Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/matricesforhomalg/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 7.8.2025 mit Größe 6 kB image not shown  

Quelle  chapA.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/matricesforhomalg/doc/chapA.html


<?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 (MatricesForHomalg) - Appendix A: The Basic Matrix Operations</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="chapA"  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="chapA.html">A</a>  <a href="chapB.html">B</a>  <a href="chapC.html">C</a>  <a href="chapD.html">D</a>  <a href="chapE.html">E</a>  <a href="chapF.html">F</a>  <a href="chapBib.html">Bib</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="chap6.html">[Previous Chapter]</a>    <a href="chapB.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chapA_mj.html">[MathJax on]</a></p>
<p><a id="X7CB422647C7DD289" name="X7CB422647C7DD289"></a></p>
<div class="ChapSects"><a href="chapA.html#X7CB422647C7DD289">A <span class="Heading">The Basic Matrix Operations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X810454AB85D336F5">A.1 <span class="Heading">Main</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X8435BB2E7A819478">A.2 <span class="Heading">Effective</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X7B1023F47EAB7A97">A.3 <span class="Heading">Relative</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X7A0B865E7E70DB3D">A.4 <span class="Heading">Reduced</span></a>
</span>
</div>
</div>

<h3>A <span class="Heading">The Basic Matrix Operations</span></h3>

<p>These are the operations used to solve one-sided (in)homogeneous linear systems <span class="SimpleMath">XA=B</span> resp. <span class="SimpleMath">AX=B</span>.</p>

<p><a id="X810454AB85D336F5" name="X810454AB85D336F5"></a></p>

<h4>A.1 <span class="Heading">Main</span></h4>


<ul>
<li><p><code class="func">BasisOfRowModule</code> (<a href="chap5.html#X80ADBE0D82CC6E85"><span class="RefLink">5.5-28</span></a>)</p>

</li>
<li><p><code class="func">BasisOfColumnModule</code> (<a href="chap5.html#X868CDA327D6C8DDC"><span class="RefLink">5.5-29</span></a>)</p>

</li>
</ul>

<ul>
<li><p><code class="func">DecideZeroRows</code> (<a href="chap5.html#X7F851EC7861170D1"><span class="RefLink">5.5-30</span></a>)</p>

</li>
<li><p><code class="func">DecideZeroColumns</code> (<a href="chap5.html#X86C97DBB787BAD6D"><span class="RefLink">5.5-31</span></a>)</p>

</li>
</ul>

<ul>
<li><p><code class="func">SyzygiesGeneratorsOfRows</code> (<a href="chap5.html#X86ECEA9B7A4AE578"><span class="RefLink">5.5-32</span></a>)</p>

</li>
<li><p><code class="func">SyzygiesGeneratorsOfColumns</code> (<a href="chap5.html#X86504B757F6DC990"><span class="RefLink">5.5-33</span></a>)</p>

</li>
</ul>
<p><a id="X8435BB2E7A819478" name="X8435BB2E7A819478"></a></p>

<h4>A.2 <span class="Heading">Effective</span></h4>


<ul>
<li><p><code class="func">BasisOfRowsCoeff</code> (<a href="chap5.html#X7D9DEC6081AF0003"><span class="RefLink">5.5-40</span></a>)</p>

</li>
<li><p><code class="func">BasisOfColumnsCoeff</code> (<a href="chap5.html#X7BBC885F7C24DEC2"><span class="RefLink">5.5-41</span></a>)</p>

</li>
</ul>

<ul>
<li><p><code class="func">DecideZeroRowsEffectively</code> (<a href="chap5.html#X8513963C84A9F8CB"><span class="RefLink">5.5-42</span></a>)</p>

</li>
<li><p><code class="func">DecideZeroColumnsEffectively</code> (<a href="chap5.html#X7A06BF7779830815"><span class="RefLink">5.5-43</span></a>)</p>

</li>
</ul>
<p><a id="X7B1023F47EAB7A97" name="X7B1023F47EAB7A97"></a></p>

<h4>A.3 <span class="Heading">Relative</span></h4>


<ul>
<li><p><code class="func">SyzygiesGeneratorsOfRows</code> (<a href="chap5.html#X84A93458804F16F6"><span class="RefLink">5.5-34</span></a>)</p>

</li>
<li><p><code class="func">SyzygiesGeneratorsOfColumns</code> (<a href="chap5.html#X7D3FC0CE7B63AAF1"><span class="RefLink">5.5-35</span></a>)</p>

</li>
</ul>
<p><a id="X7A0B865E7E70DB3D" name="X7A0B865E7E70DB3D"></a></p>

<h4>A.4 <span class="Heading">Reduced</span></h4>


<ul>
<li><p><code class="func">ReducedBasisOfRowModule</code> (<a href="chap5.html#X82E0FF517DC38040"><span class="RefLink">5.5-36</span></a>)</p>

</li>
<li><p><code class="func">ReducedBasisOfColumnModule</code> (<a href="chap5.html#X84CED11F7A633BDA"><span class="RefLink">5.5-37</span></a>)</p>

</li>
</ul>

<ul>
<li><p><code class="func">ReducedSyzygiesGeneratorsOfRows</code> (<a href="chap5.html#X7DE458D67B9B85BF"><span class="RefLink">5.5-38</span></a>)</p>

</li>
<li><p><code class="func">ReducedSyzygiesGeneratorsOfColumns</code> (<a href="chap5.html#X8699114D7A865C11"><span class="RefLink">5.5-39</span></a>)</p>

</li>
</ul>

<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap6.html">[Previous Chapter]</a>    <a href="chapB.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="chapA.html">A</a>  <a href="chapB.html">B</a>  <a href="chapC.html">C</a>  <a href="chapD.html">D</a>  <a href="chapE.html">E</a>  <a href="chapF.html">F</a>  <a href="chapBib.html">Bib</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>

100%


¤ Dauer der Verarbeitung: 0.13 Sekunden  (vorverarbeitet)  ¤

*© Formatika GbR, Deutschland




Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.