This is the manual for the Semigroups package for GAP version 5.4.0. Semigroups 5.4.0 is a distant descendant of the Monoid package for GAP 3 by Goetz Pfeiffer, Steve A. Linton, Edmund F. Robertson, and Nik Ruskuc.
From Version 3.0.0, Semigroups includes a copy of the libsemigroups C++ library which contains implementations of the Froidure-Pin, Todd-Coxeter, and Knuth-Bendix algorithms (among others) that Semigroups utilises.
If you find a bug or an issue with the package, please visit the issue tracker.
This manual is organised as follows:
the different types of elements that are introduced in Semigroups are described in Chapters 3, 4, and 5. These include Bipartition (3.2-1), PBR (4.2-1), and Matrix (5.1-5), which supplement those already defined in the GAP library, such as Transformation (Reference: Transformation for an image list) or PartialPerm (Reference: PartialPerm for a domain and image).
functions and operations for creating semigroups and monoids defined by generating sets (of the type described in Part I) are described in Chapter 6.
standard examples of semigroups, such as FullBooleanMatMonoid (7.6-1) or UniformBlockBijectionMonoid (7.3-8), are described in Chapter 7, and standard constructions, such as DirectProduct (8.1-1) are given in Chapter 8.
the functionality for determining various structural properties of a given semigroup or monoid are described in Chapters 9, 10, 11, and 12.
methods for creating and manipulating congruences and homomorphisms are described by Chapters 13 and 14.
methods for finitely presented semigroups and monoids, in particular, for Tietze transformations can be found in Chapters 15.
functions for reading and writing semigroups and their elements, and for visualising semigroups, and some of their elements, can be found in Chapters 16 and 17.
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