Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/repndecomp/doc/   (GAP Algebra Version 4.15.1©)  Datei vom 12.8.2025 mit Größe 12 kB image not shown  

Quelle  chap0.html

  Sprache: HTML 		 

 products/Sources/formale Sprachen/GAP/pkg/repndecomp/doc/chap0.html


<?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 (RepnDecomp) - 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="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>

<p id="mathjaxlink" class="pcenter"><a href="chap0_mj.html">[MathJax on]</a></p>
<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">

<h1>RepnDecomp</h1>


<h2>Decompose representations of finite groups into irreducibles</h2>

<p>
    1.3.1</p>

<p>
    10 September 2025
  </p>

</div>
<p><b>
    Kaashif Hymabaccus



  </b>
<br />Email: <span class="URL"><a href="mailto:kaashif@kaashif.co.uk">kaashif@kaashif.co.uk</a></span>
<br />Homepage: <span class="URL"><a href="https://kaashif.co.uk">https://kaashif.co.uk</a></span>
</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<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#X789233A47A277072">1.1 <span class="Heading">Getting started with RepnDecomp</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8360C04082558A12">1.1-1 <span class="Heading">Installation</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X792C0F507B4A3B89">1.1-2 <span class="Heading">Note on what is meant by a representation</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8315479878D25E37">1.1-3 <span class="Heading">API Overview</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap2.html#X7D9B253E794EF912">2 <span class="Heading">Isomorphisms between representations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7AEE81C2809E0B98">2.1 <span class="Heading">Finding explicit isomorphisms</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7F0D3CFB7800149A">2.1-1 LinearRepresentationIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X841DE7D08491325F">2.1-2 LinearRepresentationIsomorphismSlow</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X85DAC9E583D8EFB9">2.2 <span class="Heading">Testing isomorphisms</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X86EB9DD586958473">2.2-1 AreRepsIsomorphic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X81080E1B7917B361">2.2-2 IsLinearRepresentationIsomorphism</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X83B4D1DB7F92BD3A">3 <span class="Heading">Algorithms for unitary representations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X870B3D0D80CFADB1">3.1 <span class="Heading">Unitarising representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X86B2367A79BE5B9F">3.1-1 UnitaryRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X87D121227C027253">3.1-2 IsUnitaryRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X78F7DFD186A4E7CA">3.1-3 LDLDecomposition</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7974D0C580C833D1">3.2 <span class="Heading">Decomposing unitary representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8175C1167A31C3D6">3.2-1 IrreducibleDecompositionDixon</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4.html#X8346542B8387968B">4 <span class="Heading">Miscellaneous useful functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X87196FDB78749ECA">4.1 <span class="Heading">Predicates for representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8631A1417C3C1D88">4.1-1 IsFiniteGroupLinearRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X826D5ADF7FA87782">4.1-2 IsFiniteGroupPermutationRepresentation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X8271F7A386CFEA63">4.2 <span class="Heading">Efficient summing over groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85E8A5FC844DC09A">4.2-1 GroupSumBSGS</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X86F42D257CFB192D">4.3 <span class="Heading">Space-efficient representation of tensors of matrices</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84335C447DE377B0">4.3-1 IsTensorProductOfMatricesObj</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X868B9CB1873C93AC">4.3-2 IsTensorProductPairRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85AD76DB7D5F8B12">4.3-3 IsTensorProductKroneckerRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X86671AD582FF77E2">4.3-4 TensorProductOfMatrices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X79D0379D79F5DF9B">4.3-5 CharacterOfTensorProductOfRepresentations</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X83F160967ED7EE14">4.4 <span class="Heading">Matrices and homomorphisms</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7D17785482F143B0">4.4-1 ComposeHomFunction</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7C3EDA5E7A24196C">4.5 <span class="Heading">Representation theoretic functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X841424DF824E258B">4.5-1 TensorProductRepLists</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84EAE3DB7FA8102C">4.5-2 DirectSumOfRepresentations</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85147CF97B912CC3">4.5-3 DegreeOfRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7B14287E7BFC548D">4.5-4 PermToLinearRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7E67A4817A5E4879">4.5-5 IsOrthonormalSet</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5.html#X7F968DF987DE4A6E">5 <span class="Heading">Computing decompositions of representations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7E29883984400D2C">5.1 <span class="Heading">Block diagonalizing</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8361AD057AD282AC">5.1-1 BlockDiagonalBasisOfRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X86EB837579C1416D">5.1-2 BlockDiagonalRepresentation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X863A16A179A7486B">5.2 <span class="Heading">Algorithms due to the authors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X831574AD864C94A8">5.2-1 REPN_ComputeUsingMyMethod</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7DB659DB7E48D502">5.2-2 REPN_ComputeUsingMyMethodCanonical</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7C22F13E80A74438">5.3 <span class="Heading">Algorithms due to Serre</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7E95B0367992BEC4">5.3-1 CanonicalDecomposition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X795C63F386C45308">5.3-2 IrreducibleDecomposition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X87E91CBE7992D126">5.3-3 IrreducibleDecompositionCollected</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7C1CF0547D72D354">5.3-4 REPN_ComputeUsingSerre</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6.html#X7A0EF2C67E2DB726">6 <span class="Heading">Centralizer (commutant) rings</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7E70A3D881CD5FFA">6.1 <span class="Heading">Finding a basis for the centralizer</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7901B6A7860D35C3">6.1-1 CentralizerBlocksOfRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X86B19E2B877121E9">6.1-2 CentralizerOfRepresentation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X83C4F8C17DA976EE">6.2 <span class="Heading">Using the centralizer for computations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X87E5BAEB82DC00C3">6.2-1 ClassSumCentralizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X78719DC8868B0744">6.2-2 ClassSumCentralizerNC</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
<br />
</div>

<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</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="chapInd.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>

Messung V0.5 in Prozent
C=100 H=100 G=100

¤ Dauer der Verarbeitung: 0.18 Sekunden  (vorverarbeitet am  2026-06-05) ¤

*© Formatika GbR, Deutschland




Wurzel

Suchen

PVS Prover

Isabelle Prover

NIST Cobol Testsuite

Cephes Mathematical Library

Vienna Development Method

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.