Yann Péresse and Yanhui Wang contributed to the attribute MunnSemigroup (7.2-1).
Jhevon Smith and Ben Steinberg contributed the function CharacterTableOfInverseSemigroup (11.14-10).
Michael Young contributed the part of the package relating to congruences.
Murray Whyte was kind enough to update the bibliography in 2019.
Wilf A. Wilson contributed to the part of the package relating maximal subsemigroups and smaller degree partial permutation representations of inverse semigroups. We are also grateful to C. Donoven and R. Hancock for their contribution to the development of the algorithms for maximal subsemigroups and smaller degree partial permutation representations.
We would also like to acknowledge the support of: EPSRC grant number GR/S/56085/01; the Carnegie Trust for the Universities of Scotland for funding the PhD scholarships of Julius Jonušas and Wilf A. Wilson when they worked on this project; the Engineering and Physical Sciences Research Council (EPSRC) for funding the PhD scholarship of M. Young when he worked on this project (EP/M506631/1).
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