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<!--  manual.xml         IdRel documentation              Chris Wensley  -->
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<!--  $Id: manual.xml,v 2.02 2006/06/02 gap Exp $                        -->
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  <!-- $Id: manual.xml,v 2.02  Exp $ -->

<!DOCTYPE Book SYSTEM "gapdoc.dtd"
[<!ENTITY idrel "<Package>IdRel</Package>">] >

<Book Name="IdRel"> 

<TitlePage>
  <Title>&idrel;</Title>
  <Subtitle>A package for Identities among Relators</Subtitle>
  <Version>Version 2.02</Version>

  <Author> Anne Heyworth
    <Email>a.heyworth@mcs.le.ac.uk</Email>
    <Address>
      University of Leicester.
    </Address>
  </Author>    
  <Author> Chris Wensley
    <Email>c.d.wensley@bangor.ac.uk</Email>
    <Homepage>http://www.informatics.bangor.ac.uk/~cwensley/</Homepage>
    <Address>
      School of Informatics, University of Wales Bangor,<Br/>
      Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.
    </Address>
  </Author>

  <Date>June 2006</Date>

<Abstract>
The &idrel; package was originally implemented in 1999 using 
the &GAP;3 language, when the first author was studying for a Ph.D. in Bangor, 
and has since been converted to &GAP;4.
<P/>
This package is designed to compute a minimal set of generators 
for the module of the identities among relations 
of a group presentation. 
It does this using 
<List>
<Item>
rewriting and logged rewriting: a self-contained implementation 
of the Knuth-Bendix process using the monoid presentation 
associated to the group presentation;
</Item>
<Item>
monoid polynomials: an implementation of the monoid ring;
</Item>
<Item>
module polynomials: an implementation of the right module 
over this monoid generated by the relators. 
</Item>
<Item>
Y-sequences: used as a <E>rewriting</E> way of representing 
elements of a free crossed module 
(products of conjugates of group relators and inverse relators).
</Item>
</List>
<P/>
Bug reports, suggestions and comments are, of course, welcome. 
Please contact the second author at     
<Email>c.d.wensley@bangor.ac.uk</Email>.
</Abstract>

<Copyright> 
  &copyright; 1999-2006 by Anne Heyworth and Chris Wensley <P/>
  We adopt the copyright regulations of &GAP; as detailed in the 
  copyright notice in the &GAP; manual. 
</Copyright>

</TitlePage>

<TableOfContents/>

<Body>

<#Include SYSTEM "intro.xml">
<#Include SYSTEM "rws.xml">
<#Include SYSTEM "logrws.xml">
<#Include SYSTEM "monpoly.xml">
<#Include SYSTEM "modpoly.xml">

</Body>

<Bibliography Databases="manual"/>

<TheIndex/>

</Book>
