<?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>
<title>GAP (HAP commands) - Chapter 10:  Sparse Chain complexes</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="chap10"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chap7.html">7</a>  <a href="chap8.html">8</a>  <a href="chap9.html">9</a>  <a href="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chap12.html">12</a>  <a href="chap13.html">13</a>  <a href="chap14.html">14</a>  <a href="chap15.html">15</a>  <a href="chap16.html">16</a>  <a href="chap17.html">17</a>  <a href="chap18.html">18</a>  <a href="chap19.html">19</a>  <a href="chap20.html">20</a>  <a href="chap21.html">21</a>  <a href="chap22.html">22</a>  <a href="chap23.html">23</a>  <a href="chap24.html">24</a>  <a href="chap25.html">25</a>  <a href="chap26.html">26</a>  <a href="chap27.html">27</a>  <a href="chap28.html">28</a>  <a href="chap29.html">29</a>  <a href="chap30.html">30</a>  <a href="chap31.html">31</a>  <a href="chap32.html">32</a>  <a href="chap33.html">33</a>  <a href="chap34.html">34</a>  <a href="chap35.html">35</a>  <a href="chap36.html">36</a>  <a href="chap37.html">37</a>  <a href="chap38.html">38</a>  <a href="chap39.html">39</a>  <a href="chap40.html">40</a>  <a href="chapInd.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap9.html">[Previous Chapter]</a>    <a href="chap11.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap10_mj.html">[MathJax on]</a></p>
<p><a id="X856F202D823280F8" name="X856F202D823280F8"></a></p>
<div class="ChapSects"><a href="chap10.html#X856F202D823280F8">10 <span class="Heading"> Sparse Chain complexes</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X7CFDEEC07F15CF82">10.1 <span class="Heading">  </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X81D5E16D81934320">10.1-1 SparseMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7C85DF92798C625A">10.1-2 TransposeOfSparseMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8011873278AB2827">10.1-3 ReverseSparseMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8551FB1D81A85362">10.1-4 SparseRowMult</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X824CD2E6862435EB">10.1-5 SparseRowInterchange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X84E8FA687CABA3CD">10.1-6 SparseRowAdd</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7BE58D2983505606">10.1-7 SparseSemiEchelon</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7A7B47D380A14F28">10.1-8 RankMatDestructive</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7B21AE7987D4FB31">10.1-9 RankMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7F10BD65823B1632">10.1-10 SparseChainComplex</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8156FB007C49C020">10.1-11 SparseChainComplexOfRegularCWComplex</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7BA17DDC81AA855D">10.1-12 SparseBoundaryMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7C3327917BE532FD">10.1-13 Bettinumbers</a></span>
</div></div>
</div>

<h3>10 <span class="Heading"> Sparse Chain complexes</span></h3>

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

<h4>10.1 <span class="Heading">  </span></h4>

<p><a id="X81D5E16D81934320" name="X81D5E16D81934320"></a></p>

<h5>10.1-1 SparseMat</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SparseMat</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a matrix <span class="SimpleMath">A</span> and returns the matrix in sparse format.</p>

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

<p><a id="X7C85DF92798C625A" name="X7C85DF92798C625A"></a></p>

<h5>10.1-2 TransposeOfSparseMat</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; TransposeOfSparseMat</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a sparse matrix <span class="SimpleMath">A</span> and returns its transpose sparse format.</p>

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

<p><a id="X8011873278AB2827" name="X8011873278AB2827"></a></p>

<h5>10.1-3 ReverseSparseMat</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; ReverseSparseMat</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a sparse matrix <span class="SimpleMath">A</span> and modifies it by reversing the order of the columns. This function modifies <span class="SimpleMath">A</span> and returns no value.</p>

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

<p><a id="X8551FB1D81A85362" name="X8551FB1D81A85362"></a></p>

<h5>10.1-4 SparseRowMult</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SparseRowMult</code>( <var class="Arg">A</var>, <var class="Arg">i</var>, <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Multiplies the i-th row of a sparse matrix <span class="SimpleMath">A</span> by <span class="SimpleMath">k</span>. The sparse matrix <span class="SimpleMath">A</span> is modified but nothing is returned.</p>

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

<p><a id="X824CD2E6862435EB" name="X824CD2E6862435EB"></a></p>

<h5>10.1-5 SparseRowInterchange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SparseRowInterchange</code>( <var class="Arg">A</var>, <var class="Arg">i</var>, <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Interchanges the i-th and j-th rows of a sparse matrix <span class="SimpleMath">A</span> by <span class="SimpleMath">k</span>. The sparse matrix <span class="SimpleMath">A</span> is modified but nothing is returned.</p>

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

<p><a id="X84E8FA687CABA3CD" name="X84E8FA687CABA3CD"></a></p>

<h5>10.1-6 SparseRowAdd</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SparseRowAdd</code>( <var class="Arg">A</var>, <var class="Arg">i</var>, <var class="Arg">j</var>, <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Adds <span class="SimpleMath">k</span> times the j-th row to the i-th row of a sparse matrix <span class="SimpleMath">A</span>. The sparse matrix <span class="SimpleMath">A</span> is modified but nothing is returned.</p>

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

<p><a id="X7BE58D2983505606" name="X7BE58D2983505606"></a></p>

<h5>10.1-7 SparseSemiEchelon</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SparseSemiEchelon</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Converts a sparse matrix <span class="SimpleMath">A</span> to semi-echelon form (which means echelon form up to a permutation of rows). The sparse matrix <span class="SimpleMath">A</span> is modified but nothing is returned.</p>

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

<p><a id="X7A7B47D380A14F28" name="X7A7B47D380A14F28"></a></p>

<h5>10.1-8 RankMatDestructive</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; RankMatDestructive</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns the rank of a sparse matrix <span class="SimpleMath">A</span>. The sparse matrix <span class="SimpleMath">A</span> is modified during the calculation.</p>

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

<p><a id="X7B21AE7987D4FB31" name="X7B21AE7987D4FB31"></a></p>

<h5>10.1-9 RankMat</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; RankMat</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns the rank of a sparse matrix <span class="SimpleMath">A</span>.</p>

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

<p><a id="X7F10BD65823B1632" name="X7F10BD65823B1632"></a></p>

<h5>10.1-10 SparseChainComplex</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SparseChainComplex</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 a sparse chain complex which is chain homotopy equivalent to the cellular chain complex of <span class="SimpleMath">Y</span>. The function uses discrete vector fields to calculate a smallish chain complex.</p>

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

<p><a id="X8156FB007C49C020" name="X8156FB007C49C020"></a></p>

<h5>10.1-11 SparseChainComplexOfRegularCWComplex</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SparseChainComplexOfRegularCWComplex</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 its cellular chain complex as a sparse chain complex. The function SparseChainComplex(Y) will usually return a smaller chain complex.</p>

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

<p><a id="X7BA17DDC81AA855D" name="X7BA17DDC81AA855D"></a></p>

<h5>10.1-12 SparseBoundaryMatrix</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SparseBoundaryMatrix</code>( <var class="Arg">C</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a sparse chain complex <span class="SimpleMath">C</span> and integer <span class="SimpleMath">n</span>. Returns the n-th boundary matrix of the chain complex in sparse format.</p>

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

<p><a id="X7C3327917BE532FD" name="X7C3327917BE532FD"></a></p>

<h5>10.1-13 Bettinumbers</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; Bettinumbers</code>( <var class="Arg">C</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a sparse chain complex <span class="SimpleMath">C</span> and integer <span class="SimpleMath">n</span>. Returns the n-th Netti number of the chain complex.</p>

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


<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap9.html">[Previous Chapter]</a>    <a href="chap11.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chap7.html">7</a>  <a href="chap8.html">8</a>  <a href="chap9.html">9</a>  <a href="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chap12.html">12</a>  <a href="chap13.html">13</a>  <a href="chap14.html">14</a>  <a href="chap15.html">15</a>  <a href="chap16.html">16</a>  <a href="chap17.html">17</a>  <a href="chap18.html">18</a>  <a href="chap19.html">19</a>  <a href="chap20.html">20</a>  <a href="chap21.html">21</a>  <a href="chap22.html">22</a>  <a href="chap23.html">23</a>  <a href="chap24.html">24</a>  <a href="chap25.html">25</a>  <a href="chap26.html">26</a>  <a href="chap27.html">27</a>  <a href="chap28.html">28</a>  <a href="chap29.html">29</a>  <a href="chap30.html">30</a>  <a href="chap31.html">31</a>  <a href="chap32.html">32</a>  <a href="chap33.html">33</a>  <a href="chap34.html">34</a>  <a href="chap35.html">35</a>  <a href="chap36.html">36</a>  <a href="chap37.html">37</a>  <a href="chap38.html">38</a>  <a href="chap39.html">39</a>  <a href="chap40.html">40</a>  <a href="chapInd.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>