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<h1>GaussForHomalg</h1>


<h2>Gauss functionality for the homalg project</h2>

<p>
    2024.08-01</p>

<p>
    22 August 2024
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<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">GaussForHomalg</strong> package. Included in this manual is a documented list of the most important methods and functions you will need.</p>

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<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>Many thanks to Mohamed Barakat and the Lehrstuhl B für Mathematik at RWTH Aachen University in general for their support. It should be noted that <strong class="pkg">GaussForHomalg</strong> is dependant on the <strong class="pkg">GAP</strong> <strong class="pkg">MatricesForHomalg</strong> package by M. Barakat et al. <a href="chapBib.html#biBhomalg-package">[Bar20]</a>, as well as the <strong class="pkg">Gauss</strong> package by myself <a href="chapBib.html#biBGauss">[Gör08]</a>. This should be clear as <strong class="pkg">GaussForHomalg</strong> presents a link between these two packages. This manual was created with the help of the <strong class="pkg">GAPDoc</strong> package by M. Neunhöffer and F. Lübeck <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#X8585599E87114B98">1.2 <span class="Heading">Installation of the <strong class="pkg">GaussForHomalg</strong> Package</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X86A9B6F87E619FFF">2 <span class="Heading">Usage</span></a>
</div>
<div class="ContChap"><a href="chap3.html#X789AFD2A804F2CD4">3 <span class="Heading"><strong class="pkg">GaussForHomalg</strong> methods and
functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X853EA2DD78928BCB">3.1 <span class="Heading">The field of rationals</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7F4829D6808187B3">3.1-1 HomalgFieldOfRationals</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X796BBDF981806C64">3.2 <span class="Heading">The Tools</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X838F5B6C7C87C8E1">3.2-1 ZeroMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7D807ABC7FCB4E77">3.2-2 IdentityMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8304B38F8200E127">3.2-3 CopyMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7B5E86C283147027">3.2-4 ImportMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81EB2A0A8756372B">3.2-5 Involution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7BAE852578C6B839">3.2-6 CertainRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7CE203DF7F323F87">3.2-7 CertainColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81B6E8EC86BC649A">3.2-8 UnionOfRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81630C648148E324">3.2-9 UnionOfColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X792C1E46800C874C">3.2-10 DiagMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A1A3AE878C2AA3B">3.2-11 KroneckerMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7CBC76A27A8EF473">3.2-12 DualKroneckerMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X798C13F97F955B72">3.2-13 Compose</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C72971F7D0CA3C8">3.2-14 NumberRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X847D45BF7F2BC67C">3.2-15 NumberColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7AEBD5187EE3DAA4">3.2-16 IsZeroMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7EEC8E768178696E">3.2-17 IsDiagonalMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X828225E0857B1FDA">3.2-18 ZeroRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X870D761F7AB96D12">3.2-19 ZeroColumns</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X87BA6DDD812E02F4">3.3 <span class="Heading">The Basic Functions and <strong class="pkg">homalg</strong> table creation</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X791E6BF98311DE55">3.3-1 ReducedRowEchelonForm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8187F91A834A4276">3.3-2 CreateHomalgTable</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X805204B0834D63EB">3.4 <span class="Heading">Matrix entry manipulation</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X870FBE817C884AB5">3.4-1 MatElm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C33059984635480">3.4-2 SetMatElm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E0A73937C1B3966">3.4-3 AddToMatElm</a></span>
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<div class="ContChap"><a href="chap4.html#X85861B017AEEC50B">4 <span class="Heading">Example</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X791E21F47805048A">4.1 <span class="Heading">HomHom</span></a>
</span>
</div>
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<div class="ContChap"><a href="chapA.html#X82B7FBAA79447092">A <span class="Heading">An Overview of the <strong class="pkg">GaussForHomalg</strong> package source code</span></a>
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<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>
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