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<div class="pcenter">
<h1><strong class="pkg">Hap Programming</strong> – An experimental framework for objectifying the data structures of Hap</h1>
<p>( development version of
10.02.2020
)</p>
</div>
<p><b>Marc Röder
</b>
<br />Email: <span class="URL"><a href="mailto:marc.roeder(at)nuigalway.ie">marc.roeder(at)nuigalway.ie</a></span>
</p>
<p><b>Address:</b><br />
Marc Röder, Department of Mathematics, NUI Galway, Irleland</p>
<p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p>
<h3>Abstract</h3>
<p>This extension does not change the behaviour of Hap and is fully backwards-compatible. It is not a part of Hap and there is no guarantee that it will at any point be supported by Hap. Use at your own risk.</p>
<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2007 Marc Röder.</p>
<p>This package is distributed under the terms of the GNU General Public License version 2 or later (at your convenience). See the file <code class="file">LICENSE</code> or <span class="URL"><a href="https://www.gnu.org/copyleft/gpl.html">https://www.gnu.org/copyleft/gpl.html</a></span></p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>This work was supported by Marie Curie Grant No. MTKD-CT-2006-042685</p>
<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>
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<h3>Contents<a id="contents" name="contents"></a></h3>
<div class="ContChap"><a href="chap1.html#X7C6DD73E7BB931AB">1 <span class="Heading">Resolutions in Hap</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X804F611B7E23BDB1">1.1 <span class="Heading">The Standard Representation <code class="keyw">HapResolutionRep</code></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8024014D8488FE30">1.2 <span class="Heading">The <code class="keyw">HapLargeGroupResolutionRep</code> Representation</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X86374CEA7CDC6946">2 <span class="Heading">Accessing and Manipulating Resolutions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7A7225067E7895A9">2.1 <span class="Heading">Representation-Independent Access Methods</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7CBC6D4C783383BE">2.1-1 StrongestValidRepresentationForLetter</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7C10841285614D04">2.1-2 StrongestValidRepresentationForWord</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X780AD2DB7F5D4935">2.1-3 PositionInGroupOfResolution</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7A58EC7B8130D6E2">2.1-4 IsValidGroupInt</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X822604B67B2A9133">2.1-5 GroupElementFromPosition</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7D3673E8840FA0B6">2.1-6 MultiplyGroupElts</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X8540F3B37BAC695F">2.1-7 MultiplyFreeZGLetterWithGroupElt</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X826835B185CA4DAF">2.1-8 MultiplyFreeZGWordWithGroupElt</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7D8B54D7828D7C5C">2.1-9 BoundaryOfFreeZGLetter</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X81A6037F82C3C31E">2.1-10 BoundaryOfFreeZGWord</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7B94A2ED857C62D5">2.2 <span class="Heading">Converting Between Representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7EB515317948BE8E">2.2-1 ConvertStandardLetter</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7A1CB5DF7A459D76">2.2-2 ConvertStandardWord</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X83153E2682184860">2.2-3 ConvertLetterToStandardRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X848203218271A166">2.2-4 ConvertWordToStandardRep</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X84FB45EB83B5822C">2.3 <span class="Heading">Special Methods for <code class="keyw">HapResolutionRep</code></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7B803CC184BD2612">2.3-1 IsFreeZGLetter</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7A36FB7B84E9A892">2.3-2 IsFreeZGWord</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X836D3F9886EED6AC">2.3-3 MultiplyGroupEltsNC</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X85893CC5823508A8">2.3-4 MultiplyFreeZGLetterWithGroupEltNC</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X8073DE7E7AD8B7CB">2.3-5 MultiplyFreeZGWordWithGroupEltNC</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7BD3994E7C414149">2.3-6 BoundaryOfFreeZGLetterNC</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X84B1DA21805A0880">2.3-7 BoundaryOfFreeZGWordNC</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X8024014D8488FE30">2.4 <span class="Heading">The <code class="keyw">HapLargeGroupResolutionRep</code> Representation</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X861BE6C787FA8032">2.4-1 GroupRingOfResolution</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X8338F7A37F240E33">2.4-2 MultiplyGroupElts_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X86F91A948022DEBB">2.4-3 IsFreeZGLetterNoTermCheck_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X793BA61478AEBE16">2.4-4 IsFreeZGWordNoTermCheck_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X85A7BFC284E9D9CB">2.4-5 IsFreeZGLetter_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7BF4A7EC83BE61C8">2.4-6 IsFreeZGWord_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7A4B682079630694">2.4-7 MultiplyFreeZGLetterWithGroupElt_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7F2365D2851E3E3C">2.4-8 MultiplyFreeZGWordWithGroupElt_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X8355F6E8842B3D8C">2.4-9 GeneratorsOfModuleOfResolution_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X840DF79086D5473E">2.4-10 BoundaryOfGenerator_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X83D90EC28357DCCE">2.4-11 BoundaryOfFreeZGLetterNC_LargeGroupRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X78C681D37F8DC2A1">2.4-12 BoundaryOfFreeZGWord_LargeGroupRep</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X792B9CC97C670AEA">3 <span class="Heading">Contracting Homotopies</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7E957D2381DBE362">3.1 <span class="Heading">The <code class="keyw">PartialContractingHomotopy</code> Data Type</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7D899ACD7EB512FA">3.1-1 ResolutionOfContractingHomotopy</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X79C69C9B877C6D60">3.1-2 PartialContractingHomotopyLookup</a></span>
</div></div>
</div>
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