Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/GAP/pkg/xmod/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 10.6.2025 mit Größe 7 kB image not shown  

Quelle  chap13.html   Sprache: HTML

 
 products/sources/formale Sprachen/GAP/pkg/xmod/doc/chap13.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 (XMod) - Chapter 13: Interaction with HAP </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="chap13"  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="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="chap12.html">[Previous Chapter]</a>    <a href="chap14.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap13_mj.html">[MathJax on]</a></p>
<p><a id="X81EC8C8A82C15298" name="X81EC8C8A82C15298"></a></p>
<div class="ChapSects"><a href="chap13.html#X81EC8C8A82C15298">13 <span class="Heading">Interaction with HAP </span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap13.html#X865CE53A827FBE6F">13.1 <span class="Heading">Calling HAP functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X8699357D7DC6279E">13.1-1 SmallCat1Group</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X7B00E3FB82DC305D">13.1-2 CatOneGroupToXMod</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X84B7160284FD454A">13.1-3 IdCat1Group</a></span>
</div></div>
</div>

<h3>13 <span class="Heading">Interaction with HAP </span></h3>

<p>This chapter describes functions which allow functions in the package <strong class="pkg">HAP</strong> to be called from <strong class="pkg">XMod</strong>.</p>

<p><a id="X865CE53A827FBE6F" name="X865CE53A827FBE6F"></a></p>

<h4>13.1 <span class="Heading">Calling HAP functions</span></h4>

<p>In <strong class="pkg">HAP</strong> a cat<span class="SimpleMath">^1</span>-group is called a <code class="code">CatOneGroup</code> and the traditional terms <em>source</em> and <em>target</em> are used for the <code class="code">TailMap</code> and <code class="code">HeadMap</code>. A <code class="code">CatOneGroup</code> is a record <code class="code">C</code> with fields <code class="code">C!.sourceMap</code> and <code class="code">C!.targetMap</code>.</p>

<p><a id="X8699357D7DC6279E" name="X8699357D7DC6279E"></a></p>

<h5>13.1-1 SmallCat1Group</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SmallCat1Group</code>( <var class="Arg">n</var>, <var class="Arg">i</var>, <var class="Arg">j</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>This operation calls the <strong class="pkg">HAP</strong> function <code class="code">SmallCatOneGroup(n,i,j)</code> which returns a <code class="code">CatOneGroup</code> from the <strong class="pkg">HAP</strong> database. This is then converted into an <strong class="pkg">XMod</strong> cat<span class="SimpleMath">^1</span>-group. Note that the numbering is not the same as that used by the <strong class="pkg">XMod</strong> operation <code class="code">Cat1Select</code>. In the example <code class="code">C12</code> is the converted form of <code class="code">H12</code>.</p>


<div class="example"><pre>

<span class="GAPprompt">gap></span> <span class="GAPinput">H12 := SmallCatOneGroup( 12, 4, 3 );</span>
Cat-1-group with underlying group Group( [ f1, f2, f3 ] ) . 
<span class="GAPprompt">gap></span> <span class="GAPinput">C12 := SmallCat1Group( 12, 4, 3 );</span>
[Group( [ f1, f2, f3 ] )=>Group( [ f1, f2, <identity> of ... ] )]

</pre></div>

<p><a id="X7B00E3FB82DC305D" name="X7B00E3FB82DC305D"></a></p>

<h5>13.1-2 CatOneGroupToXMod</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CatOneGroupToXMod</code>( <var class="Arg">C</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Cat1GroupToHAP</code>( <var class="Arg">C</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>These two functions convert between the two alternative implementations.</p>


<div class="example"><pre>

<span class="GAPprompt">gap></span> <span class="GAPinput">C12 := CatOneGroupToXMod( H12 );    </span>
[Group( [ f1, f2, f3 ] )=>Group( [ f1, f2, <identity> of ... ] )]
<span class="GAPprompt">gap></span> <span class="GAPinput">C18 := Cat1Select( 18, 4, 3 );</span>
[(C3 x C3) : C2=>Group( [ f1, <identity> of ..., f3 ] )]
<span class="GAPprompt">gap></span> <span class="GAPinput">H18 := Cat1GroupToHAP( C18 ); </span>
Cat-1-group with underlying group (C3 x C3) : C2 . 

</pre></div>

<p><a id="X84B7160284FD454A" name="X84B7160284FD454A"></a></p>

<h5>13.1-3 IdCat1Group</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IdCat1Group</code>( <var class="Arg">C</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>This function calls the <strong class="pkg">HAP</strong> function <code class="code">IdCatOneGroup</code> on a cat<span class="SimpleMath">^1</span>-group <span class="SimpleMath">C</span>. This returns <span class="SimpleMath">[n,i,j]</span> if the cat<span class="SimpleMath">^1</span>-group is the <span class="SimpleMath">j</span>-th structure on the <code class="code">SmallGroup(n,i)</code>.</p>


<div class="example"><pre>

<span class="GAPprompt">gap></span> <span class="GAPinput">IdCatOneGroup( H18 ); </span>
[ 18, 4, 4 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">IdCat1Group( C18 ); </span>
[ 18, 4, 4 ]

</pre></div>


<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap12.html">[Previous Chapter]</a>    <a href="chap14.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="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>

97%


¤ Dauer der Verarbeitung: 0.16 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.