#SIXFORMAT GapDocGAP HELPBOOKINFOSIXTMP := rec( encoding := "UTF-8", bookname := "fr", entries := [ [ "Title page", ".", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" ], [ "Abstract", ".-1", [ 0, 0, 1 ], 35, 2, "abstract", "X7AA6C5737B711C89" ], [ "Copyright", ".-2", [ 0, 0, 2 ], 49, 2, "copyright", "X81488B807F2A1CF1" ] , [ "Acknowledgements", ".-3", [ 0, 0, 3 ], 54, 2, "acknowledgements", "X82A988D47DFAFCFA" ], [ "Colophon", ".-4", [ 0, 0, 4 ], 60, 2, "colophon", "X7982162280BC7A61" ], [ "Table of Contents", ".-5", [ 0, 0, 5 ], 85, 3, "table of contents", "X8537FEB07AF2BEC8" ], [ "\033[1XLicensing\033[0X", "1", [ 1, 0, 0 ], 1, 10, "licensing", "X86DB23CC834ABD71" ], [ "\033[1XFR package\033[0X", "2", [ 2, 0, 0 ], 1, 11, "fr package", "X7ADCE68284FB4ACF" ], [ "\033[1XA brief mathematical introduction\033[0X", "2.1", [ 2, 1, 0 ], 4, 11, "a brief mathematical introduction", "X80C332C686212786" ], [ "\033[1XAn example session\033[0X", "2.2", [ 2, 2, 0 ], 91, 12, "an example 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\033[10XFRElement\033[1Xs\033[0X", "4.1", [ 4, 1, 0 ], 37, 28, "creators for frelements", "X79DE08CD7EE57360" ], [ "\033[1XOperations and Attributes for \033[10XFRElement\033[1Xs\033[0X", "4.2", [ 4, 2, 0 ], 330, 33, "operations and attributes for frelements", "X812C932C7E2F2885" ], [ "\033[1XMealy machines and elements\033[0X", "5", [ 5, 0, 0 ], 1, 40, "mealy machines and elements", "X7C77EBC17DEF4CF6" ], [ "\033[1XCreators for \033[10XMealyMachine\033[1Xs and \033[10XMealyElement\ \033[1Xs\033[0X", "5.1", [ 5, 1, 0 ], 41, 40, "creators for mealymachines and mealyelements", "X846B89F686B50AE1" ], [ "\033[1XOperations and Attributes for \033[10XMealyMachine\033[1Xs and \ \033[10XMealyElement\033[1Xs\033[0X", "5.2", [ 5, 2, 0 ], 222, 43, "operations and attributes for mealymachines and mealyelements", "X7F673D877B205708" ], [ "\033[1XLinear machines and elements\033[0X", "6", [ 6, 0, 0 ], 1, 56, "linear machines and elements", "X84AD415C872BFB91" ], [ "\033[1XMethods and operations for \033[10XLinearFRMachine\033[1Xs and \ \033[10XLinearFRElement\033[1Xs\033[0X", "6.1", [ 6, 1, 0 ], 32, 56, "methods and operations for linearfrmachines and linearfrelements", "X812C0F7B7A31FCEF" ], [ "\033[1XSelf-similar groups, monoids and semigroups\033[0X", "7", [ 7, 0, 0 ], 1, 65, "self-similar groups monoids and semigroups", "X86C0E6F083DCCDC8" ], [ "\033[1XCreators for FR semigroups\033[0X", "7.1", [ 7, 1, 0 ], 24, 65, "creators for fr semigroups", "X80A26BAA7B53C1BD" ], [ "\033[1XOperations for FR semigroups\033[0X", "7.2", [ 7, 2, 0 ], 514, 73, "operations for fr semigroups", "X84E20571841DE1E4" ], [ "\033[1XProperties for infinite groups\033[0X", "7.3", [ 7, 3, 0 ], 1223, 85, "properties for infinite groups", "X7E8485A081EBB3AA" ], [ "\033[1XAlgebras\033[0X", "8", [ 8, 0, 0 ], 1, 88, "algebras", "X7DDBF6F47A2E021C" ], [ "\033[1XCreators for FR algebras\033[0X", "8.1", [ 8, 1, 0 ], 15, 88, "creators for fr algebras", "X842EE9427C63F92E" ], [ "\033[1XOperations for FR algebras\033[0X", "8.2", [ 8, 2, 0 ], 91, 89, "operations for fr algebras", "X7EFB4F2E7E908B9F" ], [ "\033[1XIterated monodromy groups\033[0X", "9", [ 9, 0, 0 ], 1, 91, "iterated monodromy groups", "X798DE1297EC58F59" ], [ "\033[1XCreators and operations for IMG FR machines\033[0X", "9.1", [ 9, 1, 0 ], 21, 91, "creators and operations for img fr machines", "X7CA23C95828C2A3E" ], [ "\033[1XSpiders\033[0X", "9.2", [ 9, 2, 0 ], 279, 95, "spiders", "X7C73C74D87428A33" ], [ "\033[1XExamples\033[0X", "10", [ 10, 0, 0 ], 1, 97, "examples", "X7A489A5D79DA9E5C" ], [ "\033[1XExamples of groups\033[0X", "10.1", [ 10, 1, 0 ], 8, 97, "examples of groups", "X7AF5DEF08531AFA5" ], [ "\033[1XExamples of semigroups\033[0X", "10.2", [ 10, 2, 0 ], 656, 108, "examples of semigroups", "X81B82FA1811AAF8D" ], [ "\033[1XExamples of algebras\033[0X", "10.3", [ 10, 3, 0 ], 681, 108, "examples of algebras", "X803B02408573A30E" ], [ "\033[1XBacher's determinant identities\033[0X", "10.4", [ 10, 4, 0 ], 738, 109, "bachers determinant identities", "X7989134C83AF38AE" ], [ "\033[1XVH groups\033[0X", "10.5", [ 10, 5, 0 ], 945, 112, "vh groups", "X7C4A51947E1609A8" ], [ "\033[1XFR implementation details\033[0X", "11", [ 11, 0, 0 ], 1, 115, "fr implementation details", "X86D6616E868AF75C" ], [ "\033[1XThe family of FR objects\033[0X", "11.1", [ 11, 1, 0 ], 16, 115, "the family of fr objects", "X79719CD17A948933" ], [ "\033[1XFilters for \033[10XFRObject\033[1Xs\033[0X", "11.2", [ 11, 2, 0 ], 71, 116, "filters for frobjects", "X856A3AD87C93FC1F" ], [ "\033[1XSome of the algorithms implemented\033[0X", "11.3", [ 11, 3, 0 ], 251, 119, "some of the algorithms implemented", "X7E97015E8153F782" ], [ "\033[1XOrder of FR elements\033[0X", "11.3-2", [ 11, 3, 2 ], 281, 119, "order of fr elements", "X84B4FF607DA18152" ], [ "\033[1XMembership in semigroups\033[0X", "11.3-3", [ 11, 3, 3 ], 299, 120, "membership in semigroups", "X847B4AFF809D2A56" ], [ "\033[1XOrder of groups\033[0X", "11.3-4", [ 11, 3, 4 ], 329, 120, "order of groups", "X7A0AC96784ACE0BE" ], [ "\033[1XImages and preimages of some groups in f.p. and l.p. groups\033[0X\ ", "11.3-5", [ 11, 3, 5 ], 346, 120, "images and preimages of some groups in f.p. and l.p. groups", "X8329884F790E1542" ], [ "\033[1XComparison of FR, Mealy, vector, and algebra elements\033[0X", "11.3-6", [ 11, 3, 6 ], 375, 121, "comparison of fr mealy vector and algebra elements", "X7F4247367D1EBEB9" ], [ "\033[1XInverses of linear elements\033[0X", "11.3-7", [ 11, 3, 7 ], 401, 121, "inverses of linear elements", "X81F95FEB7C72ABFF" ], [ "\033[1XMiscellanea\033[0X", "12", [ 12, 0, 0 ], 1, 123, "miscellanea", "X785C6C0B80936CC8" ], [ "\033[1XHelpers\033[0X", "12.1", [ 12, 1, 0 ], 4, 123, "helpers", "X7E665607810488EE" ], [ "\033[1XUser settings\033[0X", "12.2", [ 12, 2, 0 ], 530, 131, "user settings", "X7ADFF37084706CEC" ], [ "Bibliography", "bib", [ "Bib", 0, 0 ], 1, 133, "bibliography", "X7A6F98FD85F02BFE" ], [ "References", "bib", [ "Bib", 0, 0 ], 1, 133, "references", "X7A6F98FD85F02BFE" ], [ "Index", "ind", [ "Ind", 0, 0 ], 1, 137, "index", "X83A0356F839C696F" ], [ "\033[2XFRMachineNC\033[0X (family,free,listlist,list)", "3.3-1", [ 3, 3, 1 ], 84, 17, "frmachinenc family free listlist list", "X80D310EF7FD5EA44" ], [ "\033[2XFRMachine\033[0X ([list,]list,list)", "3.3-2", [ 3, 3, 2 ], 107, 17, "frmachine [list ]list list", "X808F3BD97EDA8CE8" ], [ "\033[2XFRMachine\033[0X (semigroup,list,list)", "3.3-2", [ 3, 3, 2 ], 107, 17, "frmachine semigroup list list", "X808F3BD97EDA8CE8" ], [ "\033[2XUnderlyingFRMachine\033[0X", "3.3-3", [ 3, 3, 3 ], 165, 18, "underlyingfrmachine", "X7C383F4383D22BFC" ], [ "\033[2XAsGroupFRMachine\033[0X", "3.3-4", [ 3, 3, 4 ], 183, 19, "asgroupfrmachine", "X7BF186227C0ABE8D" ], [ "\033[2XAsMonoidFRMachine\033[0X", "3.3-4", [ 3, 3, 4 ], 183, 19, "asmonoidfrmachine", "X7BF186227C0ABE8D" ], [ "\033[2XAsSemigroupFRMachine\033[0X", "3.3-4", [ 3, 3, 4 ], 183, 19, "assemigroupfrmachine", "X7BF186227C0ABE8D" ], [ "\033[2XChangeFRMachineBasis\033[0X", "3.3-5", [ 3, 3, 5 ], 288, 20, "changefrmachinebasis", "X814F53B97C3F43F5" ], [ "\033[2XStateSet\033[0X (FR machine)", "3.4-1", [ 3, 4, 1 ], 328, 21, "stateset fr machine", "X8000470D7DA7FFBD" ], [ "\033[2XGeneratorsOfFRMachine\033[0X", "3.4-2", [ 3, 4, 2 ], 346, 21, "generatorsoffrmachine", "X7F77F5DD789FA2F4" ], [ "\033[2XOutput\033[0X (FR machine,state)", "3.4-3", [ 3, 4, 3 ], 361, 22, "output fr machine state", "X80B52A8A7F30878E" ], [ "\033[2XOutput\033[0X (FR machine,state,letter)", "3.4-3", [ 3, 4, 3 ], 361, 22, "output fr machine state letter", "X80B52A8A7F30878E" ], [ "\033[2XTransition\033[0X (FR machine,state,input)", "3.4-4", [ 3, 4, 4 ], 384, 22, "transition fr machine state input", "X7AEE87BC8393FA54" ], [ "\033[2XWreathRecursion\033[0X", "3.4-5", [ 3, 4, 5 ], 402, 22, "wreathrecursion", "X7D95D1498586E5D0" ], [ "\033[2XStructuralGroup\033[0X", "3.5-1", [ 3, 5, 1 ], 428, 23, "structuralgroup", "X8289C2F77D67EDC3" ], [ 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"treewreathproduct fr machine", "X7A0858097AA3FBDA" ], [ "\033[2XSubFRMachine\033[0X", "3.5-9", [ 3, 5, 9 ], 657, 26, "subfrmachine", "X811B5BF17A3FE577" ], [ "\033[2XMinimized\033[0X (FR machine)", "3.5-10", [ 3, 5, 10 ], 676, 27, "minimized fr machine", "X81B382BD81B2BD34" ], [ "\033[2XCorrespondence\033[0X (FR machine)", "3.5-11", [ 3, 5, 11 ], 700, 27, "correspondence fr machine", "X7C107A42815F91DA" ], [ "\033[2XFRElementNC\033[0X (family,free,listlist,list,assocword)", "4.1-1", [ 4, 1, 1 ], 40, 28, "frelementnc family free listlist list assocword", "X7839813183881054" ] , [ "\033[2XFRElement\033[0X ([list,]list,list,list)", "4.1-2", [ 4, 1, 2 ], 65, 29, "frelement [list ]list list list", "X7CF5EDEB874BF9E3" ], [ "\033[2XFRElement\033[0X (semigroup,list,list,list)", "4.1-2", [ 4, 1, 2 ], 65, 29, "frelement semigroup list list list", "X7CF5EDEB874BF9E3" ], [ "\033[2XFRElement\033[0X (machine/element,list)", "4.1-3", [ 4, 1, 3 ], 120, 30, "frelement machine/element list", "X86181654827919EE" ], [ "\033[2XComposeElement\033[0X (elementcoll,perm)", "4.1-4", [ 4, 1, 4 ], 145, 30, "composeelement elementcoll perm", "X80D518E2804ABF70" ], [ "\033[2XVertexElement\033[0X", "4.1-5", [ 4, 1, 5 ], 170, 31, "vertexelement", "X7CE388057DAB4802" ], [ "\033[2XDiagonalElement\033[0X", "4.1-6", [ 4, 1, 6 ], 195, 31, "diagonalelement", "X848EB430831097E6" ], [ "\033[2XAsGroupFRElement\033[0X", "4.1-7", [ 4, 1, 7 ], 270, 32, "asgroupfrelement", "X7EB5DE3978840CDF" ], [ "\033[2XAsMonoidFRElement\033[0X", "4.1-7", [ 4, 1, 7 ], 270, 32, "asmonoidfrelement", "X7EB5DE3978840CDF" ], [ "\033[2XAsSemigroupFRElement\033[0X", "4.1-7", [ 4, 1, 7 ], 270, 32, "assemigroupfrelement", "X7EB5DE3978840CDF" ], [ "\033[2XOutput\033[0X (FR element)", "4.2-1", [ 4, 2, 1 ], 333, 33, "output fr element", "X78F819CF7DDBF310" ], [ "\033[2XActivity\033[0X", "4.2-2", [ 4, 2, 2 ], 351, 34, "activity", "X8732D01C82999F32" ], [ "\033[2XActivityInt\033[0X", "4.2-2", [ 4, 2, 2 ], 351, 34, "activityint", "X8732D01C82999F32" ], [ "\033[2XActivityTransformation\033[0X", "4.2-2", [ 4, 2, 2 ], 351, 34, "activitytransformation", "X8732D01C82999F32" ], [ "\033[2XActivityPerm\033[0X", "4.2-2", [ 4, 2, 2 ], 351, 34, "activityperm", "X8732D01C82999F32" ], [ "\033[2XTransition\033[0X (FR element,input)", "4.2-3", [ 4, 2, 3 ], 392, 34, "transition fr element input", "X7CE58B2D837B2845" ], [ "\033[2XPortrait\033[0X", "4.2-4", [ 4, 2, 4 ], 410, 35, "portrait", "X84A193C67CDBDA35" ], [ "\033[2XPortraitInt\033[0X", "4.2-4", [ 4, 2, 4 ], 410, 35, "portraitint", "X84A193C67CDBDA35" ], [ "\033[2XDecompositionOfFRElement\033[0X", "4.2-5", [ 4, 2, 5 ], 440, 35, "decompositionoffrelement", "X850EB66E7804BA3B" ], [ "\033[2XStateSet\033[0X (FR element)", "4.2-6", [ 4, 2, 6 ], 461, 35, "stateset fr element", "X85441F1683E9D820" ], [ "\033[2XState\033[0X", "4.2-7", [ 4, 2, 7 ], 479, 36, "state", "X819E3E3080297347" ], [ "\033[2XStates\033[0X", "4.2-8", [ 4, 2, 8 ], 500, 36, "states", "X7B0C97BC7C3BA20D" ], [ "\033[2XFixedStates\033[0X", "4.2-9", [ 4, 2, 9 ], 533, 37, "fixedstates", "X804B2E0F7E37F5B8" ], [ "\033[2XLimitStates\033[0X", "4.2-10", [ 4, 2, 10 ], 565, 37, "limitstates", "X8303B36C83371FB3" ], [ "\033[2XIsFiniteStateFRElement\033[0X", "4.2-11", [ 4, 2, 11 ], 591, 37, "isfinitestatefrelement", "X7C4076707CBBE945" ], [ "\033[2XIsFiniteStateFRMachine\033[0X", "4.2-11", [ 4, 2, 11 ], 591, 37, "isfinitestatefrmachine", "X7C4076707CBBE945" ], [ "\033[2XInitialState\033[0X", "4.2-12", [ 4, 2, 12 ], 616, 38, "initialstate", "X79E65E818690B4EB" ], [ "\033[2X\\^\033[0X (POW)", "4.2-13", [ 4, 2, 13 ], 633, 38, "^ pow", "X823B6E3D819432D6" ], [ "\033[2X\\*\033[0X (PROD)", "4.2-14", [ 4, 2, 14 ], 659, 39, "* prod", "X7C3CF6AF86336EDC" ], [ "\033[2X\\[\\]\033[0X (ELMLIST)", "4.2-15", [ 4, 2, 15 ], 683, 39, "[] elmlist", "X78C19ACA78F9F067" ], [ "\033[2X\\{\\}\033[0X (ELMSLIST)", "4.2-15", [ 4, 2, 15 ], 683, 39, "{} elmslist", "X78C19ACA78F9F067" ], [ "\033[2XMealyMachine\033[0X ([list,]listlist,list)", "5.1-1", [ 5, 1, 1 ], 44, 40, "mealymachine [list ]listlist list", "X7EF3E00080624B70" ], [ "\033[2XMealyElement\033[0X ([list,]listlist,list,int)", "5.1-1", [ 5, 1, 1 ], 44, 40, "mealyelement [list ]listlist list int", "X7EF3E00080624B70" ], [ "\033[2XMealyMachine\033[0X (domain,domain,function,function)", "5.1-2", [ 5, 1, 2 ], 104, 41, "mealymachine domain domain function function", "X875B8FED7FD20FA1" ], [ "\033[2XMealyElement\033[0X (domain,domain,function,function,obj)", "5.1-2", [ 5, 1, 2 ], 104, 41, "mealyelement domain domain function function obj", "X875B8FED7FD20FA1" ], [ "\033[2XMealyMachineNC\033[0X (family,listlist,list)", "5.1-3", [ 5, 1, 3 ], 135, 42, "mealymachinenc family listlist list", "X8578657C7F4B6254" ], [ "\033[2XMealyElementNC\033[0X (family,listlist,list,int)", "5.1-3", [ 5, 1, 3 ], 135, 42, "mealyelementnc family listlist list int", "X8578657C7F4B6254" ], [ "\033[2XAllMealyMachines\033[0X", "5.1-4", [ 5, 1, 4 ], 174, 42, "allmealymachines", "X83BBE01884D6E315" ], [ "\033[2XDraw\033[0X", "5.2-1", [ 5, 2, 1 ], 225, 43, "draw", "X7DF9F3AD86602DFC" ], [ "\033[2XMinimized\033[0X (Mealy machine)", "5.2-2", [ 5, 2, 2 ], 248, 44, "minimized mealy machine", "X8395542D846FA2B9" ], [ "\033[2XDualMachine\033[0X", "5.2-3", [ 5, 2, 3 ], 283, 44, "dualmachine", "X809F069B798ED985" ], [ "\033[2XIsReversible\033[0X", "5.2-4", [ 5, 2, 4 ], 305, 45, "isreversible", "X7D5D480C782FCC0B" ], [ "\033[2XIsMinimized\033[0X", "5.2-5", [ 5, 2, 5 ], 319, 45, "isminimized", "X8310A1C08158793C" ], [ "\033[2XAlphabetInvolution\033[0X", "5.2-6", [ 5, 2, 6 ], 341, 45, "alphabetinvolution", "X7CCB79B981912CCC" ], [ "\033[2XIsBireversible\033[0X", "5.2-7", [ 5, 2, 7 ], 359, 46, "isbireversible", "X80D2545D7D0990A2" ], [ "\033[2XStateGrowth\033[0X", "5.2-8", [ 5, 2, 8 ], 375, 46, "stategrowth", "X83364DAB825D7A0D" ], [ "\033[2XDegree\033[0X (FR element)", "5.2-9", [ 5, 2, 9 ], 399, 46, "degree fr element", 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