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<div class="ChapSects"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
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<h3>1 <span class="Heading">Introduction</span></h3>
<p>This manual describes the <strong class="pkg">IdRel</strong> (version 2.05) <strong class="pkg">GAP</strong> package for computing the identities among relators of a group presentation using rewriting, logged rewriting, monoid polynomials, module polynomials and Y-sequences.</p>
<p>The theoretical background for these computations is contained in Brown and Huebschumann <a href="chapBib.html#biBBrHu">[BH82]</a>, Brown and Razak Salleh <a href="chapBib.html#biBBrSa">[BS99]</a> and is surveyed in <a href="chapBib.html#biBanne-thesis">[Hey99]</a>.</p>
<p><strong class="pkg">IdRel</strong> 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 Y-sequences are used as a <em>rewriting</em> way of representing elements of a free crossed module (products of conjugates of group relators and inverse relators). The package is written entirely in <strong class="pkg">GAP</strong>4, and requires no compilation.</p>
<p>The package is loaded into <strong class="pkg">GAP</strong> with the <code class="code">LoadPackage</code> command, and on-line help is available in the usual way.</p>
<table class="example">
<tr><td><pre>
gap> LoadPackage( "idrel" );
gap> ?idrel
</pre></td></tr></table>
<p>A pdf version of the <strong class="pkg">IdRel</strong> manual is available in the <code class="file">doc</code> directory of the home directory of <strong class="pkg">IdRel</strong>. The information parameter <code class="code">InfoIdRel</code> has default value <code class="code">0</code>. When raised to a higher value, additional information is printed out. <strong class="pkg">IdRel</strong> was originally developed in 1999 using <strong class="pkg">GAP</strong>3, partially supported by a University of Wales Research Assistantship for the first author, Anne Heyworth.</p>
<p>If you use <strong class="pkg">IdRel</strong> 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 <a href="chapBib.html#biBHeWe1">[HW03]</a> and <a href="chapBib.html#biBanne-thesis">[Hey99]</a>.</p>
<p>The new version (2.05) was required in November 2008 because the Mathematics website at Bangor moved to a different network, and the <strong class="pkg">IdRel</strong> pages moved with it.</p>
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