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<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">
<h1><strong class="pkg">HAPprime</strong></h1>
<h2>More homological algebra with prime power groups </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 class="ContSect"><span class="nocss"> </span><a href="chap1.html#X7EC1C3E779AE8717">1.1 <span class="Heading">Introduction to the <strong class="pkg">HAPprime</strong> package</span></a>
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<div class="ContSect"><span class="nocss"> </span><a href="chap1.html#X7D20BAAF862B41E9">1.2 <span class="Heading">Required software</span></a>
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<div class="ContSect"><span class="nocss"> </span><a href="chap1.html#X7CFA390D7DE91268">1.3 <span class="Heading">Installing <strong class="pkg">HAPprime</strong></span></a>
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<div class="ContSect"><span class="nocss"> </span><a href="chap1.html#X84983C5A84213019">1.4 <span class="Heading">Loading and testing <strong class="pkg">HAPprime</strong></span></a>
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<div class="ContSect"><span class="nocss"> </span><a href="chap1.html#X7F4F8D6F7CD6B765">1.5 <span class="Heading">Documentation</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X80F4100D783E407A">1.5-1 MakeHAPprimeDoc</a></span>
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<div class="ContSect"><span class="nocss"> </span><a href="chap1.html#X845E795E8537ABBA">1.6 <span class="Heading">Displaying progress and calculation information</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X80E9D70E843A8C2C">1.6-1 InfoHAPprime</a></span>
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<div class="ContChap"><a href="chap2.html#X7A489A5D79DA9E5C">2 <span class="Heading">Examples</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X81FB934A87FCAA22">2.1 <span class="Heading">Computing the mod p group cohomology</span></a>
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<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X78EE4D0386321E3B">2.2 <span class="Heading">Computing mod-p cohomology rings and their Poincaré series</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X81BCBAA18423E1C8">2.2-1 <span class="Heading">A ring presentation for the mod p cohomology (up to degree n)</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X825971A27C00C1B6">2.2-2 <span class="Heading">Calculating a provably-correct mod-p cohomology</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X78F3639083A7DE62">2.2-3 <span class="Heading">Computing Poincaré series</span></a>
</span>
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<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X87AD96A584D60140">2.3 <span class="Heading">Comparing the memory usage and speed of <strong class="pkg">HAPprime</strong> and <strong class="pkg">HAP</strong>'s
<code class="keyw">ResolutionPrimePowerGroup</code> functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X85FFD31A7B362DFF">2.3-1 <span class="Heading"><strong class="pkg">HAPprime</strong> takes less memory to store resolutions</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X848CF4C483C3F6E4">2.3-2 <span class="Heading"><strong class="pkg">HAPprime</strong> takes less memory to compute resolutions</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7CA386948072CFF4">2.3-3 <span class="Heading">Automatic selection of the best method</span></a>
</span>
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<div class="ContChap"><a href="chap3.html#X7EE4339B83BFDA2D">3 <span class="Heading">Functions for Homological Algebra</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X7C0B125E7D5415B4">3.1 <span class="Heading">Resolutions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X86934BE9858F7199">3.1-1 <span class="Heading">ResolutionPrimePowerGroup</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7B435C307F28D44F">3.1-2 <span class="Heading">ExtendResolutionPrimePowerGroup</span></a>
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<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X7FF2605B79D7B5F8">3.2 <span class="Heading">Poincaré Series</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7E1A4C8781A02CD0">3.2-1 PoincareSeriesLHS</a></span>
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<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X7A9561E47A4994F5">3.3 <span class="Heading">Cohomology Ring structure</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X85CFF2AB7A7A99D2">3.3-1 ModPCohomologyRingPresentation</a></span>
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