Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/GAP/pkg/gradedmodules/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 22.11.2024 mit Größe 6 kB image not shown  

Quelle  chap2_mj.html   Sprache: HTML

 
 products/sources/formale Sprachen/GAP/pkg/gradedmodules/doc/chap2_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 (GradedModules) - Chapter 2: Ring Maps</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="chap2"  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="chapBib_mj.html">Bib</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="chap1_mj.html">[Previous Chapter]</a>    <a href="chap3_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap2.html">[MathJax off]</a></p>
<p><a id="X7B222197819984A6" name="X7B222197819984A6"></a></p>
<div class="ChapSects"><a href="chap2_mj.html#X7B222197819984A6">2 <span class="Heading">Ring Maps</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7EBF1DD67BD0758F">2.1 <span class="Heading">Ring Maps: Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X87C00FFB79FA93A8">2.1-1 KernelSubobject</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7C7401BA7E2221CB">2.2 <span class="Heading">Ring Maps: Operations and Functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7B7DDDA17837AEF5">2.2-1 SegreMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X78E0B36179C5646C">2.2-2 PlueckerMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X816B9AB287EEF9A5">2.2-3 VeroneseMap</a></span>
</div></div>
</div>

<h3>2 <span class="Heading">Ring Maps</span></h3>

<p><a id="X7EBF1DD67BD0758F" name="X7EBF1DD67BD0758F"></a></p>

<h4>2.1 <span class="Heading">Ring Maps: Attributes</span></h4>

<p><a id="X87C00FFB79FA93A8" name="X87C00FFB79FA93A8"></a></p>

<h5>2.1-1 KernelSubobject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ KernelSubobject</code>( <var class="Arg">phi</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> submodule</p>

<p>The kernel ideal of the ring map <var class="Arg">phi</var>.</p>

<p><a id="X7C7401BA7E2221CB" name="X7C7401BA7E2221CB"></a></p>

<h4>2.2 <span class="Heading">Ring Maps: Operations and Functions</span></h4>

<p><a id="X7B7DDDA17837AEF5" name="X7B7DDDA17837AEF5"></a></p>

<h5>2.2-1 SegreMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SegreMap</code>( <var class="Arg">R</var>, <var class="Arg">s</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> ring map</p>

<p>The ring map corresponding to the Segre embedding of <span class="SimpleMath">\(MultiProj(\textit{R})\)</span> into the projective space according to <span class="SimpleMath">\(P(W_1)\times P(W_2) \to P(W_1\otimes W_2)\)</span>.</p>

<p><a id="X78E0B36179C5646C" name="X78E0B36179C5646C"></a></p>

<h5>2.2-2 PlueckerMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PlueckerMap</code>( <var class="Arg">l</var>, <var class="Arg">n</var>, <var class="Arg">A</var>, <var class="Arg">s</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> ring map</p>

<p>The ring map corresponding to the Plücker embedding of the Grassmannian <span class="SimpleMath">\(G_l(P^{\textit{n}}(\textit{A}))=G_l(P(W))\)</span> into the projective space <span class="SimpleMath">\(P(\bigwedge^l W)\)</span>, where <span class="SimpleMath">\(W=V^*\)</span> is the <span class="SimpleMath">\(\textit{A}\)</span>-dual of the free module <span class="SimpleMath">\(V=A^{\textit{n}+1}\)</span> of rank <span class="SimpleMath">\(\textit{n}+1\)</span>.</p>

<p><a id="X816B9AB287EEF9A5" name="X816B9AB287EEF9A5"></a></p>

<h5>2.2-3 VeroneseMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ VeroneseMap</code>( <var class="Arg">n</var>, <var class="Arg">d</var>, <var class="Arg">A</var>, <var class="Arg">s</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> ring map</p>

<p>The ring map corresponding to the Veronese embedding of the projective space <span class="SimpleMath">\(P^{\textit{n}}(\textit{A})=P(W)\)</span> into the projective space <span class="SimpleMath">\(P(S^d W)\)</span>, where <span class="SimpleMath">\(W=V^*\)</span> is the <span class="SimpleMath">\(\textit{A}\)</span>-dual of the free module <span class="SimpleMath">\(V=A^{\textit{n}+1}\)</span> of rank <span class="SimpleMath">\(\textit{n}+1\)</span>.</p>


<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Previous Chapter]</a>    <a href="chap3_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="chapBib_mj.html">Bib</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>

95%


¤ 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.