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products/Sources/formale Sprachen/GAP/pkg/utils/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 11.8.2025 mit Größe 1 kB image not shown  
tdclass="">>(  )/></tr/able/div
<p>Inputs a pure cubical complex (or cubical complex) <span class="SimpleMath">\(K\)</span> and returns the corresponding regular CW-complex. If a positive integer <span class="SimpleMath">\(n\)</span> is entered as an optional second argument, then just the < class="func"><table class="func" width="100%"><tr><td=""<code=func#2;CubicalComplexToRegularCWComplex<ar ="">java.lang.StringIndexOutOfBoundsException: Range [161, 160) out of bounds for length 265

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

<p><a id="X802E1927807969C1" name="X802E1927807969C1"></a></p>

<h5>30.1-3 CriticalCellsOfRegularCWComplex</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CriticalCellsOfRegularCWComplex</code>( <var class="Arg">Y</var> )</td><td class="java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
< classfunc>tableclass"" width"100">tr<tdclass"&827;C</code(<varclassArg></>, < classArg<var)/>t ="tdright>(nbsp;function )/tr>
<p>Inputs a regular CW-complex <span class="SimpleMath">\(Y\)</span> and returns the critical cells of <span class="SimpleMath">\(Y\)</span> with respect to some discrete vector field. If <span class="SimpleMath">\(Y\)</span> does not initially have a discrete vector field then one is constructed.</p>

<p>If a positive integer <span class="SimpleMath">\(n\)</span> is given as a second optional input, then just the critical cells in dimensions up to and including <span class="SimpleMath">\(n\)</span> are returned.</p>

<p>The function <span class="SimpleMath">\(CriticalCellsOfRegularCWComplex(Y)\)</span> works by homotopy reducing cells starting at the top dimension. The function <span class="SimpleMath">\(CriticalCellsOfRegularCWComplex(Y,n)\)</span> works by homotopy coreducing cells starting at dimension 0. The two methods may well return different numbers of cells.</p>

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

<p><a id="X7A1C427578108B7E" name="X7A1C427578108B7E"></a></p>

<h5>30.1-4 ChainComplex</h5

<div
<>Inputs CW-complexspan classSimpleMath>Y)/span>the chain of CW-complex W whose cells correspond to criticalcells <span=SimpleMath(\<span respect  discrete vector field. If <span class="SimpleMath">\(Y\)</span> does not initially a discrete vectorfield one is.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap3.html">2</a></span> , <span class="URL"><a href="../tutorial/chap4.html">3</a></span> , <span class="URL"><a href="../tutorial/chap10.html">4</a></span> , <span class="URL"><a href="../tutorial/chap12.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutMetrics.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutBredon.html">7</a></span> , <span class<> a regular <span class"SimpleMath"\Y)/pan>and the chain  a  W  cells to   of =>()/> respectto some discrete  field span=SimpleMath(\</pan not   iscrete  thenis<p

<p><a id="X8307D5A57EFAC8EE" name="X8307D5A57EFAC8EE"></a></p>

<h5>30.1-5 ChainComplexOfRegularCWComplex</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ChainComplexOfRegularCWComplex</code>( <var class="Arg">Y</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a regular CW-complex <span class="SimpleMath">\(Y\)</span> and returns the cellular chain complex of <span class="SimpleMath">\(Y\)</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap10.html">2</a></span> </p>

<p><a id="X7EAE7E4181546C17" name="X7EAE7E4181546C17"></a></p>

<h5>30.1-6 FundamentalGroup</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FundamentalGroup</code>( <var class="Arg">Y</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">‣ FundamentalGroup</code>( <var class="Arg">Y</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
pInputsregularCW-complex <span=SimpleMath>(\)/> , optionally  number  0-ellIt  the  of<span="">(Y)</>based  0ell< class""\\)</span.    as finitelygroup IfspanclassSimpleMath\n\</>isnot  itisset class"">\n=1\)<span.Thealgorithma  vector   span=SimpleMath>(\</> If< class"">(\)<spandoes   adiscretefield  ./>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap2.html">2</a></span> , <span class="URL"><a href="../tutorial/chap3.html">3</a></span> , <span class="URL"><a href="../tutorial/chap4.html">4</a></span> , <span class="URL"><a href="../tutorial/chap5.html">5</a></span> , <span class="URL"><a href="../tutorial/chap11.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutLinks.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPeripheral.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">10</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">11</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutRandomComplexes.html">12</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnots.html">13</a<>Inputs  egular < class""(Y<> the  java.lang.StringIndexOutOfBoundsException: Range [111, 110) out of bounds for length 153


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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap30_mj.
  >012CubicalComplexToRegularCWComplex</a<span
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< class=""ContSSbr/><span classnocss>nbspnbsp/><a href".htmlX7EAE7E4181546C17">30.1-6 FundamentalGroup</a></span>
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<h3>30 <span class="Heading">Regular CW-Complexes</span></h3>

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

<h4/></>

<p><a 

<h5

<div class="<43.1>\(K\)</> andreturns corresponding CW-complex./>

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

<p><a id="X8723DF8A7AA8AE9E" name="X8723DF8A7AA8AE9E"></a></p>

<h5>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CubicalComplexToRegularCWComplex</code>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<iv classfunc< class"func" width=00"





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