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<h1><strong class="pkg">kan</strong></h1>
<h2>A package for Induced Category Actions</h2>
<p>Version 0.97</p>
<p>November 2008</p>
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<p><b> Anne Heyworth
</b>
<br />Email: <span class="URL"><a href="mailto:anne.heyworth@googlemail.com">anne.heyworth@googlemail.com</a></span>
</p><p><b> Chris Wensley
</b>
<br />Email: <span class="URL"><a href="mailto:c.d.wensley@bangor.ac.uk">c.d.wensley@bangor.ac.uk</a></span>
<br />Homepage: <span class="URL"><a href="http://www.bangor.ac.uk/~mas023/">http://www.bangor.ac.uk/~mas023/</a></span>
<br />Address: <br />School of Computer Science, Bangor University,<br /> Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.
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<h3>Abstract</h3>
<p>The <strong class="pkg">kan</strong> package was originally implemented in 1997 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>Bug reports, suggestions and comments are, of course, welcome. Please contact the second author at <span class="URL"><a href="mailto:c.d.wensley@bangor.ac.uk">c.d.wensley@bangor.ac.uk</a></span>.</p>
<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2005-2008 Anne Heyworth and Chris Wensley</p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>This <strong class="pkg">kan</strong> package is released under the GNU General Public License (GPL). This file is part of <strong class="pkg">kan</strong>, though as documentation it is released under the GNU Free Documentation License (see <span class="URL"><a href="http://www.gnu.org/licenses/licenses.html#FDL">http://www.gnu.org/licenses/licenses.html#FDL</a></span>).</p>
<p><strong class="pkg">kan</strong> 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><strong class="pkg">kan</strong> is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.</p>
<p>You should have received a copy of the GNU General Public License along with <strong class="pkg">kan</strong>; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.</p>
<p>For more details, see <span class="URL"><a href="http://www.fsf.org/licenses/gpl.html">http://www.fsf.org/licenses/gpl.html</a></span>.</p>
<p>This documentation was prepared with the <strong class="pkg">GAPDoc</strong> package of Frank L\"ubeck and Max Neunh\"offer.</p>
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<h3>Contents</h3>
<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
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<div class="ContChap"><a href="chap2.html#X7F197C8D835A6F45">2 <span class="Heading">Double Coset Rewriting Systems</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X7CA8FCFD81AA1890">2.1 <span class="Heading">Rewriting Systems</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X87A3823483E4FF86">2.1-1 KnuthBendixRewritingSystem</a></span>
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<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X846F0B22859B601A">2.2 <span class="Heading">Example 1 -- free product of two cyclic groups</span></a>
<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#X83FF05087E7B133A">2.2-2 WordAcceptorOfReducedRws</a></span>
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<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X838CC08E7E92EBC0">2.3 <span class="Heading">Example 2 -- the trefoil group</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X83DE506B828F4B0D">2.3-1 PartialDoubleCosetRewritingSystem</a></span>
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<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X86DACE357868DC1B">2.4 <span class="Heading">Example 3 -- an infinite rewriting system</span></a>
<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#X7AF0265982B42E47">2.4-3 NextWord</a></span>
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<div class="ContChap"><a href="chap3.html#X810C43BC7F63C4B4">3 <span class="Heading">Development History</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X8192EA4C7B7CC5CD">3.1 <span class="Heading">Versions of the package</span></a>
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<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X83D1530487593182">3.2 <span class="Heading">What needs doing next?</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X852CC057809CE3EE">3.2-1 DoubleCosetsAutomaton</a></span>
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