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<?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 (Modules) - Chapter 11: Symmetric Algebra and Koszul Complex</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="chap11" onload="jscontent()"> <div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a <div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#con <p id="mathjaxlink" class="pcenter"><a href="chap11_mj.html">[MathJax on]</a></p> <p><a id="X7E3E740C80F42986" name="X7E3E740C80F42986"></a></p> <div class="ChapSects"><a href="chap11.html#X7E3E740C80F42986">11 <span class="Heading">Sy <div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X </span> <div class="ContSSBlock"> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X79E2C2AF842E8419"> </div></div> <div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X </span> <div class="ContSSBlock"> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X79AECE877A31293F"> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X8750195584FAA0B2"> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7D9225D083DDDB0C"> </div></div> </div> <h3>11 <span class="Heading">Symmetric Algebra and Koszul Complex</span></h3> <p><a id="X78E07AD87CE14F53" name="X78E07AD87CE14F53"></a></p> <h4>11.1 <span class="Heading">Symmetric Algebra: Constructor</span></h4> <p><a id="X79E2C2AF842E8419" name="X79E2C2AF842E8419"></a></p> <h5>11.1-1 SymmetricPower</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Sy <p>Returns: a <strong class="pkg">homalg</strong> module</p> <p>Construct the <var class="Arg">k</var>-th exterior power of module <var class="Arg">M</var>.</p> <p><a id="X7A26D0AD7E8F9FB2" name="X7A26D0AD7E8F9FB2"></a></p> <h4>11.2 <span class="Heading">Symmetric Algebra: Properties and Attributes</span></h4> <p><a id="X79AECE877A31293F" name="X79AECE877A31293F"></a></p> <h5>11.2-1 IsSymmetricPower</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Is <p>Returns: <code class="code">true</code> or <code class="code">false</code></p> <p>Marks a module as an symmetric power of another module.</p> <p><a id="X8750195584FAA0B2" name="X8750195584FAA0B2"></a></p> <h5>11.2-2 SymmetricPowerExponent</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Sy <p>Returns: an integer</p> <p>The exponent of the symmetric power.</p> <p><a id="X7D9225D083DDDB0C" name="X7D9225D083DDDB0C"></a></p> <h5>11.2-3 SymmetricPowerBaseModule</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Sy <p>Returns: a homalg module</p> <p>The module that <var class="Arg">M</var> is an symmetric power of.</p> <div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#con <div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a <hr /> <p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GA </body> </html>
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