<?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 >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >RepnDecomp</h1 >div >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 "X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"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 />"foot" >generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " >GAPDoc2HTML</a></p>body >html >quality 95%
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