Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/hap/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 19.6.2025 mit Größe 28 kB image not shown  

Quelle  chap32_mj.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/hap/doc/chap32_mj.html


<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<script type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (HAP commands) - Chapter 32:  Knots and Quandles </title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap32"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chap9_mj.html">9</a>  <a href="chap10_mj.html">10</a>  <a href="chap11_mj.html">11</a>  <a href="chap12_mj.html">12</a>  <a href="chap13_mj.html">13</a>  <a href="chap14_mj.html">14</a>  <a href="chap15_mj.html">15</a>  <a href="chap16_mj.html">16</a>  <a href="chap17_mj.html">17</a>  <a href="chap18_mj.html">18</a>  <a href="chap19_mj.html">19</a>  <a href="chap20_mj.html">20</a>  <a href="chap21_mj.html">21</a>  <a href="chap22_mj.html">22</a>  <a href="chap23_mj.html">23</a>  <a href="chap24_mj.html">24</a>  <a href="chap25_mj.html">25</a>  <a href="chap26_mj.html">26</a>  <a href="chap27_mj.html">27</a>  <a href="chap28_mj.html">28</a>  <a href="chap29_mj.html">29</a>  <a href="chap30_mj.html">30</a>  <a href="chap31_mj.html">31</a>  <a href="chap32_mj.html">32</a>  <a href="chap33_mj.html">33</a>  <a href="chap34_mj.html">34</a>  <a href="chap35_mj.html">35</a>  <a href="chap36_mj.html">36</a>  <a href="chap37_mj.html">37</a>  <a href="chap38_mj.html">38</a>  <a href="chap39_mj.html">39</a>  <a href="chap40_mj.html">40</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap31_mj.html">[Previous Chapter]</a>    <a href="chap33_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap32.html">[MathJax off]</a></p>
<p><a id="X83856E7178651841" name="X83856E7178651841"></a></p>
<div class="ChapSects"><a href="chap32_mj.html#X83856E7178651841">32 <span class="Heading"> Knots and Quandles </span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap32_mj.html#X7CFDEEC07F15CF82">32.1 <span class="Heading">  </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X8110BAD17D13F62D">32.1-1 PresentationKnotQuandle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7E82CBA08724AEAA">32.1-2 PD2GC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X81B7CD81869D5583">32.1-3 PlanarDiagramKnot</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7E9458058084E240">32.1-4 GaussCodeKnot</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X8012B9B17BD20990">32.1-5 PresentationKnotQuandleKnot</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X83DE5BA878103191">32.1-6 NumberOfHomomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X84A706527FE23BEB">32.1-7 PartitionedNumberOfHomomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X82013FC97875ADBC">32.1-8 ConjugationQuandle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7F14F7B478D2BEB9">32.1-9 FirstQuandleAxiomIsSatisfied</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7CD0A53778B4B316">32.1-10 IsQuandle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7A57441D7B508D15">32.1-11 Quandles</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X87EF4BF57864D642">32.1-12 Quandle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7BB746B478EC8B5F">32.1-13 IdQuandle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7AAECD4B7A1EA8A3">32.1-14 IsLatin</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X876784FB7A4F28AF">32.1-15 IsConnectedQuandle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X78C1102681E84FDC">32.1-16 ConnectedQuandles</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7C27E982797F6B08">32.1-17 ConnectedQuandle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X841BBAA87A1710E6">32.1-18 IdConnectedQuandle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X82D6ECA279C543B9">32.1-19 IsQuandleEnvelope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X87C70FD17E57A4C5">32.1-20 QuandleQuandleEnvelope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7DAE45E17A191E6E">32.1-21 KnotInvariantCedric</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X82F7689578D5EBAD">32.1-22 RightMultiplicationGroupAsPerm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X85EA01BD7F66DE1B">32.1-23 RightMultiplicationGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7C9885CC825835FC">32.1-24 AutomorphismGroupQuandleAsPerm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap32_mj.html#X7B3890EB85EB004A">32.1-25 AutomorphismGroupQuandle</a></span>
</div></div>
</div>

<h3>32 <span class="Heading"> Knots and Quandles </span></h3>

<p><a id="X7CFDEEC07F15CF82" name="X7CFDEEC07F15CF82"></a></p>

<h4>32.1 <span class="Heading">  </span></h4>

<p>Knots</p>

<p><a id="X8110BAD17D13F62D" name="X8110BAD17D13F62D"></a></p>

<h5>32.1-1 PresentationKnotQuandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PresentationKnotQuandle</code>( <var class="Arg">gaussCode</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Gauss Code of a knot (with the orientations; see <span class="SimpleMath">\(GaussCodeOfPureCubicalKnot\)</span> in HAP package) and outputs the generators and relators of the knot quandle associated (in the form of a record).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap6.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">4</a></span> </p>

<p><a id="X7E82CBA08724AEAA" name="X7E82CBA08724AEAA"></a></p>

<h5>32.1-2 PD2GC</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PD2GC</code>( <var class="Arg">PD</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a Planar Diagram of a knot; outputs the Gauss Code associated (with the orientations).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">3</a></span> </p>

<p><a id="X81B7CD81869D5583" name="X81B7CD81869D5583"></a></p>

<h5>32.1-3 PlanarDiagramKnot</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PlanarDiagramKnot</code>( <var class="Arg">n</var>, <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns a Planar Diagram for the <span class="SimpleMath">\(k\)</span>-th knot with <span class="SimpleMath">\(n\)</span> crossings (<span class="SimpleMath">\(n \leq 12\)</span>) if it exists; fail otherwise.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">3</a></span> </p>

<p><a id="X7E9458058084E240" name="X7E9458058084E240"></a></p>

<h5>32.1-4 GaussCodeKnot</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GaussCodeKnot</code>( <var class="Arg">n</var>, <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns a Gauss Code (with orientations) for the <span class="SimpleMath">\(k\)</span>-th knot with <span class="SimpleMath">\(n\)</span> crossings (<span class="SimpleMath">\(n \leq 12\)</span>) if it exists; fail otherwise.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X8012B9B17BD20990" name="X8012B9B17BD20990"></a></p>

<h5>32.1-5 PresentationKnotQuandleKnot</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PresentationKnotQuandleKnot</code>( <var class="Arg">n</var>, <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns generators and relators (in the form of a record) for the <span class="SimpleMath">\(k\)</span>-th knot with <span class="SimpleMath">\(n\)</span> crossings (<span class="SimpleMath">\(n \leq 12\)</span>) if it exists; fail otherwise.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">3</a></span> </p>

<p><a id="X83DE5BA878103191" name="X83DE5BA878103191"></a></p>

<h5>32.1-6 NumberOfHomomorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NumberOfHomomorphisms</code>( <var class="Arg">genRelQ</var>, <var class="Arg">finiteQ</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs generators and relators <span class="SimpleMath">\(genRelQ\)</span> of a knot quandle (in the form of a record, see above) and a finite quandle <span class="SimpleMath">\(finiteQ\)</span>; outputs the number of homomorphisms from the former to the latter.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap6.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">3</a></span> </p>

<p><a id="X84A706527FE23BEB" name="X84A706527FE23BEB"></a></p>

<h5>32.1-7 PartitionedNumberOfHomomorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PartitionedNumberOfHomomorphisms</code>( <var class="Arg">genRelQ</var>, <var class="Arg">finiteQ</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs generators and relators <span class="SimpleMath">\(genRelQ\)</span> of a knot quandle (in the form of a record, see above) and a finite connected quandle <span class="SimpleMath">\(finiteQ\)</span>; outputs a partition of the number of homomorphisms from the former to the latter.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">1</a></span> </p>

<p>Quandles</p>

<p><a id="X82013FC97875ADBC" name="X82013FC97875ADBC"></a></p>

<h5>32.1-8 ConjugationQuandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ConjugationQuandle</code>( <var class="Arg">G</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a finite group <span class="SimpleMath">\(G\)</span> and an integer <span class="SimpleMath">\(n\)</span>; outputs the associated <span class="SimpleMath">\(n\)</span>-fold conjugation quandle.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> </p>

<p><a id="X7F14F7B478D2BEB9" name="X7F14F7B478D2BEB9"></a></p>

<h5>32.1-9 FirstQuandleAxiomIsSatisfied</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FirstQuandleAxiomIsSatisfied</code>( <var class="Arg">M</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SecondQuandleAxiomIsSatisfied</code>( <var class="Arg">M</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ThirdQuandleAxiomIsSatisfied</code>( <var class="Arg">M</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a finite magma <span class="SimpleMath">\(M\)</span>; returns true if <span class="SimpleMath">\(M\)</span> satisfy the first/second/third axiom of a quandle, false otherwise.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7CD0A53778B4B316" name="X7CD0A53778B4B316"></a></p>

<h5>32.1-10 IsQuandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsQuandle</code>( <var class="Arg">M</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a finite magma <span class="SimpleMath">\(M\)</span>; returns true if <span class="SimpleMath">\(M\)</span> is a quandle, false otherwise.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">3</a></span> </p>

<p><a id="X7A57441D7B508D15" name="X7A57441D7B508D15"></a></p>

<h5>32.1-11 Quandles</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Quandles</code>( <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns a list of all quandles of size <span class="SimpleMath">\(n\)</span>, <span class="SimpleMath">\(n \leq 6\)</span>. If <span class="SimpleMath">\(n \geq 7\)</span>, it returns fail.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutPersistent.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">6</a></span> </p>

<p><a id="X87EF4BF57864D642" name="X87EF4BF57864D642"></a></p>

<h5>32.1-12 Quandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Quandle</code>( <var class="Arg">n</var>, <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns the <span class="SimpleMath">\(k\)</span>-th quandle of size <span class="SimpleMath">\(n\)</span> (<span class="SimpleMath">\(n \leq 6\)</span>) if such a quandle exists, fail otherwise.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap6.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPersistent.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">7</a></span> </p>

<p><a id="X7BB746B478EC8B5F" name="X7BB746B478EC8B5F"></a></p>

<h5>32.1-13 IdQuandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IdQuandle</code>( <var class="Arg">Q</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a quandle <span class="SimpleMath">\(Q\)</span>; and outputs a list of integers [<span class="SimpleMath">\(n\)</span>,<span class="SimpleMath">\(k\)</span>] such that <span class="SimpleMath">\(Q\)</span> is isomorphic to <span class="SimpleMath">\(Quandle(n,k)\)</span>. If <span class="SimpleMath">\(n \geq 7\)</span>, then it returns [<span class="SimpleMath">\(n\)</span>,fail] (where <span class="SimpleMath">\(n\)</span> is the size of <span class="SimpleMath">\(Q\)</span>).</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7AAECD4B7A1EA8A3" name="X7AAECD4B7A1EA8A3"></a></p>

<h5>32.1-14 IsLatin</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsLatin</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>Inputs a finite quandle <span class="SimpleMath">\(Q\)</span>; returns true if <span class="SimpleMath">\(Q\)</span> is latin, false otherwise.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X876784FB7A4F28AF" name="X876784FB7A4F28AF"></a></p>

<h5>32.1-15 IsConnectedQuandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsConnectedQuandle</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>Inputs a finite quandle <span class="SimpleMath">\(Q\)</span>; returns true if <span class="SimpleMath">\(Q\)</span> is connected, false otherwise.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X78C1102681E84FDC" name="X78C1102681E84FDC"></a></p>

<h5>32.1-16 ConnectedQuandles</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ConnectedQuandles</code>( <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns a list of all connected quandles of size <span class="SimpleMath">\(n\)</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">3</a></span> </p>

<p><a id="X7C27E982797F6B08" name="X7C27E982797F6B08"></a></p>

<h5>32.1-17 ConnectedQuandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ConnectedQuandle</code>( <var class="Arg">n</var>, <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns the <span class="SimpleMath">\(k\)</span>-th quandle of size <span class="SimpleMath">\(n\)</span> if such a quandle exists, fail otherwise.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap6.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">4</a></span> </p>

<p><a id="X841BBAA87A1710E6" name="X841BBAA87A1710E6"></a></p>

<h5>32.1-18 IdConnectedQuandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IdConnectedQuandle</code>( <var class="Arg">Q</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a connected quandle <span class="SimpleMath">\(Q\)</span>; and outputs a list of integers [<span class="SimpleMath">\(n\)</span>,<span class="SimpleMath">\(k\)</span>] such that <span class="SimpleMath">\(Q\)</span> is isomorphic to <span class="SimpleMath">\(ConnectedQuandle(n,k)\)</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">1</a></span> </p>

<p><a id="X82D6ECA279C543B9" name="X82D6ECA279C543B9"></a></p>

<h5>32.1-19 IsQuandleEnvelope</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsQuandleEnvelope</code>( <var class="Arg">Q</var>, <var class="Arg">G</var>, <var class="Arg">e</var>, <var class="Arg">stigma</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a set <span class="SimpleMath">\(Q\)</span>, a permutation group <span class="SimpleMath">\(G\)</span>, an element <span class="SimpleMath">\(e \in Q\)</span> and an element <span class="SimpleMath">\(stigma \in G\)</span>; returns true if this structure describes a quandle envelope, false otherwise.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">3</a></span> </p>

<p><a id="X87C70FD17E57A4C5" name="X87C70FD17E57A4C5"></a></p>

<h5>32.1-20 QuandleQuandleEnvelope</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ QuandleQuandleEnvelope</code>( <var class="Arg">Q</var>, <var class="Arg">G</var>, <var class="Arg">e</var>, <var class="Arg">stigma</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a set <span class="SimpleMath">\(Q\)</span>, a permutation group <span class="SimpleMath">\(G\)</span>, an element <span class="SimpleMath">\(e \in Q\)</span> and an element <span class="SimpleMath">\(stigma \in G\)</span>. If this structure describes a quandle envelope, the function returns the quandle from this quandle envelope; and fail otherwise. Nb: this quandle is a connected quandle.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">3</a></span> </p>

<p><a id="X7DAE45E17A191E6E" name="X7DAE45E17A191E6E"></a></p>

<h5>32.1-21 KnotInvariantCedric</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ KnotInvariantCedric</code>( <var class="Arg">genRelQ</var>, <var class="Arg">n</var>, <var class="Arg">m</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs generators and relators of a knot quandle (in the form of a record, see above) and two integers <span class="SimpleMath">\(n\)</span> and <span class="SimpleMath">\(m\)</span>; outputs a list [<span class="SimpleMath">\(n\)</span>1,<span class="SimpleMath">\(n\)</span>2,...,<span class="SimpleMath">\(n\)</span>k] where <span class="SimpleMath">\(n\)</span>j is a partition of the number of homomorphisms from the considered knot quandle to the <span class="SimpleMath">\(j\)</span>-th connected quandle of size <span class="SimpleMath">\(n \leq i \leq m\)</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X82F7689578D5EBAD" name="X82F7689578D5EBAD"></a></p>

<h5>32.1-22 RightMultiplicationGroupAsPerm</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightMultiplicationGroupAsPerm</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>Inputs a connected quandle <span class="SimpleMath">\(Q\)</span>; output its right multiplication group whose elements are permutations.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X85EA01BD7F66DE1B" name="X85EA01BD7F66DE1B"></a></p>

<h5>32.1-23 RightMultiplicationGroup</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightMultiplicationGroup</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>Inputs a connected quandle <span class="SimpleMath">\(Q\)</span>; output its right multiplication group whose elements are mappings from <span class="SimpleMath">\(Q\)</span> to <span class="SimpleMath">\(Q\)</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7C9885CC825835FC" name="X7C9885CC825835FC"></a></p>

<h5>32.1-24 AutomorphismGroupQuandleAsPerm</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AutomorphismGroupQuandleAsPerm</code>( <var class="Arg">Q</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a connected quandle <span class="SimpleMath">\(Q\)</span>; outputs its automorphism group whose elements are permutations.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7B3890EB85EB004A" name="X7B3890EB85EB004A"></a></p>

<h5>32.1-25 AutomorphismGroupQuandle</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AutomorphismGroupQuandle</code>( <var class="Arg">Q</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a connected quandle <span class="SimpleMath">\(Q\)</span>; outputs its automorphism group whose elements are mappings from <span class="SimpleMath">\(Q\)</span> to <span class="SimpleMath">\(Q\)</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnotsQuandles.html">3</a></span> </p>


<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap31_mj.html">[Previous Chapter]</a>    <a href="chap33_mj.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chap9_mj.html">9</a>  <a href="chap10_mj.html">10</a>  <a href="chap11_mj.html">11</a>  <a href="chap12_mj.html">12</a>  <a href="chap13_mj.html">13</a>  <a href="chap14_mj.html">14</a>  <a href="chap15_mj.html">15</a>  <a href="chap16_mj.html">16</a>  <a href="chap17_mj.html">17</a>  <a href="chap18_mj.html">18</a>  <a href="chap19_mj.html">19</a>  <a href="chap20_mj.html">20</a>  <a href="chap21_mj.html">21</a>  <a href="chap22_mj.html">22</a>  <a href="chap23_mj.html">23</a>  <a href="chap24_mj.html">24</a>  <a href="chap25_mj.html">25</a>  <a href="chap26_mj.html">26</a>  <a href="chap27_mj.html">27</a>  <a href="chap28_mj.html">28</a>  <a href="chap29_mj.html">29</a>  <a href="chap30_mj.html">30</a>  <a href="chap31_mj.html">31</a>  <a href="chap32_mj.html">32</a>  <a href="chap33_mj.html">33</a>  <a href="chap34_mj.html">34</a>  <a href="chap35_mj.html">35</a>  <a href="chap36_mj.html">36</a>  <a href="chap37_mj.html">37</a>  <a href="chap38_mj.html">38</a>  <a href="chap39_mj.html">39</a>  <a href="chap40_mj.html">40</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>

100%


¤ Dauer der Verarbeitung: 0.23 Sekunden  ¤

*© Formatika GbR, Deutschland




Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.