5.4.0
19 October 2024
James Mitchell
Email: jdm3@st-andrews.ac.uk
Homepage: https://jdbm.me
Address:
Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
Marina Anagnostopoulou-Merkouri
Email: marina.anagnostopoulou-merkouri@bristol.ac.uk
Homepage: https://marinaanagno.github.io
Thomas Breuer
Email: sam@math.rwth-aachen.de
Homepage: https://www.math.rwth-aachen.de/~Thomas.Breuer/
Stuart Burrell
Email: stuartburrell1994@gmail.com
Homepage: https://stuartburrell.github.io
Reinis Cirpons
Email: rc234@st-andrews.ac.uk
Homepage: https://reinisc.id.lv/
Address:
Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
Tom Conti-Leslie
Email: tom.contileslie@gmail.com
Homepage: https://tomcontileslie.com/
Joseph Edwards
Email: jde1@st-andrews.ac.uk
Homepage: https://github.com/Joseph-Edwards
Address:
Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
Attila Egri-Nagy
Email: attila@egri-nagy.hu
Homepage: http://www.egri-nagy.hu
Luke Elliott
Email: le27@st-andrews.ac.uk
Homepage: https://le27.github.io/Luke-Elliott/
Address:
Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
Fernando Flores Brito
Email: ffloresbrito@gmail.com
Tillman Froehlich
Email: trf1@st-andrews.ac.uk
Nick Ham
Email: nicholas.charles.ham@gmail.com
Homepage: https://n-ham.github.io
Robert Hancock
Email: robert.hancock@maths.ox.ac.uk
Homepage: https://sites.google.com/view/robert-hancock/
Max Horn
Email: horn@mathematik.uni-kl.de
Homepage: https://www.quendi.de/math
Address:
Fachbereich Mathematik, TU Kaiserslautern, Gottlieb-Daimler-Straße 48, 67663 Kaiserslautern, Germany
Christopher Jefferson
Email: caj21@st-andrews.ac.uk
Homepage: https://heather.cafe/
Address:
Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9SX, Scotland
Julius Jonusas
Email: j.jonusas@gmail.com
Homepage: http://julius.jonusas.work
Chinmaya Nagpal
Olexandr Konovalov
Email: obk1@st-andrews.ac.uk
Homepage: https://olexandr-konovalov.github.io/
Address:
Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9SX, Scotland
Artemis Konstantinidi
Hyeokjun Kwon
Dima V. Pasechnik
Email: dmitrii.pasechnik@cs.ox.ac.uk
Homepage: http://users.ox.ac.uk/~coml0531/
Address:
Pembroke College, St. Aldates, Oxford OX1 1DW, England
Markus Pfeiffer
Email: markus.pfeiffer@morphism.de
Homepage: https://markusp.morphism.de/
Christopher Russell
Jack Schmidt
Email: jack.schmidt@uky.edu
Homepage: https://www.ms.uky.edu/~jack/
Sergio Siccha
Email: sergio.siccha@gmail.com
Finn Smith
Email: fls3@st-andrews.ac.uk
Homepage: https://flsmith.github.io/
Address:
Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
Ben Spiers
Nicolas Thiéry
Email: nthiery@users.sf.net
Homepage: https://nicolas.thiery.name/
Maria Tsalakou
Email: mt200@st-andrews.ac.uk
Homepage: https://mariatsalakou.github.io/
Address:
Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
Chris Wensley
Email: cdwensley.maths@btinternet.com
Murray Whyte
Email: mw231@st-andrews.ac.uk
Address:
Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
Wilf A. Wilson
Email: gap@wilf-wilson.net
Homepage: https://wilf.me
Tianrun Yang
Michael Young
Email: mct25@st-andrews.ac.uk
Homepage: https://mtorpey.github.io/
Address:
Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9SX, Scotland
Fabian Zickgraf
Email: f.zickgraf@dashdos.com
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.
The authors of the Semigroups package would like to thank:
who contributed to the function DotString (16.1-1).
for their contribution to the development of the algorithms for maximal subsemigroups and smaller degree partial permutation representations.
who contributed to the part of the package relating to bipartitions. We also thank the University of Western Sydney for their support of the development of this part of the package.
who contributed to the code for graph inverse semigroups; see Section 7.10.
who contributed to the attribute MunnSemigroup (7.2-1).
who contributed the function CharacterTableOfInverseSemigroup (11.14-10).
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 scholarships of F. Smith (EP/N509759/1) and M. Young (EP/M506631/1) when they worked on this project.
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