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<div class="ChapSects"><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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<h3>3 <span class="Heading">Development History</span></h3>
<p><a id="X8192EA4C7B7CC5CD" name="X8192EA4C7B7CC5CD"></a></p>
<h4>3.1 <span class="Heading">Versions of the package</span></h4>
<p>The first version of the package, written for <strong class="pkg">GAP</strong> 3, formed part of Anne Heyworth's thesis <a href="chapBib.html#biBanne-thesis">[Hey99]</a> in 1999, but was not made generally available.</p>
<p>Version, <strong class="pkg">kan</strong> 0.91, was prepared to run under <strong class="pkg">GAP</strong> 4.4.6, in July 2005.</p>
<p>Version, <strong class="pkg">kan</strong> 0.94, differed in two significant ways.</p>
<ul>
<li><p>This manual is prepared using the <strong class="pkg">GAPDoc</strong> package.</p>
</li>
<li><p>The test file <code class="file">kan/tst/kan\_manual.tst</code> sets the <code class="code">AssertionLevel</code> to <code class="code">0</code> to avoid recursion in the <strong class="pkg">Automata</strong> package.</p>
</li>
</ul>
<p>Version 0.95, of 9th October 2007, just fixed file protections and added a <code class="file">CHANGES</code> file.</p>
<p>Version 0.96 was required because the <strong class="pkg">kan</strong> website moved with the rest of the Mathematics website at Bangor.</p>
<p>Version 0.97, of November 18th 2008, deleted temporary fixes which were no longer needed once version 1.12 of <strong class="pkg">Automata</strong> became available.</p>
<p><a id="X83D1530487593182" name="X83D1530487593182"></a></p>
<h4>3.2 <span class="Heading">What needs doing next?</span></h4>
<p>There are too many items to list here, but some of the most important are as follows.</p>
<ul>
<li><p>Implement iterators and enumerators for double cosets.</p>
</li>
<li><p>At present the methods for <code class="code">DoubleCosetsNC</code> and <code class="code">RightCosetsNC</code> in this package return automata, rather than lists of cosets or coset enumerators. This needs to be fixed.</p>
</li>
<li><p>Provide methods for operations such as <code class="code">DoubleCosetRepsAndSizes</code>.</p>
</li>
<li><p>Convert the rest of the original <strong class="pkg">GAP</strong> 3 version of <strong class="pkg">kan</strong> to <strong class="pkg">GAP</strong> 4.</p>
</li>
</ul>
<p><a id="X852CC057809CE3EE" name="X852CC057809CE3EE"></a></p>
<h5>3.2-1 DoubleCosetsAutomaton</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> DoubleCosetsAutomaton</code>( <var class="Arg">G, U, V</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> RightCosetsAutomaton</code>( <var class="Arg">G, V</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Alternative methods for <code class="code">DoubleCosetsNC(G,U,V)</code> and <code class="code">RightCosetsNC(G,V)</code> <em>should be</em> provided in the cases where the group <code class="code">G</code> has a rewriting system or is known to be infinite. At present the functions <code class="code">RightCosetsAutomaton</code> and <code class="code">DoubleCosetsAutomaton</code> return minimized automata, and <code class="code">Iterators</code> for these are not yet available.</p>
<table class="example">
<tr><td><pre>
gap> F := FreeGroup(2);;
gap> rels := [ F.2^2, (F.1*F.2)^2 ];;
gap> G4 := F/rels;;
gap> genG4 := GeneratorsOfGroup( G4 );;
gap> a := genG4[1]; b := genG4[2];;
gap> U := Subgroup( G4, [a^2] );;
gap> V := Subgroup( G4, [b] );;
gap> dc4 := DoubleCosetsAutomaton( G4, U, V );;
gap> Print( dc4 );
Automaton("det",5,"HKaAbB",[ [ 2, 2, 2, 5, 2 ], [ 2, 2, 1, 2, 1 ], [ 2, 2, 2, \
2, 3 ], [ 2, 2, 2, 2, 2 ], [ 2, 2, 2, 2, 2 ], [ 2, 2, 2, 2, 2 ] ],[ 4 ],[ 1 ])\
;;
gap> rc4 := RightCosetsAutomaton( G4, V );;
gap> Print( rc4 );
Automaton("det",6,"HKaAbB",[ [ 2, 2, 2, 6, 2, 2 ], [ 2, 2, 1, 2, 1, 1 ], [ 2, \
2, 3, 2, 2, 3 ], [ 2, 2, 2, 2, 5, 5 ], [ 2, 2, 2, 2, 2, 2 ], [ 2, 2, 2, 2, 2, \
2 ] ],[ 4 ],[ 1 ]);;
</pre></td></tr></table>
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