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<!--  intro.xml           IdRel documentation             Chris Wensley  -->
<!--                                                    & Anne Heyworth  -->
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<!--  $Id: intro.xml,v 2.05 2008/11/21 gap Exp $                         -->
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<Chapter Label="intro">
<Heading>Introduction</Heading>

This manual describes the &idrel; (version 2.05) &GAP; package 
for computing the identities among relators of a group presentation 
using rewriting, logged rewriting, monoid polynomials, module polynomials 
and <M>Y</M>-sequences.
<P/>
The theoretical background for these computations is contained in 
Brown and Huebschumann <Cite Key="BrHu" />, 
Brown and Razak Salleh <Cite Key="BrSa" /> and is surveyed in 
<Cite Key="anne-thesis" />.
<P/>
&idrel; is primarily designed for the computation of a minimal set 
of generators for the module of identities among relators. 
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 <M>Y</M>-sequences are used as a <E>rewriting</E> way of representing 
elements of a free crossed module 
(products of conjugates of group relators and inverse relators).
The package is written entirely in &GAP;4, and requires no compilation.
<P/>
The package is loaded into &GAP; with the <C>LoadPackage</C> command, 
and on-line help is available in the usual way.
<Example>
<![CDATA[
gap> LoadPackage( "idrel" ); 
gap> ?idrel
]]>
</Example>

A pdf version of the &idrel; manual is available 
in the <F>doc</F> directory of the home directory of &idrel;.

The information parameter <C>InfoIdRel</C> has default value <C>0</C>.
When raised to a higher value, additional information is printed out.

&idrel; was originally developed in 1999 using &GAP;3, 
partially supported by a University of Wales Research Assistantship 
for the first author, Anne Heyworth.
<P/>
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 <Cite Key="HeWe1" />
and <Cite Key="anne-thesis" />.
<P/>
The new version (2.05) was required in November 2008 
because the Mathematics website at Bangor moved to a different network, 
and the &idrel; pages moved with it. 
</Chapter>