<?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 (tut) - Contents</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="chap0" 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="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="chap1.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >GAP — A Tutorial</h1 >div >br />Email: <span class="URL" ><a href="mailto:support@gap-system.org" >support@gap-system.org</a></span >br />Homepage: <span class="URL" ><a href="https://www.gap-system.org " >https://www.gap-system.org</a></span >"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>strong class="pkg" >GAP</strong > system by the <strong class="pkg" >GAP</strong > Group.</p>strong class="pkg" >GAP</strong > system are distributed under the terms of the GNU General Public License, see <span class="URL" ><a href="https://www.gnu.org/licenses/gpl.html " >https://www.gnu.org/licenses/gpl.html </a></span > or the file <code class="file" >GPL</code > in the <code class="file" >etc</code > directory of the <strong class="pkg" >GAP</strong > installation.</p>ound in <span class="RefLink" >Reference: Copyright and License</span >.</p>strong class="pkg" >GAP</strong > is developed over a long time and has many authors and contributors. More detailed information can be found in <span class="RefLink" >Reference: Authors and Maintainers</span >.</p>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.html#X874E1D45845007FE" >1 <span class="Heading" >Preface</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X863F306C7D32F4B0" >1.1 <span class="Heading" >The <strong class="pkg" >GAP</strong > System</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X7BF552C07E2F8F7C" >1.2 <span class="Heading" >Further Information about <strong class="pkg" >GAP</strong ></span ></a>span >div >div >div class="ContChap" ><a href="chap2.html#X7A3C7AE07D6848E3" >2 <span class="Heading" >A First Session with <strong class="pkg" >GAP</strong ></span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X84063FD486665C97" >2.1 <span class="Heading" >Starting and Leaving <strong class="pkg" >GAP</strong ></span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7B8D5EC27E33AF6D" >2.2 <span class="Heading" >Loading Source Code from a File</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7C7388A683D15599" >2.3 <span class="Heading" >The Read Evaluate Print Loop</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X86CA8242832F5F71" >2.4 <span class="Heading" >Constants and Operators</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X82F47EA88347AC2D" >2.5 <span class="Heading" >Variables versus Objects</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7F36AE347AD3CDEC" >2.6 <span class="Heading" >Objects vs. Elements</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X796E055D86856B42" >2.7 <span class="Heading" >About Functions</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7A7EADB77FF38BC9" >2.8 <span class="Heading" >Help</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X798515EF7D762548" >2.9 <span class="Heading" >Further Information introducing the System</span ></a>span >div >div >div class="ContChap" ><a href="chap3.html#X7863DAFD78E5DFB6" >3 <span class="Heading" >Lists and Records</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X81ECC2077D88E112" >3.1 <span class="Heading" >Plain Lists</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7DD65BEA7EDB0CD7" >3.2 <span class="Heading" >Identical Lists</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X8614C8207D57AD7A" >3.3 <span class="Heading" >Immutability</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X83BE0C20875DD285" >3.4 <span class="Heading" >Sets</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X79596BDE7CAF8491" >3.5 <span class="Heading" >Ranges</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7CC5B0347F8EC820" >3.6 <span class="Heading" >For and While Loops</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X879CFE0985DBA041" >3.7 <span class="Heading" >List Operations</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X851A7DD07866323F" >3.8 <span class="Heading" >Vectors and Matrices</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7CF7BBD58135B981" >3.9 <span class="Heading" >Plain Records</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X800A5E8681E28E2D" >3.10 <span class="Heading" >Further Information about Lists</span ></a>span >div >div >div class="ContChap" ><a href="chap4.html#X86FA580F8055B274" >4 <span class="Heading" >Functions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7D81680E7BB09F45" >4.1 <span class="Heading" >Writing Functions</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X801EE07E839B31B2" >4.2 <span class="Heading" >If Statements</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X797E24D67BB804A2" >4.3 <span class="Heading" >Local Variables</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7981E4197F7113EA" >4.4 <span class="Heading" >Recursion</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X85B6E21781804BBB" >4.5 <span class="Heading" >Further Information about Functions</span ></a>span >div >div >div class="ContChap" ><a href="chap5.html#X8171DAF2833FF728" >5 <span class="Heading" >Groups and Homomorphisms</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X85ED46007CED6191" >5.1 <span class="Heading" >Permutation groups</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X8493BB7D7ECB5AB2" >5.2 <span class="Heading" >Actions of Groups</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X8742F6A083ADE513" >5.3 <span class="Heading" >Subgroups as Stabilizers</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X8131EE9182385680" >5.4 <span class="Heading" >Group Homomorphisms by Images</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X7FFD731684606BC6" >5.5 <span class="Heading" >Nice Monomorphisms</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X84579FB48474079C" >5.6 <span class="Heading" >Further Information about Groups and Homomorphisms</span ></a>span >div >div >div class="ContChap" ><a href="chap6.html#X853484B982F1DF96" >6 <span class="Heading" >Vector Spaces and Algebras</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.html#X7DAD6700787EC845" >6.1 <span class="Heading" >Vector Spaces</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.html#X7DDBF6F47A2E021C" >6.2 <span class="Heading" >Algebras</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.html#X843A8D6F7A7592B5" >6.3 <span class="Heading" >Further Information about Vector Spaces and Algebras</span ></a>span >div >div >div class="ContChap" ><a href="chap7.html#X7BAF69417BB925F6" >7 <span class="Heading" >Domains</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X7D94C6F07ACEA397" >7.1 <span class="Heading" >Domains as Sets</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X81F376D67BA4F5EB" >7.2 <span class="Heading" >Algebraic Structure</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X7E8D59018638925F" >7.3 <span class="Heading" >Notions of Generation</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X85AB533B7DE21C8B" >7.4 <span class="Heading" >Domain Constructors</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X849B1C5F8136F3A9" >7.5 <span class="Heading" >Forming Closures of Domains</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X7EA77DE17DD8A231" >7.6 <span class="Heading" >Changing the Structure</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X8318352D7B5F19BA" >7.7 <span class="Heading" >Subdomains</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X7C83996381F67238" >7.8 <span class="Heading" >Further Information about Domains</span ></a>span >div >div >div class="ContChap" ><a href="chap8.html#X7AEED9AB824CD4DA" >8 <span class="Heading" >Operations and Methods</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8.html#X7C701DBF7BAE649A" >8.1 <span class="Heading" >Attributes</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8.html#X81C430C37B2F16D8" >8.2 <span class="Heading" >Properties and Filters</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8.html#X85CC8C167A280043" >8.3 <span class="Heading" >Immediate and True Methods</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a 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