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<h1>WPE</h1>


<h2>Provides efficient methods for working with wreath product elements.</h2>

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    0.8</p>

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    21 October 2024
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<p><b>
    Friedrich Rober


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<br />Email: <span class="URL"><a href="mailto:friedrich.rober@rwth-aachen.de">friedrich.rober@rwth-aachen.de</a></span>
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<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8389AD927B74BA4A">1.1 <span class="Heading">Overview</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7950ED88879EE36F">1.2 <span class="Heading">Intuitive Research</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83C9D5E6846B299E">1.2-1 <span class="Heading">The Power of Component-wise Representation</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7D96C25680814773">1.3 <span class="Heading">Efficient Computing</span></a>
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<div class="ContChap"><a href="chap2.html#X7DD31B407B9402A3">2 <span class="Heading">Notation</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7DF2AEBC8518FFA4">2.1 <span class="Heading">Wreath Products</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X83A8F3308644ACFA">2.2 <span class="Heading">Wreath Cycles</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X872BE72F7B2BBD6B">2.3 <span class="Heading">Sparse Wreath Cycles</span></a>
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<div class="ContChap"><a href="chap3.html#X81932F777898AD72">3 <span class="Heading">Tutorial</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X820D3CEF8368DB04">3.1 <span class="Heading">Creating Wreath Product Elements</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7C85A3718343D842">3.2 <span class="Heading">Displaying Wreath Product Elements</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X8345CC25855C9406">3.3 <span class="Heading">Computing in Wreath Products</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X8017E4AF7EBB72D2">3.4 <span class="Heading">Conjugacy Problem</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7D474F8F87E4E5D9">3.5 <span class="Heading">Conjugacy Classes</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7A2BF4527E08803C">3.6 <span class="Heading">Centralizer</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X87A59E867A83A798">3.7 <span class="Heading">Cycle Index Polynomial</span></a>
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<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#X794F3F697C476F75">4.1 <span class="Heading">Generic Wreath Product Representation</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7DBA9EFB82F64741">4.1-1 IsomorphismWreathProduct</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7C29594383022EDB">4.2 <span class="Heading">Accessing Components</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7A13B6B47BA67183">4.2-1 ComponentsOfWreathProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84D9A60E8614F35E">4.2-2 TopGroupOfWreathProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7E1A2F01848423EA">4.2-3 BaseGroupOfWreathProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7F1EB294829E86E5">4.2-4 TopComponentOfWreathProductElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X86B4BB78813D437E">4.2-5 BaseComponentOfWreathProductElement</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7BD2554F7FE49C2E">4.3 <span class="Heading">Properties of Wreath Product Elements</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7C57D9497D8BBC23">4.3-1 Territory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7F7DF936839FE1C7">4.3-2 IsWreathCycle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85C1618F78451F65">4.3-3 IsSparseWreathCycle</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X82BDC56A7B4298CE">4.3-4 WreathCycleDecomposition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7ED422DB79830AF7">4.3-5 Yade</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X8227AD6B7FC637DE">4.4 <span class="Heading">Printing, Viewing and Displaying</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7CA684548407A756">4.4-1 ViewObj</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X827699E287C25991">4.4-2 DisplayOptionsForWreathProductElements</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7F900588870902F7">4.4-3 SetDisplayOptionsForWreathProductElements</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7D1989B185F184F8">4.4-4 ResetDisplayOptionsForWreathProductElements</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X82513F74863B77AE">4.5 <span class="Heading">Cycle Index of Wreath Products</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X871F79767C6BC7C0">4.5-1 CycleIndexWreathProductImprimitiveAction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X799B029E79EACCC3">4.5-2 CycleIndexWreathProductProductAction</a></span>
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<div class="ContChap"><a href="chap5.html#X7DE8E16C7C2D387B">5 <span class="Heading">Operations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X8730A88E7DEB09F2">5.1 <span class="Heading">Operations List</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X787C52A28302EB30">5.1-1 <span class="Heading">Wreath Product Representations</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X80E9B35E7B9B7D98">5.1-2 <span class="Heading">Operations for all Representations</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X803D92AC7A29E51F">5.1-3 <span class="Heading">Operations for Permutation Representations</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X802ECAC97D3DA99E">5.1-4 <span class="Heading">Operations for Generic Representation</span></a>
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<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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