Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/generalizedmorphismsforcap/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 25.7.2025 mit Größe 20 kB image not shown  

Quelle  chap3_mj.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/generalizedmorphismsforcap/doc/chap3_mj.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>
<script type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (GeneralizedMorphismsForCAP) - Chapter 3: Generalized Morphism Category by Spans</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="chap3"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chap9_mj.html">9</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap2_mj.html">[Previous Chapter]</a>    <a href="chap4_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap3.html">[MathJax off]</a></p>
<p><a id="X7D54782279124748" name="X7D54782279124748"></a></p>
<div class="ChapSects"><a href="chap3_mj.html#X7D54782279124748">3 <span class="Heading">Generalized Morphism Category by Spans</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7D03633A7D98026B">3.1 <span class="Heading">GAP Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B3EA2C279A4F9E4">3.1-1 IsGeneralizedMorphismCategoryBySpans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X78F2B8E882ECF61E">3.1-2 IsGeneralizedMorphismCategoryBySpansObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A5BDCEE78549DFB">3.1-3 IsGeneralizedMorphismBySpan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X871597447BB998A1">3.2 <span class="Heading">Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A058F5C7F7116DB">3.2-1 HasIdentityAsReversedArrow</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7C701DBF7BAE649A">3.3 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7BDCF7FD7EAE01C3">3.3-1 UnderlyingHonestObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X83C847FC86AB508B">3.3-2 Arrow</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X826CC0B57D6F7F3B">3.3-3 ReversedArrow</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8082EEE27FB449E5">3.3-4 NormalizedSpanTuple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X878EE24487756BD4">3.3-5 PseudoInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X800786037C19DEF5">3.3-6 GeneralizedInverseBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B8C00217DD3A64C">3.3-7 IdempotentDefinedBySubobjectBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X82D0B42E8413A5FE">3.3-8 IdempotentDefinedByFactorobjectBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X86499E0D83A9D090">3.3-9 NormalizedSpan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7DE8E16C7C2D387B">3.4 <span class="Heading">Operations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7D3675B0866191EC">3.4-1 GeneralizedMorphismFromFactorToSubobjectBySpan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X86EC0F0A78ECBC10">3.5 <span class="Heading">Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X83FA5A4C787261DB">3.5-1 GeneralizedMorphismBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7EAF87447D2A08EE">3.5-2 GeneralizedMorphismBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79A8B50C7EB5ADE2">3.5-3 GeneralizedMorphismBySpanWithRangeAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79C48BB782BD799F">3.5-4 AsGeneralizedMorphismBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X812CBF7580098CCF">3.5-5 GeneralizedMorphismCategoryBySpans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X817694F38145FD9F">3.5-6 GeneralizedMorphismBySpansObject</a></span>
</div></div>
</div>

<h3>3 <span class="Heading">Generalized Morphism Category by Spans</span></h3>

<p><a id="X7D03633A7D98026B" name="X7D03633A7D98026B"></a></p>

<h4>3.1 <span class="Heading">GAP Categories</span></h4>

<p><a id="X7B3EA2C279A4F9E4" name="X7B3EA2C279A4F9E4"></a></p>

<h5>3.1-1 IsGeneralizedMorphismCategoryBySpans</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsGeneralizedMorphismCategoryBySpans</code>( <var class="Arg">object</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The GAP category of the category of generalized morphisms by spans.</p>

<p><a id="X78F2B8E882ECF61E" name="X78F2B8E882ECF61E"></a></p>

<h5>3.1-2 IsGeneralizedMorphismCategoryBySpansObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsGeneralizedMorphismCategoryBySpansObject</code>( <var class="Arg">object</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The GAP category of objects in the generalized morphism category by spans.</p>

<p><a id="X7A5BDCEE78549DFB" name="X7A5BDCEE78549DFB"></a></p>

<h5>3.1-3 IsGeneralizedMorphismBySpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsGeneralizedMorphismBySpan</code>( <var class="Arg">object</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The GAP category of morphisms in the generalized morphism category by spans.</p>

<p><a id="X871597447BB998A1" name="X871597447BB998A1"></a></p>

<h4>3.2 <span class="Heading">Properties</span></h4>

<p><a id="X7A058F5C7F7116DB" name="X7A058F5C7F7116DB"></a></p>

<h5>3.2-1 HasIdentityAsReversedArrow</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HasIdentityAsReversedArrow</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The argument is a generalized morphism <span class="SimpleMath">\(\alpha\)</span> by a span <span class="SimpleMath">\(a \leftarrow b \rightarrow c\)</span>. The output is <code class="code">true</code> if <span class="SimpleMath">\(a \leftarrow b\)</span> is congruent to an identity morphism, <code class="code">false</code> otherwise.</p>

<p><a id="X7C701DBF7BAE649A" name="X7C701DBF7BAE649A"></a></p>

<h4>3.3 <span class="Heading">Attributes</span></h4>

<p><a id="X7BDCF7FD7EAE01C3" name="X7BDCF7FD7EAE01C3"></a></p>

<h5>3.3-1 UnderlyingHonestObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UnderlyingHonestObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: an object in <span class="SimpleMath">\(\mathbf{A}\)</span></p>

<p>The argument is an object <span class="SimpleMath">\(a\)</span> in the generalized morphism category by spans. The output is its underlying honest object.</p>

<p><a id="X83C847FC86AB508B" name="X83C847FC86AB508B"></a></p>

<h5>3.3-2 Arrow</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Arrow</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{A}}(b,c)\)</span></p>

<p>The argument is a generalized morphism <span class="SimpleMath">\(\alpha\)</span> by a span <span class="SimpleMath">\(a \leftarrow b \rightarrow c\)</span>. The output is its arrow <span class="SimpleMath">\(b \rightarrow c\)</span>.</p>

<p><a id="X826CC0B57D6F7F3B" name="X826CC0B57D6F7F3B"></a></p>

<h5>3.3-3 ReversedArrow</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ReversedArrow</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{A}}(b,a)\)</span></p>

<p>The argument is a generalized morphism <span class="SimpleMath">\(\alpha\)</span> by a span <span class="SimpleMath">\(a \leftarrow b \rightarrow c\)</span>. The output is its reversed arrow <span class="SimpleMath">\(a \leftarrow b\)</span>.</p>

<p><a id="X8082EEE27FB449E5" name="X8082EEE27FB449E5"></a></p>

<h5>3.3-4 NormalizedSpanTuple</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NormalizedSpanTuple</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a pair of morphisms in <span class="SimpleMath">\(\mathbf{A}\)</span>.</p>

<p>The argument is a generalized morphism <span class="SimpleMath">\(\alpha: a \rightarrow b\)</span> by a span. The output is its normalized span pair <span class="SimpleMath">\((a \leftarrow d, d \rightarrow b)\)</span>.</p>

<p><a id="X878EE24487756BD4" name="X878EE24487756BD4"></a></p>

<h5>3.3-5 PseudoInverse</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PseudoInverse</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(b,a)\)</span></p>

<p>The argument is a generalized morphism <span class="SimpleMath">\(\alpha: a \rightarrow b\)</span> by a span. The output is its pseudo inverse <span class="SimpleMath">\(b \rightarrow a\)</span>.</p>

<p><a id="X800786037C19DEF5" name="X800786037C19DEF5"></a></p>

<h5>3.3-6 GeneralizedInverseBySpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GeneralizedInverseBySpan</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(b,a)\)</span></p>

<p>The argument is a morphism <span class="SimpleMath">\(\alpha: a \rightarrow b \in \mathbf{A}\)</span>. The output is its generalized inverse <span class="SimpleMath">\(b \rightarrow a\)</span> by span.</p>

<p><a id="X7B8C00217DD3A64C" name="X7B8C00217DD3A64C"></a></p>

<h5>3.3-7 IdempotentDefinedBySubobjectBySpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IdempotentDefinedBySubobjectBySpan</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(b,b)\)</span></p>

<p>The argument is a subobject <span class="SimpleMath">\(\alpha: a \hookrightarrow b \in \mathbf{A}\)</span>. The output is the idempotent <span class="SimpleMath">\(b \rightarrow b \in \mathbf{G(A)}\)</span> by span defined by <span class="SimpleMath">\(\alpha\)</span>.</p>

<p><a id="X82D0B42E8413A5FE" name="X82D0B42E8413A5FE"></a></p>

<h5>3.3-8 IdempotentDefinedByFactorobjectBySpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IdempotentDefinedByFactorobjectBySpan</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(b,b)\)</span></p>

<p>The argument is a factorobject <span class="SimpleMath">\(\alpha: b \twoheadrightarrow a \in \mathbf{A}\)</span>. The output is the idempotent <span class="SimpleMath">\(b \rightarrow b \in \mathbf{G(A)}\)</span> by span defined by <span class="SimpleMath">\(\alpha\)</span>.</p>

<p><a id="X86499E0D83A9D090" name="X86499E0D83A9D090"></a></p>

<h5>3.3-9 NormalizedSpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NormalizedSpan</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(a,b)\)</span></p>

<p>The argument is a generalized morphism <span class="SimpleMath">\(\alpha: a \rightarrow b\)</span> by a span. The output is its normalization by span.</p>

<p><a id="X7DE8E16C7C2D387B" name="X7DE8E16C7C2D387B"></a></p>

<h4>3.4 <span class="Heading">Operations</span></h4>

<p><a id="X7D3675B0866191EC" name="X7D3675B0866191EC"></a></p>

<h5>3.4-1 GeneralizedMorphismFromFactorToSubobjectBySpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GeneralizedMorphismFromFactorToSubobjectBySpan</code>( <var class="Arg">beta</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(c,a)\)</span></p>

<p>The arguments are a a factorobject <span class="SimpleMath">\(\beta: b \twoheadrightarrow c\)</span>, and a subobject <span class="SimpleMath">\(\alpha: a \hookrightarrow b\)</span>. The output is the generalized morphism by span from the factorobject to the subobject.</p>

<p><a id="X86EC0F0A78ECBC10" name="X86EC0F0A78ECBC10"></a></p>

<h4>3.5 <span class="Heading">Constructors</span></h4>

<p><a id="X83FA5A4C787261DB" name="X83FA5A4C787261DB"></a></p>

<h5>3.5-1 GeneralizedMorphismBySpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GeneralizedMorphismBySpan</code>( <var class="Arg">alpha</var>, <var class="Arg">beta</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(a,b)\)</span></p>

<p>The arguments are morphisms <span class="SimpleMath">\(\alpha: a \leftarrow c\)</span> and <span class="SimpleMath">\(\beta: c \rightarrow b\)</span> in <span class="SimpleMath">\(\mathbf{A}\)</span>. The output is a generalized morphism by span with arrow <span class="SimpleMath">\(\beta\)</span> and reversed arrow <span class="SimpleMath">\(\alpha\)</span>.</p>

<p><a id="X7EAF87447D2A08EE" name="X7EAF87447D2A08EE"></a></p>

<h5>3.5-2 GeneralizedMorphismBySpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GeneralizedMorphismBySpan</code>( <var class="Arg">alpha</var>, <var class="Arg">beta</var>, <var class="Arg">gamma</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(a,d)\)</span></p>

<p>The arguments are morphisms <span class="SimpleMath">\(\alpha: a \leftarrow b\)</span>, <span class="SimpleMath">\(\beta: b \rightarrow c\)</span>, and <span class="SimpleMath">\(\gamma: c \leftarrow d\)</span> in <span class="SimpleMath">\(\mathbf{A}\)</span>. The output is a generalized morphism by span defined by the composition of the given three arrows regarded as generalized morphisms.</p>

<p><a id="X79A8B50C7EB5ADE2" name="X79A8B50C7EB5ADE2"></a></p>

<h5>3.5-3 GeneralizedMorphismBySpanWithRangeAid</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GeneralizedMorphismBySpanWithRangeAid</code>( <var class="Arg">alpha</var>, <var class="Arg">beta</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(a,c)\)</span></p>

<p>The arguments are morphisms <span class="SimpleMath">\(\alpha: a \rightarrow b\)</span>, and <span class="SimpleMath">\(\beta: b \leftarrow c\)</span> in <span class="SimpleMath">\(\mathbf{A}\)</span>. The output is a generalized morphism by span defined by the composition of the given two arrows regarded as generalized morphisms.</p>

<p><a id="X79C48BB782BD799F" name="X79C48BB782BD799F"></a></p>

<h5>3.5-4 AsGeneralizedMorphismBySpan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AsGeneralizedMorphismBySpan</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="SimpleMath">\(\mathrm{Hom}_{\mathbf{G(A)}}(a,b)\)</span></p>

<p>The argument is a morphism <span class="SimpleMath">\(\alpha: a \rightarrow b\)</span> in <span class="SimpleMath">\(\mathbf{A}\)</span>. The output is the honest generalized morphism by span defined by <span class="SimpleMath">\(\alpha\)</span>.</p>

<p><a id="X812CBF7580098CCF" name="X812CBF7580098CCF"></a></p>

<h5>3.5-5 GeneralizedMorphismCategoryBySpans</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GeneralizedMorphismCategoryBySpans</code>( <var class="Arg">A</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a category</p>

<p>The argument is an abelian category <span class="SimpleMath">\(\mathbf{A}\)</span>. The output is its generalized morphism category <span class="SimpleMath">\(\mathbf{G(A)}\)</span> by spans.</p>

<p><a id="X817694F38145FD9F" name="X817694F38145FD9F"></a></p>

<h5>3.5-6 GeneralizedMorphismBySpansObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GeneralizedMorphismBySpansObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: an object in <span class="SimpleMath">\(\mathbf{G(A)}\)</span></p>

<p>The argument is an object <span class="SimpleMath">\(a\)</span> in an abelian category <span class="SimpleMath">\(\mathbf{A}\)</span>. The output is the object in the generalized morphism category by spans whose underlying honest object is <span class="SimpleMath">\(a\)</span>.</p>


<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap2_mj.html">[Previous Chapter]</a>    <a href="chap4_mj.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chap9_mj.html">9</a>  <a href="chapInd_mj.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>

94%


¤ Dauer der Verarbeitung: 0.17 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.