GAP (Semigroups) - Chapter 1: The Semigroups package

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1 The Semigroups package
1.1 Introduction
1.2 Overview

### 1 The Semigroups package

#### 1.1 Introduction

This is the manual for the Semigroups package for GAP version 5.2.0. Semigroups 5.2.0 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.

#### 1.2 Overview

This manual is organised as follows:

Part I: elements

  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).

Part II: semigroups and monoids defined by generating sets

  functions and operations for creating semigroups and monoids defined by generating sets (of the type descibed in Part I) are described in Chapter 6.

Part III: standard examples and constructions

  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.

Part IV: the structure of a semigroup or monoid

  the functionality for determining various structural properties of a given semigroup or monoid are described in Chapters 9, 10, 11, and 12.

Part V: congruences, quotients, and homomorphisms

  methods for creating and manipulating congruences and homomorphisms are described by Chapters 13 and 14.

Part VI: finitely presented semigroups and monoids

  methods for finitely presented semigroups and monoids, in particular, for Tietze transformations can be found in Chapters 15.

Part VII: utilities and helper functions

  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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