Quelle  chap6.html   Sprache: 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) - Chapter 6: Ring Relations</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="chap6"  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="chap5.html">[Previous Chapter]</a>    <a href="chapA.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap6_mj.html">[MathJax on]</a></p>
<p><a id="X8163F0658017F220" name="X8163F0658017F220"></a></p>
<div class="ChapSects"><a href="chap6.html#X8163F0658017F220">6 <span class="Heading">Ring Relations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7EB7C20C78788C69">6.1 <span class="Heading">Ring Relations: Categories and Representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7D50E3AD82087AE6">6.1-1 IsHomalgRingRelations</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7DECADD683403C65">6.1-2 IsHomalgRingRelationsAsGeneratorsOfLeftIdeal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X78746A217FEEB058">6.1-3 IsHomalgRingRelationsAsGeneratorsOfRightIdeal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X86CA83A081B8C8EA">6.1-4 IsRingRelationsRep</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X81D1405F81B86E4B">6.2 <span class="Heading">Ring Relations: Constructors</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7FFB5DE07BB77319">6.3 <span class="Heading">Ring Relations: Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X835DF250790EF863">6.3-1 CanBeUsedToDecideZero</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7B9398827AEEA2E6">6.3-2 IsInjectivePresentation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X849ED71B8164D1C2">6.4 <span class="Heading">Ring Relations: Attributes</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7ABFB8F982EBD7F8">6.5 <span class="Heading">Ring Relations: Operations and Functions</span></a>
</span>
</div>
</div>

<h3>6 <span class="Heading">Ring Relations</span></h3>

<p><a id="X7EB7C20C78788C69" name="X7EB7C20C78788C69"></a></p>

<h4>6.1 <span class="Heading">Ring Relations: Categories and Representations</span></h4>

<p><a id="X7D50E3AD82087AE6" name="X7D50E3AD82087AE6"></a></p>

<h5>6.1-1 IsHomalgRingRelations</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsHomalgRingRelations</code>( <var class="Arg">rel</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> category of <strong class="pkg">homalg</strong> ring relations.</p>

<p><a id="X7DECADD683403C65" name="X7DECADD683403C65"></a></p>

<h5>6.1-2 IsHomalgRingRelationsAsGeneratorsOfLeftIdeal</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsHomalgRingRelationsAsGeneratorsOfLeftIdeal</code>( <var class="Arg">rel</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> category of <strong class="pkg">homalg</strong> ring relations as generators of a left ideal.</p>

<p>(It is a subcategory of the <strong class="pkg">GAP</strong> category <code class="code">IsHomalgRingRelations</code>.)</p>

<p><a id="X78746A217FEEB058" name="X78746A217FEEB058"></a></p>

<h5>6.1-3 IsHomalgRingRelationsAsGeneratorsOfRightIdeal</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsHomalgRingRelationsAsGeneratorsOfRightIdeal</code>( <var class="Arg">rel</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> category of <strong class="pkg">homalg</strong> ring relations as generators of a right ideal.</p>

<p>(It is a subcategory of the <strong class="pkg">GAP</strong> category <code class="code">IsHomalgRingRelations</code>.)</p>

<p><a id="X86CA83A081B8C8EA" name="X86CA83A081B8C8EA"></a></p>

<h5>6.1-4 IsRingRelationsRep</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsRingRelationsRep</code>( <var class="Arg">rel</var> )</td><td class="tdright">( representation )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> representation of a finite set of relations of a <strong class="pkg">homalg</strong> ring.</p>

<p>(It is a representation of the <strong class="pkg">GAP</strong> category <code class="func">IsHomalgRingRelations</code> (<a href="chap6.html#X7D50E3AD82087AE6"><span class="RefLink">6.1-1</span></a>))</p>

<p><a id="X81D1405F81B86E4B" name="X81D1405F81B86E4B"></a></p>

<h4>6.2 <span class="Heading">Ring Relations: Constructors</span></h4>

<p><a id="X7FFB5DE07BB77319" name="X7FFB5DE07BB77319"></a></p>

<h4>6.3 <span class="Heading">Ring Relations: Properties</span></h4>

<p><a id="X835DF250790EF863" name="X835DF250790EF863"></a></p>

<h5>6.3-1 CanBeUsedToDecideZero</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; CanBeUsedToDecideZero</code>( <var class="Arg">rel</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> set of relations <var class="Arg">rel</var> can be used for normal form reductions. <br /> (no method installed)</p>

<p><a id="X7B9398827AEEA2E6" name="X7B9398827AEEA2E6"></a></p>

<h5>6.3-2 IsInjectivePresentation</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsInjectivePresentation</code>( <var class="Arg">rel</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> set of relations <var class="Arg">rel</var> has zero syzygies.</p>

<p><a id="X849ED71B8164D1C2" name="X849ED71B8164D1C2"></a></p>

<h4>6.4 <span class="Heading">Ring Relations: Attributes</span></h4>

<p><a id="X7ABFB8F982EBD7F8" name="X7ABFB8F982EBD7F8"></a></p>

<h4>6.5 <span class="Heading">Ring Relations: Operations and Functions</span></h4>


<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap5.html">[Previous Chapter]</a>    <a href="chapA.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>