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<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="chapA.html">A</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

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<h1>Gauss</h1>


<h2>Extended Gauss functionality for <strong class="pkg">GAP</strong></h2>

<p>
    2024.11-01</p>

<p>
    3 December 2024
  </p>

</div>
<p><b>
    Simon Görtzen




  </b>
<br />Email: <span class="URL"><a href="mailto:simon.goertzen@rwth-aachen.de">simon.goertzen@rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://www.linkedin.com/in/simongoertzen/">https://www.linkedin.com/in/simongoertzen/</a></span>
<br />Address: <br />Simon Görtzen<br /> Lehrstuhl B fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<br /> Germany<br />
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<h3>Abstract</h3>
<p>This document explains the primary uses of the <strong class="pkg">Gauss</strong> package. Included is a documented list of the most important methods and functions needed to work with sparse matrices and the algorithms provided by the <strong class="pkg">Gauss</strong> package.</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2007-2013 by Simon Goertzen</p>

<p>This package may be distributed under the terms and conditions of the GNU Public License Version 2 or (at your option) any later version.</p>

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<h3>Acknowledgements</h3>
<p>The <strong class="pkg">Gauss</strong> package would not have been possible without the helpful contributions by</p>


<ul>
<li><p>Max Neunhöffer, University of St Andrews, and</p>

</li>
<li><p>Mohamed Barakat, Lehrstuhl B für Mathematik, RWTH Aachen.</p>

</li>
</ul>
<p>Many thanks to these two and the Lehrstuhl B für Mathematik in general. It should be noted that the <strong class="pkg">GAP</strong> algorithms for <code class="code">SemiEchelonForm</code> and other methods formed an important and informative basis for the development of the extended Gaussian algorithms. This manual was created with the help of the <strong class="pkg">GAPDoc</strong> package by F. Lübeck and M. Neunhöffer <a href="chapBib.html#biBGAPDoc">[LN08]</a>.</p>

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<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X786BACDB82918A65">1.1 <span class="Heading">Overview over this manual</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X78AD64B87DEF5CE9">1.2 <span class="Heading">Installation of the <strong class="pkg">Gauss</strong> Package</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X823150E97BE77525">2 <span class="Heading">Extending Gauss Functionality</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X84F709227E5EEB55">2.1 <span class="Heading">The need for extended functionality</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7F21EDDF81C27747">2.2 <span class="Heading">The applications of the <strong class="pkg">Gauss</strong> package algorithms</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap3.html#X7901751583E1B976">3 <span class="Heading">The Sparse Matrix Data Type</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X81E717927E4029AB">3.1 <span class="Heading">The inner workings of <strong class="pkg">Gauss</strong>
 sparse matrices</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X812222AB7F56717A">3.1-1 <span class="Heading">A special case: GF(2)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X78FB3DC27FF8769E">3.2 <span class="Heading">Methods and functions for sparse matrices</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X829481DA85587996">3.2-1 SparseMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X801B77A67B8A16DA">3.2-2 ConvertSparseMatrixToMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X86C79A76865D4AF0">3.2-3 CopyMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C46B38A8507EB61">3.2-4 GetEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X83C9A07784AA4626">3.2-5 SetEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8729D1F87E176150">3.2-6 AddToEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7D59FA867A432607">3.2-7 SparseZeroMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X844E79E07E11A32E">3.2-8 SparseIdentityMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7D91261880BF76EC">3.2-9 TransposedSparseMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7BAE852578C6B839">3.2-10 CertainRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7CE203DF7F323F87">3.2-11 CertainColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X79745BAA86418F66">3.2-12 SparseUnionOfRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X86E358307E433F4F">3.2-13 SparseUnionOfColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A0CEF5F79A86190">3.2-14 SparseDiagMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8719F2477C0401FE">3.2-15 Nrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8300CDF181481EC6">3.2-16 Ncols</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X82615CEC7AD43F41">3.2-17 IndicesOfSparseMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E3040828757BD37">3.2-18 EntriesOfSparseMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X85766EE5848E7402">3.2-19 RingOfDefinition</a></span>
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<div class="ContChap"><a href="chap4.html#X86443AB17C0AD00C">4 <span class="Heading">Gaussian Algorithms</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X863F68B2858CC146">4.1 <span class="Heading">A list of the available algorithms</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X79093EFA828EF7D1">4.2 <span class="Heading">Methods and Functions for <strong class="pkg">Gauss</strong>ian algorithms</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8499C9FD7AD9908F">4.2-1 EchelonMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X869107627EBA2177">4.2-2 EchelonMatTransformation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X811A3B547A27A895">4.2-3 ReduceMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X816CA6D37F0DB74F">4.2-4 ReduceMatTransformation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X78E97A0E7F1ED8AA">4.2-5 KernelMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X827146F37E2AA841">4.2-6 Rank</a></span>
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<div class="ContChap"><a href="chapA.html#X78EED4F77E698478">A <span class="Heading">An Overview of the <strong class="pkg">Gauss</strong> package source code</span></a>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
<br />
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