<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 [Hey99] in 1999, but was not made generally available.
<p>Version 0.91 was prepared to run under <strong class="pkg">GAP</strong> 4.4.6, in July 2005.</p>
<p>Version 0.94 differed in two significant ways.</p>
<ul>
<li><p>The manual was produced using the <strong class="pkg">GAPDoc</strong> package.</p>
</li>
<li><p>The test file <code class="file">kan/tst/kan_manual.tst</code> set 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 1.11, of December 2014 was required when the <strong class="pkg">Kan</strong> website moved yet again. At the same time a bitbucket repository for the package was started.</p>
<p><strong class="pkg">Kan</strong> became an accepted <strong class="pkg">GAP</strong> package in May 2015.</p>
<p>Version 1.28, of May 2017, saw a great many changes to the examples, with the various rewriting systems used to perform reduction of words to reduced form.</p>
<p>Only minor changes have been made in recent years.</p>
<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>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ DoubleCosetsAutomaton</code>( <var class="Arg">G</var>, <var class="Arg">U</var>, <var class="Arg">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</var>, <var class="Arg">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>
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