<?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 (HAPprime Datatypes) - 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" />
</head>
<body>
<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="chap9.html">9</a> <a href="chap10.html">10</a> <a href="chapInd.html">Ind</a> </div>
<div class="chlinkprevnexttop"> <a href="chap0.html">Top of Book</a> <a href="chap1.html">Next Chapter</a> </div>
<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">
<h1><strong class="pkg">HAPprime</strong></h1>
<h2>Datatypes reference manual</h2>
<p>Version 0.3.2</p>
<p>13 February 2009</p>
</div>
<p><b>
Paul Smith<br />
</b>
<br />Email: <span class="URL"><a href="mailto:paul.smith@nuigalway.ie">paul.smith@nuigalway.ie</a></span>
<br />Homepage: <span class="URL"><a href="http://www.maths.nuigalway.ie/~pas">http://www.maths.nuigalway.ie/~pas</a></span>
<br />Address: <br />Department of Mathematics,<br /> National University of Ireland, Galway<br /> Galway,<br /> Ireland.
</p>
<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2006-2009 Paul Smith</p>
<p><strong class="pkg">HAPprime</strong> is released under the GNU General Public License (GPL). This file is part of <strong class="pkg">HAPprime</strong>, though as documentation it is released under the GNU Free Documentation License (see <span class="URL"><a href="http://www.gnu.org/licenses/licenses.html#FDL">http://www.gnu.org/licenses/licenses.html#FDL</a></span>).</p>
<p><strong class="pkg">HAPprime</strong> is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>
<p><strong class="pkg">HAPprime</strong> is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.</p>
<p>You should have received a copy of the GNU General Public License along with <strong class="pkg">HAPprime</strong>; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA</p>
<p>For more details, see <span class="URL"><a href="http://www.fsf.org/licenses/gpl.html">http://www.fsf.org/licenses/gpl.html</a></span>.</p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p><strong class="pkg">HAPprime</strong> is supported by a Marie Curie Transfer of Knowledge grant based at the Department of Mathematics, NUI Galway (MTKD-CT-2006-042685)</p>
<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>
<div class="contents">
<h3>Contents</h3>
<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
</div>
<div class="ContChap"><a href="chap2.html#X7C0B125E7D5415B4">2 <span class="Heading">Resolutions</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X86DA1C1B7EDE0DD8">2.1 <span class="Heading">The <code class="keyw">HAPResolution</code> datatype in <strong class="pkg">HAPprime</strong></span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X7D3C5D987DEB2360">2.2 <span class="Heading">Implementation: Constructing resolutions</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X7D61ADD17A4CF194">2.3 <span class="Heading">Resolution construction functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X784BCF7C801B6E8E">2.3-1 LengthOneResolutionPrimePowerGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X8311B9697B5F7685">2.3-2 LengthZeroResolutionPrimePowerGroup</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X84AD05E17FA85CB1">2.4 <span class="Heading">Resolution data access functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X83F7747D8585608C">2.4-1 ResolutionLength</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X806048907CE5B7B6">2.4-2 ResolutionGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7FF354AC7EEE2197">2.4-3 ResolutionFpGModuleGF</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7AFBE74B85AC3D85">2.4-4 ResolutionModuleRank</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7EBA188478844D96">2.4-5 ResolutionModuleRanks</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X803528CD872A1F4C">2.4-6 BoundaryFpGModuleHomomorphismGF</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7FB150F67DAF9059">2.4-7 ResolutionsAreEqual</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X81D7C767813647B3">2.5 <span class="Heading">Example: Computing and working with resolutions</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X79487D6C80383A6A">2.6 <span class="Heading">Miscellaneous resolution functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7AB2536286A7324D">2.6-1 BestCentralSubgroupForResolutionFiniteExtension</a></span>
</div>
</div>
<div class="ContChap"><a href="chap3.html#X8074AAF07A3E7D2C">3 <span class="Heading">Graded algebras</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X844F0654822DAFCC">3.1 <span class="Heading">Graded algebras in <strong class="pkg">HAP</strong> (and <strong class="pkg">HAPprime</strong>)</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X7DE3278D7E5DEE03">3.2 <span class="Heading">Data access functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X78ED069183AD3EEA">3.2-1 ModPRingGeneratorDegrees</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X780F21707FB7EFF4">3.2-2 ModPRingNiceBasis</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7F40E8DA7AEC5CDC">3.2-3 ModPRingNiceBasisAsPolynomials</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7E72445386B555DD">3.2-4 ModPRingBasisAsPolynomials</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X87C3D1B984960984">3.3 <span class="Heading">Other functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X79C71A2F878358BB">3.3-1 PresentationOfGradedStructureConstantAlgebra</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X790D62E37AA53C39">3.4 <span class="Heading">Example: Graded algebras and mod-p cohomology rings</span></a>
</div>
</div>
<div class="ContChap"><a href="chap4.html#X7CF4153B7903F639">4 <span class="Heading">Presentations of graded algebras</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X7F7903AE8392D54A">4.1 <span class="Heading">The <code class="keyw">GradedAlgebraPresentation</code> datatype</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X8589CD117D1ECD29">4.2 <span class="Heading">Construction function</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X84A14CBF7C499665">4.2-1 <span class="Heading">GradedAlgebraPresentation construction functions</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X7DE3278D7E5DEE03">4.3 <span class="Heading">Data access functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X877889A5792202F7">4.3-1 BaseRing</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8235D10781BE8003">4.3-2 CoefficientsRing</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X844BB80282EA3EBA">4.3-3 IndeterminatesOfGradedAlgebraPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X84299C5A7ACD6F71">4.3-4 GeneratorsOfPresentationIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7DABCC1D85B33DAC">4.3-5 PresentationIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7BFB8AC97FE6BDD6">4.3-6 IndeterminateDegrees</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7DB98FC5869F4CBC">4.3-7 <span class="Heading">Example: Constructing and accessing data of a
<code class="keyw">GradedAlgebraPresentation</code></span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X87C3D1B984960984">4.4 <span class="Heading">Other functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X87EB0B4A852CF4C6">4.4-1 <span class="Heading">TensorProduct</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8306E03281AF1CED">4.4-2 IsIsomorphicGradedAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X87B04D4580DE8E10">4.4-3 IsAssociatedGradedRing</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X85D95BF07C8E5DF7">4.4-4 DegreeOfRepresentative</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7CE381787AEC5CAC">4.4-5 MaximumDegreeForPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7EF085B67B846215">4.4-6 <span class="Heading">SubspaceDimensionDegree</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7834EE487CAA02D4">4.4-7 <span class="Heading">SubspaceBasisRepsByDegree</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X84D5111984AFDD31">4.4-8 CoefficientsOfPoincareSeries</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7B93B7D082A50E61">4.4-9 HilbertPoincareSeries</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7F5D00C97A46D686">4.4-10 LHSSpectralSequence</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X87DD66E67D0D5485">4.5 <span class="Heading">Example: Computing the Lyndon-Hoschild-Serre spectral sequence
and mod-p cohomology ring for a small p-group</span></a>
</div>
</div>
<div class="ContChap"><a href="chap5.html#X820435E87D83DF34">5 <span class="Heading">FG-modules</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X85FA0B237AC4A19D">5.1 <span class="Heading">The <code class="keyw">FpGModuleGF</code> datatype</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X79DF42E686679AFE">5.2 <span class="Heading">Implementation details: Block echelon form</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X79DDD8C37A0B8425">5.2-1 <span class="Heading">Generating vectors and their block structure</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X82F0E0067C40FDD5">5.2-2 <span class="Heading">Matrix echelon reduction and head elements</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X814C05FC87ED4035">5.2-3 <span class="Heading">Echelon block structure and minimal generators</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X86F4852785A509BF">5.2-4 <span class="Heading">Intersection of two modules</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X83D8009086035BCB">5.3 <span class="Heading">Construction functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X862AC894821415A4">5.3-1 <span class="Heading">FpGModuleGF construction functions</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X83232B1886BE75F0">5.3-2 FpGModuleFromFpGModuleGF</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X832C55197A46CB77">5.3-3 MutableCopyModule</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8315A82E7812289F">5.3-4 CanonicalAction</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X814553E382BC777E">5.3-5 <span class="Heading">Example: Constructing a <code class="keyw">FpGModuleGF</code></span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7DE3278D7E5DEE03">5.4 <span class="Heading">Data access functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X85CF62207B6F6099">5.4-1 ModuleGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X81C2789D85109789">5.4-2 ModuleGroupOrder</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7EE4E7ED86696752">5.4-3 ModuleAction</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7CFEF3B887425980">5.4-4 ModuleActionBlockSize</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X81F860F380EB55FC">5.4-5 ModuleGroupAndAction</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X78BDED977DA309FD">5.4-6 ModuleCharacteristic</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X86AC3239861EAB8A">5.4-7 ModuleField</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7A020F6F7EFDFFC7">5.4-8 ModuleAmbientDimension</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X86B97B587B7C12E7">5.4-9 AmbientModuleDimension</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7DF15EFA78F1DDF6">5.4-10 DisplayBlocks</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7E4C3C5C7CC7B559">5.4-11 <span class="Heading">Example: Accessing data about a <code class="keyw">FpGModuleGF</code></span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X85D634767E456A9D">5.5 <span class="Heading">Generator and vector space functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7D6B0216838295A2">5.5-1 ModuleGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7F643D50826E15E2">5.5-2 ModuleGeneratorsAreMinimal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7978F2DD787C2BB6">5.5-3 ModuleGeneratorsAreEchelonForm</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X85178CA8858B8616">5.5-4 ModuleIsFullCanonical</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X87572B78824FB28E">5.5-5 ModuleGeneratorsForm</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7DFFBBD6809A2B41">5.5-6 ModuleRank</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7DFAF92283C6FFDC">5.5-7 ModuleVectorSpaceBasis</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8377A6E986D36D12">5.5-8 ModuleVectorSpaceDimension</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X81C340AD7EE8FA63">5.5-9 <span class="Heading">MinimalGeneratorsModule</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7E44920683157DE2">5.5-10 RadicalOfModule</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7F9E3DF87FE60C1A">5.5-11 <span class="Heading">Example: Generators and basis vectors of a <code class="keyw">FpGModuleGF</code></span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7B989D1181EBBBB5">5.6 <span class="Heading">Block echelon functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X84E3AA228784BF01">5.6-1 EchelonModuleGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X856E45CC84B53128">5.6-2 ReverseEchelonModuleGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X83306CFA857F177C">5.6-3 <span class="Heading">Example: Converting a <code class="keyw">FpGModuleGF</code> to block echelon form</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7B22D74482E6EF40">5.7 <span class="Heading">Sum and intersection functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X879541298181840D">5.7-1 <span class="Heading">DirectSumOfModules</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X82A18B41872A8149">5.7-2 DirectDecompositionOfModule</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X83D609B679B53F5C">5.7-3 IntersectionModules</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X84A6FBC37BD8EEAB">5.7-4 SumModules</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8198B7C986776BA8">5.7-5 <span class="Heading">Example: Sum and intersection of <code class="keyw">FpGModuleGF</code>s</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X8308D685809A4E2F">5.8 <span class="Heading">Miscellaneous functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X81A073C47FB50620">5.8-1 =</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X78EB919D85362902">5.8-2 <span class="Heading">IsModuleElement</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8071ECEB7A92965A">5.8-3 IsSubModule</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X82FB0B387E53B073">5.8-4 RandomElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X84EB237885A48F03">5.8-5 <span class="Heading">Random Submodule</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap6.html#X82F28552819A6542">6 <span class="Heading">FG-module homomorphisms</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap6.html#X85481E577D3BAB8E">6.1 <span class="Heading">The <code class="keyw">FpGModuleHomomorphismGF</code> datatype</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap6.html#X83FF0EBD81A405A9">6.2 <span class="Heading">Calculating the kernel of a FG-module homorphism by splitting
into two homomorphisms</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap6.html#X8356C3B680B7110E">6.3 <span class="Heading">Calculating the kernel of a FG-module homorphism by column
reduction and partitioning</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap6.html#X83D8009086035BCB">6.4 <span class="Heading">Construction functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8640D133855BB892">6.4-1 <span class="Heading">FpGModuleHomomorphismGF construction functions</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EA7C568836E9730">6.4-2 <span class="Heading">Example: Constructing a <code class="keyw">FpGModuleHomomorphismGF</code></span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap6.html#X7DE3278D7E5DEE03">6.5 <span class="Heading">Data access functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X835A27F3877D7B04">6.5-1 SourceModule</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X810013F0852729DD">6.5-2 TargetModule</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X81173EB682B5C903">6.5-3 ModuleHomomorphismGeneratorMatrix</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EF5C42A79568EAE">6.5-4 DisplayBlocks</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7D200588818203D6">6.5-5 DisplayModuleHomomorphismGeneratorMatrix</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X831A8A6485A484D7">6.5-6 DisplayModuleHomomorphismGeneratorMatrixBlocks</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C5F52FE80BB871A">6.5-7 <span class="Heading">Example: Accessing data about a <code class="keyw">FpGModuleHomomorphismGF</code></span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap6.html#X79444C767921055C">6.6 <span class="Heading">Image and kernel functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8038F50582425ECA">6.6-1 <span class="Heading">ImageOfModuleHomomorphism</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X850FD5AE80BF6F11">6.6-2 <span class="Heading">PreImageRepresentativeOfModuleHomomorphism</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X86C7D57A825235EE">6.6-3 KernelOfModuleHomomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X795D4069832F15F8">6.6-4 <span class="Heading">Example: Kernel and Image of a <code class="keyw">FpGModuleHomomorphismGF</code></span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap7.html#X7E88C32A82E942DA">7 <span class="Heading">Ring homomorphisms</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap7.html#X7A0B792785E2AA8A">7.1 <span class="Heading">The <code class="keyw">HAPRingHomomorphism</code> datatype</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7AB84A0B83B2C1F1">7.1-1 <span class="Heading">Implementation details</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7AB0F3977DC63F54">7.1-2 <span class="Heading">Elimination orderings</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap7.html#X83D8009086035BCB">7.2 <span class="Heading">Construction functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A500F53808DDDA9">7.2-1 HAPRingToSubringHomomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A7E46337D6F47B6">7.2-2 <span class="Heading">HAPSubringToRingHomomorphism</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A77983F7D6E0AC7">7.2-3 HAPRingHomomorphismByIndeterminateMap</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7E011BEB868B14B4">7.2-4 HAPRingReductionHomomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X87F4CEBD869C46A1">7.2-5 PartialCompositionRingHomomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8288925E86054FE9">7.2-6 HAPZeroRingHomomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X78106D04821D02EC">7.2-7 InverseRingHomomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7ABEFEFC8285FD48">7.2-8 CompositionRingHomomorphism</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap7.html#X7DE3278D7E5DEE03">7.3 <span class="Heading">Data access functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7E44FAD67C045016">7.3-1 SourceGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X79FA0ADF7EA5B043">7.3-2 SourceRelations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7DDE043C789AEC3A">7.3-3 SourcePolynomialRing</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X838F30B3805177C1">7.3-4 ImageGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7F50B38D87439BEE">7.3-5 ImageRelations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X863B0F2978792F7F">7.3-6 ImagePolynomialRing</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap7.html#X7B65E0C37AAB6066">7.4 <span class="Heading">General functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8680F51E82EA1939">7.4-1 <span class="Heading">ImageOfRingHomomorphism</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7B1B2C0980375531">7.4-2 <span class="Heading">PreimageOfRingHomomorphism</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap7.html#X7A00ADEE8679D3AD">7.5 <span class="Heading">Example: Constructing and using a <code class="keyw">HAPRingHomomorphism</code></span></a>
</div>
</div>
<div class="ContChap"><a href="chap8.html#X80C0FB5A7B72B145">8 <span class="Heading">Derivations</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap8.html#X86F29D447B67B28F">8.1 <span class="Heading">The <code class="keyw">HAPDerivation</code> datatype</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap8.html#X85F99EEF86DD595D">8.2 <span class="Heading">Computing the kernel and homology of a derivation</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap8.html#X8589CD117D1ECD29">8.3 <span class="Heading">Construction function</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X7B8058948424E639">8.3-1 <span class="Heading">HAPDerivation construction functions</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap8.html#X789E616983759E10">8.4 <span class="Heading">Data access function</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X803EA43A7F21FB99">8.4-1 DerivationRing</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X7AE49BC082B7219D">8.4-2 DerivationImages</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X811828517C62421B">8.4-3 DerivationRelations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X84A549558235F536">8.4-4 <span class="Heading">Example: Constructing and accessing data of a <code class="keyw">HAPDerivation</code></span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap8.html#X7956001A816B2507">8.5 <span class="Heading">Image, kernel and homology functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X7B523CEF85223194">8.5-1 ImageOfDerivation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X842250387FC8302C">8.5-2 KernelOfDerivation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X803D9B5E7A26F749">8.5-3 HomologyOfDerivation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X78B45E8C86F90981">8.5-4 <span class="Heading">Example: Homology of a <code class="keyw">HAPDerivation</code></span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap9.html#X7FF2605B79D7B5F8">9 <span class="Heading">Poincaré series</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap9.html#X872F597F7AACA402">9.1 <span class="Heading">Computing the Poincaré series using spectral sequences</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap9.html#X7978D58181D2725F">9.2 <span class="Heading">Computing the Poincaré series using a minimal resolution</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7F0911257D80691E">9.2-1 PoincareSeriesAutoMem</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap9.html#X82A90FCC80BAC1F9">9.3 <span class="Heading">Example Poincaré series computations</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap9.html#X84E1A5148674E7E0">9.4 <span class="Heading">The Poincaré series of groups of order 64 and 128</span></a>
</div>
</div>
<div class="ContChap"><a href="chap10.html#X7B65E0C37AAB6066">10 <span class="Heading">General Functions</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X812CCAB278643A59">10.1 <span class="Heading">Matrices</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X845EA1B28618D9A7">10.1-1 SumIntersectionMatDestructive</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X8359E68C7F38BA5F">10.1-2 SolutionMat</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X872D9F5D7ED6F4AA">10.1-3 IsSameSubspace</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X789478557955E1C3">10.1-4 PrintDimensionsMat</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X8080767383F9EF31">10.1-5 <span class="Heading">Example: matrices and vector spaces</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X826D8334845549EC">10.2 <span class="Heading">Polynomials</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7E8B84388516792D">10.2-1 TermsOfPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X82862FA1817C7767">10.2-2 IsMonomial</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7A603BCA83895309">10.2-3 UnivariateMonomialsOfMonomial</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7DE6473B7AE6EC7F">10.2-4 IndeterminateAndExponentOfUnivariateMonomial</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X86FFC6697CAF53B8">10.2-5 IndeterminatesOfPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X87DE84AC7B62DC5C">10.2-6 <span class="Heading">ReduceIdeal</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X84E9467E84243B77">10.2-7 ReducedPolynomialRingPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7F8D0B27815DDA6B">10.2-8 <span class="Heading">Example: monomials, polynomials and ring presentations</span></a>
</span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X840A7A5D7AE407F2">10.3 <span class="Heading">Singular</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X783EE9057FE65731">10.3-1 SingularSetNormalFormIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7E6A0D647D39110B">10.3-2 SingularPolynomialNormalForm</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X804568497F686594">10.3-3 SingularGroebnerBasis</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7FB57C4F7D3164E6">10.3-4 SingularReducedGroebnerBasis</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X8716635F7951801B">10.4 <span class="Heading">Groups</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7FD16926859DD49B">10.4-1 <span class="Heading">HallSeniorNumber</span></a>
</span>
</div>
</div>
<br />
</div>
<div class="chlinkprevnextbot"> <a href="chap0.html">Top of Book</a> <a href="chap1.html">Next Chapter</a> </div>
<div class="chlinkbot"><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="chap9.html">9</a> <a href="chap10.html">10</a> <a href="chapInd.html">Ind</a> </div>
<hr />
<p class="foot">generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>
distrib
>
Mandriva
>
2010.0
>
i586
>
media
>
contrib-release
>
by-pkgid
>
91213ddcfbe7f54821d42c2d9e091326
>
files
>
1447
