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<div class="ChapSects"><a href="chap38_mj.html#X7AE3B902812A10B0">38 <span class="Heading"> Some functions for accessing basic data</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap38_mj.html#X7CFDEEC07F15CF82">38.1 <span class="Heading">  </span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X7AF313D387F6BA22">38.1-1 BoundaryMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X826F7E8087BD7649">38.1-2 BoundaryMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X7E6926C6850E7C4E">38.1-3 Dimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X7AE270A381B40E6D">38.1-4 EvaluateProperty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X7EDAA4E080F7DC03">38.1-5 GroupOfResolution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X780769238600AFD1">38.1-6 Length</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X7FB5B44378CA318C">38.1-7 Map</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X7DE8173F80E07AB1">38.1-8 Source</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap38_mj.html#X7C76423782BA2868">38.1-9 Target</a></span>
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<h3>38 <span class="Heading"> Some functions for accessing basic data</span></h3>

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

<h4>38.1 <span class="Heading">  </span></h4>

<p><a id="X7AF313D387F6BA22" name="X7AF313D387F6BA22"></a></p>

<h5>38.1-1 BoundaryMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ BoundaryMap</code>( <var class="Arg">C</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a resolution, chain complex or cochain complex <span class="SimpleMath">\(C\)</span> and returns the function <span class="SimpleMath">\(C!.boundary\)</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap2.html">1</a></span> , <span class="URL"><a href="../tutorial/chap10.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTopology.html">3</a></span> </p>

<p><a id="X826F7E8087BD7649" name="X826F7E8087BD7649"></a></p>

<h5>38.1-2 BoundaryMatrix</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ BoundaryMatrix</code>( <var class="Arg">C</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a chain or cochain complex <span class="SimpleMath">\(C\)</span> and integer <span class="SimpleMath">\(n\)</span>><span class="SimpleMath">\(0\)</span>. It returns the <span class="SimpleMath">\(n\)</span>-th boundary map of <span class="SimpleMath">\(C\)</span> as a matrix.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap11.html">1</a></span> </p>

<p><a id="X7E6926C6850E7C4E" name="X7E6926C6850E7C4E"></a></p>

<h5>38.1-3 Dimension</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Dimension</code>( <var class="Arg">C</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">‣ Dimension</code>( <var class="Arg">M</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a resolution, chain complex or cochain complex <span class="SimpleMath">\(C\)</span> and returns the function <span class="SimpleMath">\(C!.dimension\)</span> .</p>

<p>Alternatively, inputs an <span class="SimpleMath">\(FpG\)</span>-module <span class="SimpleMath">\(M\)</span> and returns its dimension as a vector space over the field of <span class="SimpleMath">\(p\)</span> elements.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap3.html">1</a></span> , <span class="URL"><a href="../tutorial/chap5.html">2</a></span> , <span class="URL"><a href="../tutorial/chap7.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutDefinitions.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTDA.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTopology.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutLieCovers.html">9</a></span> </p>

<p><a id="X7AE270A381B40E6D" name="X7AE270A381B40E6D"></a></p>

<h5>38.1-4 EvaluateProperty</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EvaluateProperty</code>( <var class="Arg">X</var>, <var class="Arg">str</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a component object <span class="SimpleMath">\(X\)</span> (such as a <span class="SimpleMath">\(ZG\)</span>-resolution or chain map) and a string <span class="SimpleMath">\(str\)</span>="name" (such as "characteristic" or "type"). It searches <span class="SimpleMath">\(X.property\)</span> for the pair ["name",value] and returns value. If <span class="SimpleMath">\(X.property\)</span> does not exist, or if ["name",value] does not exist, it returns fail.</p>

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

<p><a id="X7EDAA4E080F7DC03" name="X7EDAA4E080F7DC03"></a></p>

<h5>38.1-5 GroupOfResolution</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GroupOfResolution</code>( <var class="Arg">R</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">\(ZG\)</span>-resolution <span class="SimpleMath">\(R\)</span> and returns the group <span class="SimpleMath">\(G\)</span>.</p>

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

<p><a id="X780769238600AFD1" name="X780769238600AFD1"></a></p>

<h5>38.1-6 Length</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Length</code>( <var class="Arg">R</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a resolution <span class="SimpleMath">\(R\)</span> and returns its length (i.e. the number of terms of <span class="SimpleMath">\(R\)</span> that HAP has computed).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap3.html">1</a></span> , <span class="URL"><a href="../tutorial/chap4.html">2</a></span> , <span class="URL"><a href="../tutorial/chap5.html">3</a></span> , <span class="URL"><a href="../tutorial/chap6.html">4</a></span> , <span class="URL"><a href="../tutorial/chap10.html">5</a></span> , <span class="URL"><a href="../tutorial/chap12.html">6</a></span> , <span class="URL"><a href="../tutorial/chap13.html">7</a></span> , <span class="URL"><a href="../tutorial/chap14.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutArithmetic.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutBogomolov.html">10</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPerformance.html">11</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">12</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">13</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">14</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutquasi.html">15</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutRandomComplexes.html">16</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutGouter.html">17</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTensorSquare.html">18</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTopology.html">19</a></span> </p>

<p><a id="X7FB5B44378CA318C" name="X7FB5B44378CA318C"></a></p>

<h5>38.1-7 Map</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Map</code>( <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a chain map, or cochain map or equivariant chain map <span class="SimpleMath">\(f\)</span> and returns the mapping function (as opposed to the target or the source of <span class="SimpleMath">\(f\)</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/chap2.html">2</a></span> , <span class="URL"><a href="../tutorial/chap4.html">3</a></span> , <span class="URL"><a href="../tutorial/chap5.html">4</a></span> , <span class="URL"><a href="../tutorial/chap6.html">5</a></span> , <span class="URL"><a href="../tutorial/chap7.html">6</a></span> , <span class="URL"><a href="../tutorial/chap10.html">7</a></span> , <span class="URL"><a href="../tutorial/chap13.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutAbelianCategories.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoefficientSequence.html">10</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCohomologyRings.html">11</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPoincareSeries.html">12</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">13</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">14</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutFunctorial.html">15</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutGouter.html">16</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTopology.html">17</a></span> </p>

<p><a id="X7DE8173F80E07AB1" name="X7DE8173F80E07AB1"></a></p>

<h5>38.1-8 Source</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Source</code>( <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a chain map, or cochain map, or equivariant chain map, or <span class="SimpleMath">\(FpG\)</span>-module homomorphism <span class="SimpleMath">\(f\)</span> and returns it source.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap2.html">1</a></span> , <span class="URL"><a href="../tutorial/chap4.html">2</a></span> , <span class="URL"><a href="../tutorial/chap7.html">3</a></span> , <span class="URL"><a href="../tutorial/chap8.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutAbelianCategories.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutNonabelian.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoefficientSequence.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutFunctorial.html">10</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutLieCovers.html">11</a></span> </p>

<p><a id="X7C76423782BA2868" name="X7C76423782BA2868"></a></p>

<h5>38.1-9 Target</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Target</code>( <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a chain map, or cochain map, or equivariant chain map, or <span class="SimpleMath">\(FpG\)</span>-module homomorphism <span class="SimpleMath">\(f\)</span> and returns its target.</p>

<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/chap7.html">3</a></span> , <span class="URL"><a href="../tutorial/chap8.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutAbelianCategories.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoefficientSequence.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">8</a></span> </p>


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