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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="chap11_mj.html" >11 </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 >Functionally recursive groups</h1 >2 .4 .13 </p>11 /01 /2024 </p>div >br />Email: <span class="URL" ><a href="mailto:laurent dot bartholdi at gmail dot com " >laurent dot bartholdi at gmail dot com </a></span >br />Homepage: <span class="URL" ><a href="https://www.math.uni-sb.de/ag/bartholdi/ " >https://www.math.uni-sb.de/ag/bartholdi/</a></span >Address :</b><br />br /> Bunsenstraße 3 -5 <br /> D-37073 Göttingen<br /> Germany</p>"X7AA6C5737B711C89" name="X7AA6C5737B711C89" ></a></p>strong class="pkg" >FR</strong >, which implements in <strong class="pkg" >GAP</strong > the basic objects of Mealy machines and functional recursions; and handles groups that they generate.</p>strong class="pkg" >GAP</strong > is available at <span class="URL" ><a href="https://www.gap-system.org " >https://www.gap-system.org</a></span >.</p>strong class="pkg" >FR</strong > is available at <span class="URL" ><a href="https://docs.gap-system.org/pkg/fr/doc/manual.pdf " >https://docs.gap-system.org/pkg/fr/doc/manual.pdf</a></span > in PDF format, and may be accessed online at <span class="URL" ><a href="https://gap-packages.github.io/fr/" >https://gap-packages.github.io/fr/</a></span >.</p>span class="URL" ><a href="https://github.com/gap-packages/fr/archive/2.4.13.tar.gz " >https://github.com/gap-packages/fr/archive/2 .4 .13 .tar.gz</a></span > (tar, gzipped). The latest repository version (possibly unstable) may be downloaded as <span class="URL" ><a href="https://github.com/gap-packages/fr/tarball/master" >https://github.com/gap-packages/fr/tarball/master</a></span > (tar, gzipped), <span class="URL" ><a href="https://github.com/gap-packages/fr.git" >https://github.com/gap-packages/fr.git</a></span > (git repository), or explored at <span class="URL" ><a href="https://github.com/gap-packages/fr/tree/master/" >https://github.com/gap-packages/fr/tree/master/</a></span >.</p>strong class="pkg" >GAP</strong their elements.</p>strong class="pkg" >FR</strong > please contact the author; this package is still under development.</p>"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>2006 -2012 by Laurent Bartholdi</p>"X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></p>"Swiss National Fund for Scientific Research" and the "German Science Foundation" .</p>"X7982162280BC7A61" name="X7982162280BC7A61" ></a></p>1990 s, when, as a PhD student I did many calculations with groups generated by automata, and realized the similarities between all calculations; it quickly became clear that these calculations could be done much better by a computer than by a human.</p>s to get insight from fast calculations within <strong class="pkg" >GAP</strong >. The results then had to be proved correct within the infinite group under consideration, and this often involved guessing appropriate words in the infinite group with a given image in the finite quotient.</p>2000 , I had developed quite a few routines, which I assembled in a <strong class="pkg" >GAP</strong > package, that dealt directly with infinite groups. This package was primitive at its core, but was extended with various routines as they became useful.</p>2005 to start a new package from scratch, that would encorporate as much functionality as possible in a uniform manner; that would handle semigroups as well as groups; that could be easily extended; and with a complete, understandable documentation. I hope I am not too far from these objectives.</p>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1_mj.html#X86DB23CC834ABD71" >1 <span class="Heading" >Licensing</span ></a>div >div class="ContChap" ><a href="chap2_mj.html#X7ADCE68284FB4ACF" >2 <span class="Heading" >FR package</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X80C332C686212786" >2 .1 <span class="Heading" >A brief mathematical introduction</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X78DF4DE18260BD80" >2 .2 <span class="Heading" >An example session</span ></a>span >div >div >div class="ContChap" ><a href="chap3_mj.html#X7D65CA8B876E514C" >3 <span class="Heading" >Functionally recursive machines</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7D52F7ED83E2D153" >3 .1 <span class="Heading" >Types of machines</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7EB36FBB78F4F26A" >3 .2 <span class="Heading" >Products of machines</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X828640667D2E5280" >3 .3 <span class="Heading" >Creators for <code class="code" >FRMachine</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80D310EF7FD5EA44" >3 .3 -1 FRMachineNC</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X808F3BD97EDA8CE8" >3 .3 -2 FRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C383F4383D22BFC" >3 .3 -3 UnderlyingFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7BF186227C0ABE8D" >3 .3 -4 AsGroupFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X78130FC97C58AFC4" >3 .3 -5 AsGroupFRMachine</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X8753FA157B2AD6DC" >3 .4 <span class="Heading" >Attributes for <code class="code" >FRMachine</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8000470D7DA7FFBD" >3 .4 -1 StateSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F77F5DD789FA2F4" >3 .4 -2 GeneratorsOfFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DBC41D4808979BC" >3 .4 -3 Output </a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7AEE87BC8393FA54" >3 .4 -4 Transition</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X82B3A8AB80B5E181" >3 .4 -5 Transitions</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D95D1498586E5D0" >3 .4 -6 WreathRecursion</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X8158A8307CA98A3D" >3 .5 <span class="Heading" >Operations for <code class="code" >FRMachine</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8289C2F77D67EDC3" >3 .5 -1 StructuralGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F2703417F270341" ><code >3 .5 -2 \+</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7857704878577048" ><code >3 .5 -3 \*</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C0677148107F7FE" >3 .5 -4 TensorSumOp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8077C8A47E22FCB5" >3 .5 -5 TensorProductOp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D248C737D29A7CC" >3 .5 -6 DirectSumOp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81456F10820CAC87" >3 .5 -7 DirectProductOp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7A0858097AA3FBDA" >3 .5 -8 TreeWreathProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X811B5BF17A3FE577" >3 .5 -9 SubFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X814F53B97C3F43F5" >3 .5 -10 ChangeFRMachineBasis</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81B382BD81B2BD34" >3 .5 -11 Minimized</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C107A42815F91DA" >3 .5 -12 Correspondence</a></span >div ></div >div >div class="ContChap" ><a href="chap4_mj.html#X863D82207A1320F1" >4 <span class="Heading" >Functionally recursive elements</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X79DE08CD7EE57360" >4 .1 <span class="Heading" >Creators for <code class="code" >FRElement</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7839813183881054" >4 .1 -1 FRElementNC</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7CF5EDEB874BF9E3" >4 .1 -2 FRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X86181654827919EE" >4 .1 -3 FRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X80D518E2804ABF70" >4 .1 -4 ComposeElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7CE388057DAB4802" >4 .1 -5 VertexElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X848EB430831097E6" >4 .1 -6 DiagonalElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7EB5DE3978840CDF" >4 .1 -7 AsGroupFRElement</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X812C932C7E2F2885" >4 .2 <span class="Heading" >Operations and Attributes for <code class="code" >FRElement</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X78F819CF7DDBF310" >4 .2 -1 Output </a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X8732D01C82999F32" >4 .2 -2 Activity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7CE58B2D837B2845" >4 .2 -3 Transition</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7D4248467B1B097A" >4 .2 -4 Transitions</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X84A193C67CDBDA35" >4 .2 -5 Portrait</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X850EB66E7804BA3B" >4 .2 -6 DecompositionOfFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X85441F1683E9D820" >4 .2 -7 StateSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X819E3E3080297347" >4 .2 -8 State</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7B0C97BC7C3BA20D" >4 .2 -9 States</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X804B2E0F7E37F5B8" >4 .2 -10 FixedStates</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X8303B36C83371FB3" >4 .2 -11 LimitStates</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7C4076707CBBE945" >4 .2 -12 IsFiniteStateFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X829A87E087F15194" >4 .2 -13 NucleusOfFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X79E65E818690B4EB" >4 .2 -14 InitialState</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X823B6E3D819432D6" ><code >4 .2 -15 \^</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7C3CF6AF86336EDC" ><code >4 .2 -16 \*</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X78C19ACA78F9F067" ><code >4 .2 -17 <span >\</span >[<span >\</span >]</code ></a></span >div ></div >div >div class="ContChap" ><a href="chap5_mj.html#X7C77EBC17DEF4CF6" >5 <span class="Heading" >Mealy machines and elements</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X846B89F686B50AE1" >5 .1 <span class="Heading" >Creators for <code class="code" >MealyMachine</code code class="code" >MealyElement</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7EF3E00080624B70" >5 .1 -1 MealyMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X875B8FED7FD20FA1" >5 .1 -2 MealyMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8578657C7F4B6254" >5 .1 -3 MealyMachineNC</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X83BBE01884D6E315" >5 .1 -4 AllMealyMachines</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7F673D877B205708" >5 .2 <span class="Heading" >Operations and Attributes for <code class="code" >MealyMachine</code >s and <code class="code" >MealyElement</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DF9F3AD86602DFC" >5 .2 -1 Draw</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8395542D846FA2B9" >5 .2 -2 Minimized</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X809F069B798ED985" >5 .2 -3 DualMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7D5D480C782FCC0B" >5 .2 -4 IsReversible</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8310A1C08158793C" >5 .2 -5 IsMinimized</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7CCB79B981912CCC" >5 .2 -6 AlphabetInvolution</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X80D2545D7D0990A2" >5 .2 -7 IsBireversible</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X83364DAB825D7A0D" >5 .2 -8 StateGrowth</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X84BE780A81CAC69C" >5 .2 -9 Degree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X793C427084F830CE" >5 .2 -10 IsFinitaryFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E5E8B2C79688DC0" >5 .2 -11 Depth</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X82F4410E85C54C7E" >5 .2 -12 IsBoundedFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X81D4A3F27C5FAD96" >5 .2 -13 IsPolynomialGrowthFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7ECE17387910C023" >5 .2 -14 Signatures</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X83DFDC3384EA4634" >5 .2 -15 VertexTransformationsFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E0CB3767CE08692" >5 .2 -16 FixedRay</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7A519D4C86CC4786" >5 .2 -17 IsLevelTransitiveFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X79EFE2C97D2CCEEC" >5 .2 -18 AsMealyMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X80F9A18483F98442" >5 .2 -19 AsMealyMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7FB3F0A2878DD2CF" >5 .2 -20 AsMealyElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7FBBBD9A839011C8" >5 .2 -21 AsIntMealyMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8191456B7E586785" >5 .2 -22 TopElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7A87ED9D789245E4" >5 .2 -23 ConfinalityClasses</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X81592E3D79745A40" >5 .2 -24 Germs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F76AF2D7C0279F9" >5 .2 -25 HasOpenSetConditionFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X795017598575FCA3" >5 .2 -26 LimitFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F8163B5816969C8" >5 .2 -27 NucleusMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7B29565784A591EC" >5 .2 -28 GuessMealyElement</a></span >div ></div >div >div class="ContChap" ><a href="chap6_mj.html#X84AD415C872BFB91" >6 <span class="Heading" >Linear machines and elements</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X812C0F7B7A31FCEF" >6 .1 <span class="Heading" >Methods and operations for <code class="code" >LinearFRMachine</code >s and <code class="code" >LinearFRElement</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7F1EB8CB87229764" >6 .1 -1 VectorMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X825CA46481197C7A" >6 .1 -2 AssociativeObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7F65118683209DC5" >6 .1 -3 AlgebraMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A19036B828BBA0C" >6 .1 -4 Transition</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X846683198081BA82" >6 .1 -5 Transitions</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X80F694298399E78D" >6 .1 -6 NestedMatrixState</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7FCEE3BF86B02CC6" >6 .1 -7 ActivitySparse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8436BEA67F1C3C27" >6 .1 -8 Activities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7EF5B7417AE6B3F8" >6 .1 -9 IsConvergent</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8136C21885019A4A" >6 .1 -10 TransposedFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X796B736286CACF85" >6 .1 -11 LDUDecompositionFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X783E8F427A23EAD1" >6 .1 -12 GuessVectorElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X865EE2E887ECC079" >6 .1 -13 AsLinearMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X82586DFB8458EF05" >6 .1 -14 AsVectorMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7818245A7DABB311" >6 .1 -15 AsAlgebraMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7BDD40B27F7541B2" >6 .1 -16 AsVectorMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8120605981DDE434" >6 .1 -17 AsAlgebraMachine</a></span >div ></div >div >div class="ContChap" ><a href="chap7_mj.html#X86C0E6F083DCCDC8" >7 <span class="Heading" >Self-similar groups, monoids and semigroups</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X80A26BAA7B53C1BD" >7 .1 <span class="Heading" >Creators for FR semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7AE8F92383272329" >7 .1 -1 FRGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D4A6996874A3DF3" >7 .1 -2 NewSemigroupFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X853E3F0680C76F56" >7 .1 -3 SCGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F15D57A7959FEF6" >7 .1 -4 Correspondence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D0B8334786E2802" >7 .1 -5 FullSCGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7DB92C34827D513F" >7 .1 -6 FRMachineFRGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7BF4AC9F830A8E1A" >7 .1 -7 IsomorphismFRGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7DE1CAE981F2825B" >7 .1 -8 IsomorphismMealyGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7BB8DDEA83946C73" >7 .1 -9 FRGroupByVirtualEndomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X79D75A7D80DD9AD1" >7 .1 -10 TreeWreathProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X85840A047C04BFC6" >7 .1 -11 WeaklyBranchedEmbedding</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X84E20571841DE1E4" >7 .2 <span class="Heading" >Operations for FR semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7C6D7BA0818A3A3D" >7 .2 -1 PermGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8620BEAF7957FA4D" >7 .2 -2 PcGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X83834FF77F972912" >7 .2 -3 TransformationMonoid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8768C22D859BE75F" >7 .2 -4 TransformationSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7BDC634086437315" >7 .2 -5 EpimorphismGermGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X812242E584462766" >7 .2 -6 GermData</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X87378D53791D0B70" >7 .2 -7 StabilizerImage</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7B4CD9CA872BA368" >7 .2 -8 LevelStabilizer</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7C5002E683A044C1" >7 .2 -9 IsStateClosed</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X79246DB482BEAF2D" >7 .2 -10 StateClosure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7E2F34417EBB7673" >7 .2 -11 IsRecurrentFRSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X825688FD7CE96479" >7 .2 -12 IsLevelTransitiveFRGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D95219481AEDD20" >7 .2 -13 IsInfinitelyTransitive</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A6CB30181662C77" >7 .2 -14 IsFinitaryFRSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X791BCD9D782C6237" >7 .2 -15 Degree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7FA67E4387C91BD8" >7 .2 -16 HasOpenSetConditionFRSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D870F9E82ACB54C" >7 .2 -17 HasCongruenceProperty</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7EAB4B5B843C0EC5" >7 .2 -18 IsContracting</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7CA062A67C1554BB" >7 .2 -19 NucleusOfFRSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8443D711796F06E4" >7 .2 -20 NucleusMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X824A9E177F5A9753" >7 .2 -21 AdjacencyBasesWithOne</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A874A107D4944E1" >7 .2 -22 BranchingSubgroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X78ADACCD8586D3C7" >7 .2 -23 FindBranchingSubgroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X832D98E47ACA099C" >7 .2 -24 IsBranched</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A905CE87B49213F" >7 .2 -25 IsBranchingSubgroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8404ECA782F2521A" >7 .2 -26 BranchStructure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8749E0797A99F531" >7 .2 -27 TopVertexTransformations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7C56C90086070A2E" >7 .2 -28 VertexTransformations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7DF2D9838625CDED" >7 .2 -29 VirtualEndomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7C81CB1C7F0D7A90" >7 .2 -30 EpimorphismFromFpGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8740656382656D63" >7 .2 -31 IsomorphismSubgroupFpGroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X7E8485A081EBB3AA" >7 .3 <span class="Heading" >Properties for infinite groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X840ED7D279ECAB7F" >7 .3 -1 IsTorsionGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7914F2D68077F503" >7 .3 -2 IsTorsionFreeGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X87E93FFC820ED40E" >7 .3 -3 IsAmenableGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X873C0A7C8422C0C9" >7 .3 -4 IsVirtuallySimpleGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X79A3A0CF82B6F089" >7 .3 -5 IsResiduallyFinite</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X86E1182E7EEFAADB" >7 .3 -6 IsSQUniversal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7FDAEAFF78A5E7D2" >7 .3 -7 IsJustInfinite</a></span >div ></div >div >div class="ContChap" ><a href="chap8_mj.html#X7DDBF6F47A2E021C" >8 <span class="Heading" >Algebras</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X842EE9427C63F92E" >8 .1 <span class="Heading" >Creators for FR algebras</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X812FEA6778152E49" >8 .1 -1 FRAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X844B890F7BF56236" >8 .1 -2 SCAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7B8330F180BABC43" >8 .1 -3 NucleusOfFRAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X81D8D0E886C8E143" >8 .1 -4 BranchingIdeal</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X7EFB4F2E7E908B9F" >8 .2 <span class="Heading" >Operations for FR algebras</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X8115B018871FD364" >8 .2 -1 MatrixQuotient</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X8150FC4E84D208C6" >8 .2 -2 ThinnedAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X8572DCAE7F888DDA" >8 .2 -3 Nillity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X85163F29824C944D" >8 .2 -4 DegreeOfHomogeneousElement</a></span >div ></div >div >div class="ContChap" ><a href="chap9_mj.html#X7A489A5D79DA9E5C" >9 <span class="Heading" >Examples</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7AF5DEF08531AFA5" >9 .1 <span class="Heading" >Examples of groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7D774B847D81E6DE" >9 .1 -1 FullBinaryGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X813F53C57F41F5F5" >9 .1 -2 BinaryKneadingGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7B8D49D079D336E8" >9 .1 -3 BasilicaGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8449487686E00D22" >9 .1 -4 FornaessSibonyGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X85F4FDF787173863" >9 .1 -5 AddingGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7A4BB24A805CDF63" >9 .1 -6 BinaryAddingGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X78AFA63B86C94227" >9 .1 -7 MixerGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X84C97E0687F119C0" >9 .1 -8 SunicGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X79E3F3BE80F34590" >9 .1 -9 GrigorchukMachines</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X85BAE48780E665A4" >9 .1 -10 GrigorchukMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X800640597E9C707D" >9 .1 -11 GrigorchukOverGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7E765AF77AAC21A6" >9 .1 -12 GrigorchukTwistedTwin</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F93EC437B5AE276" >9 .1 -13 BrunnerSidkiVieiraGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F8A028B799946D3" >9 .1 -14 AleshinGroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7C286D3A84790ECE" >9 .1 -15 AleshinGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7E024B4D7BA411B1" >9 .1 -16 BabyAleshinGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8108E3A8872A6FFE" >9 .1 -17 SidkiFreeGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X82D3CB6A7C189C78" >9 .1 -18 GuptaSidkiGroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X83E59288860EF661" >9 .1 -19 GuptaSidkiGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8521B4FF7BA189B2" >9 .1 -20 NeumannGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X878D1C7080EA9797" >9 .1 -21 FabrykowskiGuptaGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7C5ADAE77EA3876D" >9 .1 -22 ZugadiSpinalGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7A0319827CB51ED0" >9 .1 -23 GammaPQMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X80B617717C2887D4" >9 .1 -24 RattaggiGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7A0BE9F57B401C5C" >9 .1 -25 HanoiGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7C7A0EEF7EFF8B99" >9 .1 -26 DahmaniGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7C958AB78484E256" >9 .1 -27 MamaghaniGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86D952E8784E4D97" >9 .1 -28 WeierstrassGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X80D59AFF7E7D3B8B" >9 .1 -29 StrichartzGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86B124758135DFBD" >9 .1 -30 FRAffineGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7CFBE31A78F2681B" >9 .1 -31 CayleyGroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X81B82FA1811AAF8D" >9 .2 <span class="Heading" >Examples of semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X87541DA582705033" >9 .2 -1 I2Machine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7B32ED3D8715FA4B" >9 .2 -2 I4Machine</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X803B02408573A30E" >9 .3 <span class="Heading" >Examples of algebras</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X80E15ABC879F8EE2" >9 .3 -1 PSZAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7D015CA5829FAA2A" >9 .3 -2 GrigorchukThinnedAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7B66ED537D0A43AF" >9 .3 -3 GuptaSidkiThinnedAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86CE9A8787F69DBC" >9 .3 -4 GrigorchukLieAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7B0B5B09878C7CEA" >9 .3 -5 SidkiFreeAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7988B29F836BAA62" >9 .3 -6 SidkiMonomialAlgebra</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7989134C83AF38AE" >9 .4 <span class="Heading" >Bacher's determinant identities</span></a> span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7C4A51947E1609A8" >9 .5 <span class="Heading" >VH groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7E0071D4838B239D" >9 .5 -1 VHStructure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F852A357D7E2E76" >9 .5 -2 VerticalAction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86B1C2F079FE8D82" >9 .5 -3 VHGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7D1FCB877D1B96EA" >9 .5 -4 IsIrreducibleVHGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X84DB7FA4846075A7" >9 .5 -5 MaximalSimpleSubgroup</a></span >div ></div >div >div class="ContChap" ><a href="chap10_mj.html#X86D6616E868AF75C" >10 <span class="Heading" >FR implementation details </span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X79719CD17A948933" >10 .1 <span class="Heading" >The family of FR objects</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7F5497A47F8C81DD" >10 .1 -1 FRMFamily</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7C6A63427F6DB4C6" >10 .1 -2 FREFamily</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7BC9CD3685C26823" >10 .1 -3 AlphabetOfFRObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X793E0E1283BE7C73" >10 .1 -4 AsPermutation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7B41902D87A48EDB" >10 .1 -5 AsTransformation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X856A3AD87C93FC1F" >10 .2 <span class="Heading" >Filters for <code class="code" >FRObject</code >s</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7CC0BFD67CE7060E" >10 .2 -1 IsGroupFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8157AE587CBA24C4" >10 .2 -2 IsFRMachineStrRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X79C2395A7D65214B" >10 .2 -3 IsMealyMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7C86614187606A4C" >10 .2 -4 IsMealyElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X78E206B28015A395" >10 .2 -5 IsMealyMachineIntRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7AE5B4257E2DB7E6" >10 .2 -6 IsMealyMachineDomainRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8087EE9F79E8E339" >10 .2 -7 IsVectorFRMachineRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7859869E7FEDA49F" >10 .2 -8 IsAlgebraFRMachineRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X877B1EBD80170001" >10 .2 -9 IsLinearFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X823F46A67D458AAD" >10 .2 -10 IsLinearFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7966F9B982B1DFE1" >10 .2 -11 IsFRElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X847A4BBE82C736B6" >10 .2 -12 IsFRMealyElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X785D09F27DBDF6A8" >10 .2 -13 IsFRObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7C22A1A28058F754" >10 .2 -14 IsFRMachine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X83AEFB8184F4B023" >10 .2 -15 IsInvertible</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X81D717E187305F2A" >10 .2 -16 IsFRGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X853B16B381CB5366" >10 .2 -17 IsFRAlgebra</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X7E97015E8153F782" >10 .3 <span class="Heading" >Some of the algorithms implemented</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X84278D6F7AAD101F" >10 .3 -1 FRMachineRWS</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X84B4FF607DA18152" >10 .3 -2 <span class="Heading" >Order of FR elements</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X847B4AFF809D2A56" >10 .3 -3 <span class="Heading" >Membership in semigroups</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7F24533B7F846FC4" >10 .3 -4 <span class="Heading" >The conjugacy problem</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8735D8087DADCCC9" >10 .3 -5 OrbitSignalizer</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X817F734280E22447" >10 .3 -6 FRConjugacyAlgorithm</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X82A289077D4DAA03" >10 .3 -7 FRBranchGroupConjugacyData</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7A0AC96784ACE0BE" >10 .3 -8 <span class="Heading" >Order of groups</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8329884F790E1542" >10 .3 -9 <span class="Heading" >Images and preimages of some groups inspan ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7F4247367D1EBEB9" >10 .3 -10 <span class="Heading" >Comparison of FR, Mealy, vector,span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X81F95FEB7C72ABFF" >10 .3 -11 <span class="Heading" >Inverses of linear elements</span ></a>span >div ></div >div >div class="ContChap" ><a href="chap11_mj.html#X785C6C0B80936CC8" >11 <span class="Heading" >Miscellanea</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X783AA02C7BEF48A9" >11 .1 <span class="Heading" >Generic operations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X844D3035877B5052" >11 .1 -1 TensorSum</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X87EB0B4A852CF4C6" >11 .1 -2 TensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X82AD6F187B550060" >11 .1 -3 DirectSum</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X816865747DD51C11" >11 .2 <span class="Heading" >Periodic lists</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7E5CC87E871F35A3" >11 .2 -1 PeriodicListsFamily</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7B401DFE817D3927" >11 .2 -2 PeriodicList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7AFE88F37FC58083" >11 .2 -3 CompressPeriodicList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7CA5FA3F7AF9BA3D" >11 .2 -4 IsConfinal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X86AB4AFF7B1613E3" >11 .2 -5 ConfinalityClass</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X84FB28807BC8A502" >11 .2 -6 LargestCommonPrefix</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X7A336C66855E632D" >11 .3 <span class="Heading" >Word growth</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7BFF1432803C9172" >11 .3 -1 WordGrowth</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X791D4D398201C17D" >11 .4 <span class="Heading" >Finding short relations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X868E478F86A10CFF" >11 .4 -1 ShortGroupRelations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7B9942AA84B0753E" >11 .4 -2 ShortGroupWordInSet</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X82712E6C815DB9B2" >11 .5 <span class="Heading" >Braid groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X84472A637B648C47" >11 .5 -1 SurfaceBraidFpGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X87E12292861FFE79" >11 .5 -2 CharneyBraidFpGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X814375977D2E4AD9" >11 .5 -3 ArtinRepresentation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X839ED1F982DB3469" >11 .6 <span class="Heading" >Dirichlet series</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X82D4E885838CFBD6" >11 .6 -1 DirichletSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7C8CD28D797A527F" >11 .6 -2 DegreeDirichletSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X81EA791C7CA3C3FF" >11 .6 -3 SpreadDirichletSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7D792C6985BF482B" >11 .6 -4 ShiftDirichletSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X80571E4A86B38D53" >11 .6 -5 ShrunkDirichletSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X850F072E8523EE9D" >11 .6 -6 ZetaSeriesOfGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7F49DDBC829F18C8" >11 .6 -7 ValueOfDirichletSeries</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X86256BD187D9A7FF" >11 .7 <span class="Heading" >Projective representations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7CE116C27EF109D1" >11 .7 -1 IsProjectiveRepresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X80EEB0F58467ED68" >11 .7 -2 ProjectiveRepresentationByFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7FC5A28278EB1E51" >11 .7 -3 LinearRepresentationByImages</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X87BC132B815B4638" >11 .7 -4 DegreeOfProjectiveRepresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X81AF3D937F219A6D" >11 .7 -5 ProjectiveExtension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7C4E2ED57C2DDBE6" >11 .7 -6 ProjectiveQuotient</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X785C6C0B80936CC8" >11 .8 <span class="Heading" >Miscellanea</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7B5DD261825523A3" >11 .8 -1 ForwardOrbit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7E4966327C37C790" >11 .8 -2 StringByInt</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7CE65002842C0BD8" >11 .8 -3 PositionInTower</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X856E72B180084639" >11 .8 -4 RenameSubobjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X79016B3878B5EFAA" >11 .8 -5 CoefficientsInAbelianExtension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8624AFAD872509D8" >11 .8 -6 MagmaEndomorphismByImagesNC</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7F7E6457877F69EC" >11 .8 -7 MagmaHomomorphismByImagesNC</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7A2A9D24781AFC34" >11 .8 -8 Draw</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X816A18137E5116E9" >11 .8 -9 IsFIFO</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X86AC1C028093204D" >11 .8 -10 ProductIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X794940277C9AD85C" >11 .8 -11 DimensionSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X825149467C57DEFC" >11 .8 -12 AlgebraHomomorphismByFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X837F6C2A797FFD41" >11 .8 -13 IsFpLieAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8692ADD581359CA1" >11 .8 -14 JenningsLieAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7F5427847E43CD62" >11 .8 -15 SolutionMatModN</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X80E9634283E2DF18" >11 .8 -16 SolutionMatMod1</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7D2CEF7F845D2AF2" >11 .8 -17 CyclotomicByArgument</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7A6CB5FE86501506" >11 .8 -18 ArgumentOfCyclotomic</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X7ADFF37084706CEC" >11 .9 <span class="Heading" >User settings</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7E95AC267805E4C1" >11 .9 -1 InfoFR</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X835FBD72853595BE" >11 .9 -2 SEARCH@</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 href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</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="chap11_mj.html" >11 </a> <a href="chapBib_mj.html" >Bib</a> <a href="chapInd_mj.html" >Ind</a> </div 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