<?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" "https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >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_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" 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</span ><a href="chap11_mj.html#X78E07AD87CE14F53" >11.1 <span class="Heading" >Symmetric Algebra: Constructor</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X79E2C2AF842E8419" >11.1-1 SymmetricPower</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X7A26D0AD7E8F9FB2" >11.2 <span class="Heading" >Symmetric Algebra: Properties and Attributes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X79AECE877A31293F" >11.2-1 IsSymmetricPower</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8750195584FAA0B2" >11.2-2 SymmetricPowerExponent</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7D9225D083DDDB0C" >11.2-3 SymmetricPowerBaseModule</a></span >div ></div >div >span class="Heading" >Symmetric Algebra and Koszul Complex</span ></h3>"X78E07AD87CE14F53" name="X78E07AD87CE14F53" ></a></p>span class="Heading" >Symmetric Algebra: Constructor</span ></h4>"X79E2C2AF842E8419" name="X79E2C2AF842E8419" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ SymmetricPower</code >( <var class="Arg" >k</var >, <var class="Arg" >M</var > )</td ><td class="tdright" >( operation )</td ></tr ></table ></div >strong class="pkg" >homalg</strong > module</p>var class="Arg" >k</var >-th exterior power of module <var class="Arg" >M</var >.</p>"X7A26D0AD7E8F9FB2" name="X7A26D0AD7E8F9FB2" ></a></p>span class="Heading" >Symmetric Algebra: Properties and Attributes</span ></h4>"X79AECE877A31293F" name="X79AECE877A31293F" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsSymmetricPower</code >( <var class="Arg" >M</var > )</td ><td class="tdright" >( property )</td ></tr ></table ></div >code class="code" >true</code > or <code class="code" >false</code ></p>"X8750195584FAA0B2" name="X8750195584FAA0B2" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ SymmetricPowerExponent</code >( <var class="Arg" >M</var > )</td ><td class="tdright" >( attribute )</td ></tr table ></div >"X7D9225D083DDDB0C" name="X7D9225D083DDDB0C" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ SymmetricPowerBaseModule</code >( <var class="Arg" >M</var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >var class="Arg" >M</var > is an symmetric power of.</p>div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap10_mj.html" >[Previous Chapter]</a> <a href="chap12_mj.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a 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