GAP (IdRel) - Chapter 1: Introduction

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### 1. Introduction

This manual describes the IdRel (version 2.02) GAP share package for computing the identities among relations of a group presentation using rewriting, logged rewriting, monoid polynomials, module polynomials and Y-sequences.

The theoretical background for these computations is contained in Brown and Huebschumann [BH82], Brown and Razak Salleh [BR99] and is surveyed in [H99].

IdRel is primarily designed for the computation of a minimal set of generators for the module of identities among relations. It also contains functions which compute logged rewrite systems for group presentations (and complete them where possible), functions for operations involving elements of monoid rings and functions for operations with elements of right modules over monoid rings. The Y-sequences are used as a rewriting way of representing elements of a free crossed module (products of conjugates of group relators and inverse relators). The package is written entirely in GAP4, and requires no compilation.

The package is loaded into GAP with the `LoadPackage` command, and on-line help is available in the usual way.

    gap> LoadPackage( "idrel" );
    gap> ?idrel

The usual dvi, pdf and PostScript versions of the IdRel manual are available (as `manual.dvi`, `manual.pdf` and `manual.ps` respectively) in the `doc` directory of the home directory of IdRel. The information parameter `InfoIdRel` has default value `0`. When raised to a higher value, additional information is printed out. IdRel was originally developed in 1999 using GAP3, partially supported by a University of Wales Research Assistantship for the first author, Anne Heyworth. If you use IdRel to solve a problem then please send a short email to the second author, to whom bug reports, suggestions and other comments should also be sent. You may reference the package by mentioning [HW03] and [H99].

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