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/a> <a href="chap1_mj.html" >1</a> <a href="chap2_mj.html" >2</a> <a href="chap3_mj.html" >3</a> <a href="chap4_mj.html" >4</a> <a href="chap5_mj.html" >5</a> <a href="chap6_mj.html" >6</a> <a href="chap7_mj.html" >7</a> <a href="chap8_mj.html" >8</a> <a href="chap9_mj.html" >9</a> <a href="chap10_mj.html" >10</a> <a href="chapBib_mj.html" >Bib</a> <a href="chapInd_mj.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0.html" >[MathJax off]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >TwistedConjugacy</h1 >div >br />Email: <span class="URL" ><a href="mailto:sam.tertooy@kuleuven.be" >sam.tertooy@kuleuven.be</a></span >br />Homepage: <span class="URL" ><a href="https://stertooy.github.io/ " >https://stertooy.github.io/</a></span >br />Address : <br />Wiskunde<br /> KU Leuven, Kulak Kortrijk Campus<br /> Etienne Sabbelaan 53<br /> 8500 Kortrijk<br /> Belgium<br /> <br />"X7AA6C5737B711C89" name="X7AA6C5737B711C89" ></a></p>strong class="pkg" >TwistedConjugacy</strong > package provides methods for solving the twisted conjugacy problem (including the "search" and "multiple" variants) and for computing Reidemeister classes, numbers, spectra, and zeta functions. It also includes utility functions for working with (double) cosets, group homomorphisms, and group derivations.</p>infinite) provided by the <strong class="pkg" >Polycyclic</strong > package.</p>"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>strong class="pkg" >TwistedConjugacy</strong > package is free software, it may be redistributed and/or modified under the terms and conditions of the <span class="URL" ><a href=" https://www.gnu.org/licenses/old-licenses/gpl-2.0.en.html " >GNU Public License Version 2</a></span > or (at your option ) any later version.</p>"X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></p>strong class="pkg" >GAPDoc</strong > and <strong class="pkg" >AutoDoc</strong > packages.</p>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1_mj.html#X78FCE1F07D997CB7" >1 <span class="Heading" >The TwistedConjugacy package</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X8360C04082558A12" >1.1 <span class="Heading" >Installation</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X861ED1338181C66D" >1.2 <span class="Heading" >Loading</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X7A178B0587668C3E" >1.3 <span class="Heading" >Citing</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X7B689C0284AC4296" >1.4 <span class="Heading" >Support</span ></a>span >div >div >div class="ContChap" ><a href="chap2_mj.html#X7EF1B6708069B0C7" >2 <span class="Heading" >Mathematical background</span ></a>div >div class="ContChap" ><a href="chap3_mj.html#X78DFA75A82655B7F" >3 <span class="Heading" >Twisted conjugacy</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X86BE54A080E991A8" >3.1 <span class="Heading" >The twisted conjugation action</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X79CF6BDA7851496D" >3.1-1 TwistedConjugation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7838A5A678158C68" >3.2 <span class="Heading" >The twisted conjugacy (search) problem</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X809D34107CFE8082" >3.2-1 IsTwistedConjugate</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8493E3818276A562" >3.2-2 RepresentativeTwistedConjugation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X8554A80A7A7430C4" >3.3 <span class="Heading" >The multiple twisted conjugacy (search) problem</span ></a>span >div >div >div class="ContChap" ><a href="chap4_mj.html#X78F9595B78DAC70D" >4 <span class="Heading" >Twisted conjugacy classes</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7CACD3337A7C90F0" >4.1 <span class="Heading" >Creating a twisted conjugacy class</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X79690F4D7F2660B3" >4.1-1 TwistedConjugacyClass</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7FA74F8E7BB7915D" >4.2 <span class="Heading" >Operations on twisted conjugacy classes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X865507568182424E" >4.2-1 <span class="Heading" >Representative</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7B9DB15D80CE28B4" >4.2-2 <span class="Heading" >ActingDomain</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X86153CB087394DC1" >4.2-3 <span class="Heading" >FunctionAction</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X87BDB89B7AAFE8AD" >4.2-4 <span class="Heading" >\in</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X858ADA3B7A684421" >4.2-5 <span class="Heading" >Size</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X867840C67C990840" >4.2-6 <span class="Heading" >StabiliserOfExternalSet</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7EBA57FC7CCF8449" >4.2-7 <span class="Heading" >List</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X79730D657AB219DB" >4.2-8 <span class="Heading" >Random</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X806A4814806A4814" >4.2-9 <span class="Heading" >\=</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X8238998382FE372A" >4.3 <span class="Heading" >Calculating all twisted conjugacy classes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X797192EA7D30C78F" >4.3-1 TwistedConjugacyClasses</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X862C49C0834E01D7" >4.3-2 RepresentativesTwistedConjugacyClasses</a></span >div ></div >div >div class="ContChap" ><a href="chap5_mj.html#X7B27E1F98083C837" >5 <span class="Heading" >Reidemeister numbers and spectra</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7FE8086286A91524" >5.1 <span class="Heading" >Reidemeister numbers</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8330E244852075A7" >5.1-1 ReidemeisterNumber</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7CED57E379712C3A" >5.2 <span class="Heading" >Reidemeister spectra</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8777B3F77DBF01AF" >5.2-1 ReidemeisterSpectrum</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8122B246860C1617" >5.2-2 ExtendedReidemeisterSpectrum</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X78839C0886EBDB71" >5.2-3 CoincidenceReidemeisterSpectrum</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DB417F182B155C5" >5.2-4 TotalReidemeisterSpectrum</a></span >div ></div >div >div class="ContChap" ><a href="chap6_mj.html#X862C248A828A2C4A" >6 <span class="Heading" >Reidemeister zeta functions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X862C248A828A2C4A" >6.1 <span class="Heading" >Reidemeister zeta functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X78F0CE5987B70AA2" >6.1-1 ReidemeisterZetaCoefficients</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X79A2CD257BA1E037" >6.1-2 IsRationalReidemeisterZeta</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7959DBAF78CC4401" >6.1-3 ReidemeisterZeta</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X829058F97A8858F1" >6.1-4 PrintReidemeisterZeta</a></span >div ></div >div >div class="ContChap" ><a href="chap7_mj.html#X86AB2EC37E2F6C19" >7 <span class="Heading" >Cosets of PcpGroups</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X7A16782E7B3F98F6" >7.1 <span class="Heading" >Right cosets</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X827675EB8157DF2D" >7.1-1 Intersection</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X78B98B257E981046" >7.2 <span class="Heading" >Double cosets</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X87BDB89B7AAFE8AD" >7.2-1 <span class="Heading" >\in</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X858ADA3B7A684421" >7.2-2 <span class="Heading" >Size</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7EBA57FC7CCF8449" >7.2-3 <span class="Heading" >List</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X806A4814806A4814" >7.2-4 <span class="Heading" >\=</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A5EFABB86E6D4D5" >7.2-5 <span class="Heading" >DoubleCosets</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A25B1C886CF8C6A" >7.2-6 <span class="Heading" >DoubleCosetRepsAndSizes</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X805F0F1E803BE255" >7.2-7 <span class="Heading" >DoubleCosetIndex</span ></a>span >div ></div >div >div class="ContChap" ><a href="chap8_mj.html#X83702FC27B3C3098" >8 <span class="Heading" >Group homomorphisms</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X80DDEC8C82E2A4F1" >8.1 <span class="Heading" >Representatives of homomorphisms between groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X78ADEE0C83819159" >8.1-1 RepresentativesAutomorphismClasses</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7A7935B286050886" >8.1-2 RepresentativesEndomorphismClasses</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X81E5CF92816BF199" >8.1-3 RepresentativesHomomorphismClasses</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X8164A34A86155DFB" >8.2 <span class="Heading" >Coincidence and fixed point groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X799546928394FF8B" >8.2-1 FixedPointGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X780DF6247E3E9190" >8.2-2 CoincidenceGroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X8084A06782AE362E" >8.3 <span class="Heading" >Induced and restricted group homomorphisms</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7F6D0625837B7B94" >8.3-1 InducedHomomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7DBA352982923900" >8.3-2 RestrictedHomomorphism</a></span >div ></div >div >div class="ContChap" ><a href="chap9_mj.html#X7B8C20A9826087E1" >9 <span class="Heading" >Group derivations</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7AAB25B587D3DF70" >9.1 <span class="Heading" >Creating group derivations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8303ADE37FFAA109" >9.1-1 GroupDerivationByImages</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7C9D096A7B996E89" >9.1-2 GroupDerivationByFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8341EA2B7FBAE696" >9.1-3 GroupDerivationByAffineAction</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7AE626D685C68CF0" >9.2 <span class="Heading" >Operations for group derivations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F065FD7822C0A12" >9.2-1 <span class="Heading" >IsInjective</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X784ECE847E005B8F" >9.2-2 <span class="Heading" >IsSurjective</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X878F56AB7B342767" >9.2-3 <span class="Heading" >IsBijective</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7DCD99628504B810" >9.2-4 <span class="Heading" >Kernel</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X87F4D35A826599C6" >9.2-5 <span class="Heading" >Image</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7AE24A1586B7DE79" >9.2-6 <span class="Heading" >PreImagesRepresentative</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X85C8590E832002EF" >9.2-7 <span class="Heading" >PreImages</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X801FDEFE8155D0B1" >9.3 <span class="Heading" >Images of group derivations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X87BDB89B7AAFE8AD" >9.3-1 <span class="Heading" >\in</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X858ADA3B7A684421" >9.3-2 <span class="Heading" >Size</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7EBA57FC7CCF8449" >9.3-3 <span class="Heading" >List</span ></a>span >div ></div >div >div class="ContChap" ><a href="chap10_mj.html#X87A5683C7B645EA1" >10 <span class="Heading" >Affine actions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X7E00F3E17A88ED4B" >10.1 <span class="Heading" >Creating an affine action</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8116545B7DBE00AC" >10.1-1 AffineActionByGroupDerivation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X86DD85AA827068A2" >10.2 <span class="Heading" >Operations for affine actions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X84AFABF98784C123" >10.2-1 <span class="Heading" >OrbitAffineAction</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7E8F571A83D951B0" >10.2-2 <span class="Heading" >OrbitsAffineAction</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8020B50487227359" >10.2-3 <span class="Heading" >NrOrbitsAffineAction</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X860FBE2378E0696D" >10.2-4 <span class="Heading" >StabiliserAffineAction</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7B111FAB7D2A8C99" >10.2-5 <span class="Heading" >RepresentativeAffineAction</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X81B54C657AE4B06F" >10.3 <span class="Heading" >Operations on orbits of affine actions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X865507568182424E" >10.3-1 <span class="Heading" >Representative</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7B9DB15D80CE28B4" >10.3-2 <span class="Heading" >ActingDomain</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X86153CB087394DC1" >10.3-3 <span class="Heading" >FunctionAction</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X87BDB89B7AAFE8AD" >10.3-4 <span class="Heading" >\in</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X858ADA3B7A684421" >10.3-5 <span class="Heading" >Size</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X867840C67C990840" >10.3-6 <span class="Heading" >StabiliserOfExternalSet</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7EBA57FC7CCF8449" >10.3-7 <span class="Heading" >List</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X79730D657AB219DB" >10.3-8 <span class="Heading" >Random</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X806A4814806A4814" >10.3-9 <span class="Heading" >\=</span ></a>span >div ></div >div >div class="ContChap" ><a href="chapBib_mj.html" ><span class="Heading" >References</span ></a></div >div class="ContChap" ><a href="chapInd_mj.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a 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