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<h1>kan</h1>


<h2>including double coset rewriting systems</h2>

<p>
    1.37</p>

<p>
    23 January 2024
  </p>

</div>
<p><b>
    Anne Heyworth

  </b>
</p><p><b>
    Chris Wensley



  </b>
<br />Email: <span class="URL"><a href="mailto:cdwensley.maths@btinternet.com">cdwensley.maths@btinternet.com</a></span>
<br />Homepage: <span class="URL"><a href="https://github.com/cdwensley">https://github.com/cdwensley</a></span>
</p>

<p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p>
<h3>Abstract</h3>
<p><strong class="pkg">Kan</strong> is a <strong class="pkg">GAP</strong> package originally implemented in 1996 using the <strong class="pkg">GAP</strong> 3 language, to compute induced actions of categories, when the first author was studying for a Ph.D. in Bangor.</p>

<p>This reduced version only provides functions for the computation of normal forms of representatives of double cosets of finitely presented groups.</p>

<p><strong class="pkg">Kan</strong> became an accepted <strong class="pkg">GAP</strong> package in May 2015.</p>

<p>Bug reports, suggestions and comments are, of course, welcome. Please contact the last author at <span class="URL"><a href="mailto:cdwensley.maths@btinternet.com">cdwensley.maths@btinternet.com</a></span> or submit an issue at the GitHub repository <span class="URL"><a href="https://github.com/gap-packages/kan/issues/">https://github.com/gap-packages/kan/issues/</a></span>.</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 1996-2024 Anne Heyworth and Chris Wensley</p>

<p>The <strong class="pkg">Kan</strong> package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>This documentation was prepared using the <strong class="pkg">GAPDoc</strong> <a href="chapBib.html#biBGAPDoc">[LN17]</a> and <strong class="pkg">AutoDoc</strong> <a href="chapBib.html#biBAutoDoc">[GH17]</a> packages.</p>

<p>The procedure used to produce new releases uses the package <strong class="pkg">GitHubPagesForGAP</strong> <a href="chapBib.html#biBGitHubPagesForGAP">[Hor17]</a> and the package <strong class="pkg">ReleaseTools</strong>.</p>

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<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
</div>
<div class="ContChap"><a href="chap2.html#X7F197C8D835A6F45">2 <span class="Heading">Double Coset Rewriting Systems</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7CA8FCFD81AA1890">2.1 <span class="Heading">Rewriting Systems</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X87A3823483E4FF86">2.1-1 KnuthBendixRewritingSystem</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7AF0265982B42E47">2.1-2 NextWord</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X80B18B248603B3D6">2.2 <span class="Heading">Example 2 -- free product of two cyclic groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X825D1F4D85DE122D">2.2-1 DoubleCosetRewritingSystem</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X82E14C4284D89ADF">2.2-2 DisplayAsString</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X83FF05087E7B133A">2.2-3 WordAcceptorOfReducedRws</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X82FE46C27FE55A84">2.3 <span class="Heading">Example 3 -- the trefoil group</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X83DE506B828F4B0D">2.3-1 PartialDoubleCosetRewritingSystem</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7ED711187E2ECAC7">2.4 <span class="Heading">Example 4 -- an infinite rewriting system</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8722C57284F51940">2.4-1 KBMagRewritingSystem</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X815C08FD87D014B5">2.4-2 DCrules</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X84B36973833F3B54">2.4-3 WordToString</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X810C43BC7F63C4B4">3 <span class="Heading">Development History</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X8192EA4C7B7CC5CD">3.1 <span class="Heading">Versions of the package</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X83D1530487593182">3.2 <span class="Heading">What needs doing next?</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X852CC057809CE3EE">3.2-1 DoubleCosetsAutomaton</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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