#SIXFORMAT GapDocGAP HELPBOOKINFOSIXTMP := rec( encoding := "UTF-8", bookname := "RCWA", entries := [ [ "Title page", "", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" ], [ "Abstract", "-2", [ 0, 0, 2 ], 31, 2, "abstract", "X7AA6C5737B711C89" ], [ "Copyright", "-1", [ 0, 0, 1 ], 56, 2, "copyright", "X81488B807F2A1CF1" ], [ "Acknowledgements", "-3", [ 0, 0, 3 ], 62, 2, "acknowledgements", "X82A988D47DFAFCFA" ], [ "Table of contents", "-4", [ 0, 0, 4 ], 76, 3, "table of contents", "X8537FEB07AF2BEC8" ], [ "\033[1XAbout the RCWA Package\033[0X", "1.", [ 1, 0, 0 ], 1, 6, "about the rcwa package", "X83A8C2927FAE2C23" ], [ "\033[1XMotivation\033[0X", "1.1", [ 1, 1, 0 ], 4, 6, "motivation", "X816FA3667FFEDC3F" ], [ "\033[1XPurpose of this package\033[0X", "1.2", [ 1, 2, 0 ], 26, 6, "purpose of this package", "X78FE3F9D80DB633E" ], [ "\033[1XGroups which this package can deal with\033[0X", "1.3", [ 1, 3, 0 ], 44, 7, "groups which this package can deal with", "X82190FB67F7F3325" ], [ "\033[1XScope of this package\033[0X", "1.4", [ 1, 4, 0 ], 81, 7, "scope of this package", "X84BA84177E640F2B" ], [ "\033[1XResidue-Class-Wise Affine Mappings\033[0X", "2.", [ 2, 0, 0 ], 1, 8, "residue-class-wise affine mappings", "X7FD73FCB8510050E" ], [ "\033[1XBasic definitions\033[0X", "2.1", [ 2, 1, 0 ], 12, 8, "basic definitions", "X78ED07E37FC2BD46" ], [ "\033[1XEntering residue-class-wise affine mappings\033[0X", "2.2", [ 2, 2, 0 ], 54, 9, "entering residue-class-wise affine mappings", "X86BC55648302D643" ], [ "\033[1XRcwaMapping (the general constructor)\033[0X", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping the general constructor", "X8799551B83644B37" ], [ "\033[1XBasic arithmetic for residue-class-wise affine mappings\033[0X", "2.3", [ 2, 3, 0 ], 433, 15, "basic arithmetic for residue-class-wise affine mappings", "X78E796B8824C4FC8" ], [ "\033[1XAttributes and properties of residue-class-wise affine mappings\ \033[0X", "2.4", [ 2, 4, 0 ], 553, 17, "attributes and properties of residue-class-wise affine mappings", "X7C16D22C7BD40FDC" ], [ "\033[1XFactoring residue-class-wise affine permutations\033[0X", "2.5", [ 2, 5, 0 ], 751, 20, "factoring residue-class-wise affine permutations" , "X8475F844869DD060" ], [ "\033[1XExtracting roots of residue-class-wise affine mappings\033[0X", "2.6", [ 2, 6, 0 ], 880, 22, "extracting roots of residue-class-wise affine mappings", "X8141065381B0942B" ], [ "\033[1XSpecial functions for non-bijective mappings\033[0X", "2.7", [ 2, 7, 0 ], 912, 23, "special functions for non-bijective mappings", "X8322C6848305EC4C" ], [ "\033[1XOn trajectories and cycles of residue-class-wise affine mappings\ \033[0X", "2.8", [ 2, 8, 0 ], 986, 24, "on trajectories and cycles of residue-class-wise affine mappings", "X7A34724386A2E9F3" ], [ "\033[1XTrajectory (methods for rcwa mappings)\033[0X", "2.8-1", [ 2, 8, 1 ], 991, 24, "trajectory methods for rcwa mappings", "X7C72174D7CCB6348" ], [ "\033[1XTrajectory (methods for rcwa mappings -- \"accumulated coefficient\ s\")\033[0X", "2.8-2", [ 2, 8, 2 ], 1025, 24, "trajectory methods for rcwa mappings -- accumulated coefficients", "X7FFD09837E934853" ], [ "\033[1XIncreasingOn & DecreasingOn (for an rcwa mapping)\033[0X", "2.8-3", [ 2, 8, 3 ], 1054, 25, "increasingon & decreasingon for an rcwa mapping", "X7E0244A386744185" ] , [ "\033[1XSources & Sinks (of an rcwa mapping)\033[0X", "2.8-8", [ 2, 8, 8 ], 1158, 27, "sources & sinks of an rcwa mapping", "X81DBA2D58526BE7E" ], [ "\033[1XThe categories and families of rcwa mappings\033[0X", "2.9", [ 2, 9, 0 ], 1275, 29, "the categories and families of rcwa mappings", "X83FA71DD842377F0" ], [ "\033[1XResidue-Class-Wise Affine Groups\033[0X", "3.", [ 3, 0, 0 ], 1, 30, "residue-class-wise affine groups", "X874A3BB684F0639A" ], [ "\033[1XConstructing residue-class-wise affine groups\033[0X", "3.1", [ 3, 1, 0 ], 7, 30, "constructing residue-class-wise affine groups", "X81242A6586A604A3" ], [ "\033[1XWreathProduct (for an rcwa group over Z, with a permutation group \ or (Z,+))\033[0X", "3.1-5", [ 3, 1, 5 ], 132, 32, "wreathproduct for an rcwa group over z with a permutation group or z +" , "X7AEFAB7E7F81444B" ], [ "\033[1XRestriction (of an rcwa mapping or -group, by an injective rcwa ma\ pping)\033[0X", "3.1-6", [ 3, 1, 6 ], 179, 33, "restriction of an rcwa mapping or -group by an injective rcwa mapping", "X852EF2C079E4D7FF" ], [ "\033[1XInduction (of an rcwa mapping or -group, by an injective rcwa mapp\ ing)\033[0X", "3.1-7", [ 3, 1, 7 ], 207, 33, "induction of an rcwa mapping or -group by an injective rcwa mapping", "X82171D7287CBED95" ], [ "\033[1XBasic routines for investigating residue-class-wise affine groups\ \033[0X", "3.2", [ 3, 2, 0 ], 253, 34, "basic routines for investigating residue-class-wise affine groups", "X80C042BE82EE0F9A" ], [ "\033[1XThe natural action of an rcwa group on the underlying ring\033[0X" , "3.3", [ 3, 3, 0 ], 535, 39, "the natural action of an rcwa group on the underlying ring", "X8151BE577FFDCE87" ], [ "\033[1XOrbit (for an rcwa group and either a point or a set)\033[0X", "3.3-1", [ 3, 3, 1 ], 558, 39, "orbit for an rcwa group and either a point or a set", "X7C046BE97EE53692" ], [ "\033[1XShortOrbits (for rcwa groups) & ShortCycles (for rcwa permutations\ )\033[0X", "3.3-3", [ 3, 3, 3 ], 636, 40, "shortorbits for rcwa groups & shortcycles for rcwa permutations", "X78F145197F63A25D" ], [ "\033[1XBall (for group, element and radius or group, point, radius and ac\ tion)\033[0X", "3.3-4", [ 3, 3, 4 ], 677, 41, "ball for group element and radius or group point radius and action", "X8735855587CC029F" ], [ "\033[1XSpecial attributes of tame residue-class-wise affine groups\033[0X\ ", "3.4", [ 3, 4, 0 ], 852, 44, "special attributes of tame residue-class-wise affine groups", "X781CBEFA7F39B58D" ], [ "\033[1XRespectedPartition (of a tame rcwa group or -permutation)\033[0X", "3.4-1", [ 3, 4, 1 ], 864, 44, "respectedpartition of a tame rcwa group or -permutation", "X7F523A6B87825AB8" ], [ "\033[1XActionOnRespectedPartition & KernelOfActionOnRespectedPartition\ \033[0X", "3.4-2", [ 3, 4, 2 ], 904, 45, "actiononrespectedpartition & kernelofactiononrespectedpartition", "X831ADC1584DE6113" ], [ "\033[1XGenerating pseudo-random elements of RCWA(R) and CT(R)\033[0X", "3.5", [ 3, 5, 0 ], 965, 46, "generating pseudo-random elements of rcwa r and ct r", "X81941A247942FB99" ], [ "\033[1XThe categories of residue-class-wise affine groups\033[0X", "3.6", [ 3, 6, 0 ], 1026, 47, "the categories of residue-class-wise affine groups", "X86327F6C83D09798" ], [ "\033[1XResidue-Class-Wise Affine Monoids\033[0X", "4.", [ 4, 0, 0 ], 1, 48, "residue-class-wise affine monoids", "X81C90F7C7BA25BDF" ], [ "\033[1XConstructing residue-class-wise affine monoids\033[0X", "4.1", [ 4, 1, 0 ], 8, 48, "constructing residue-class-wise affine monoids", "X83D42E26849D5580" ], [ "\033[1XComputing with residue-class-wise affine monoids\033[0X", "4.2", [ 4, 2, 0 ], 78, 49, "computing with residue-class-wise affine monoids", "X8759954F7EB1A658" ], [ "\033[1XBall (for monoid, element and radius or monoid, point, radius and \ action)\033[0X", "4.2-2", [ 4, 2, 2 ], 165, 51, "ball for monoid element and radius or monoid point radius and action", "X787848137DF1C245" ], [ "\033[1XExamples\033[0X", "5.", [ 5, 0, 0 ], 1, 52, "examples", "X7A489A5D79DA9E5C" ], [ "\033[1XFactoring Collatz' permutation of the integers\033[0X", "5.1", [ 5, 1, 0 ], 23, 52, "factoring collatz permutation of the integers", "X86C2BAE3876985A6" ], [ "\033[1XAn rcwa mapping which seems to be contracting, but very slow\033[0\ X", "5.2", [ 5, 2, 0 ], 137, 54, "an rcwa mapping which seems to be contracting but very slow", "X878499AF7889FD9E" ], [ "\033[1XChecking a result by P. Andaloro\033[0X", "5.3", [ 5, 3, 0 ], 225, 56, "checking a result by p. andaloro", "X84A915BA833E0BDE" ], [ "\033[1XTwo examples by Matthews and Leigh\033[0X", "5.4", [ 5, 4, 0 ], 266, 57, "two examples by matthews and leigh", "X7E8CD9B67ED78735" ], [ "\033[1XExploring the structure of a wild rcwa group\033[0X", "5.5", [ 5, 5, 0 ], 379, 59, "exploring the structure of a wild rcwa group", "X7A8F55CA87A16900" ], [ "\033[1XA wild rcwa mapping which has only finite cycles\033[0X", "5.6", [ 5, 6, 0 ], 485, 61, "a wild rcwa mapping which has only finite cycles" , "X7D0928AE839F1C49" ], [ "\033[1XAn abelian rcwa group over a polynomial ring\033[0X", "5.7", [ 5, 7, 0 ], 688, 65, "an abelian rcwa group over a polynomial ring", "X7A8605E680F664BF" ], [ "\033[1XA tame group generated by commutators of wild permutations\033[0X" , "5.8", [ 5, 8, 0 ], 781, 66, "a tame group generated by commutators of wild permutations", "X87383623856ED81B" ], [ "\033[1XChecking for solvability\033[0X", "5.9", [ 5, 9, 0 ], 906, 69, "checking for solvability", "X78DFE4B4821E07A6" ], [ "\033[1XSome examples over (semi)localizations of the integers\033[0X", "5.10", [ 5, 10, 0 ], 958, 70, "some examples over semi localizations of the integers", "X783D54DC7A646273" ], [ "\033[1XTwisting 257-cycles into an rcwa mapping with modulus 32\033[0X", "5.11", [ 5, 11, 0 ], 1112, 73, "twisting 257-cycles into an rcwa mapping with modulus 32", "X846D7D087861E0AC" ], [ "\033[1XThe behaviour of the moduli of powers\033[0X", "5.12", [ 5, 12, 0 ], 1168, 74, "the behaviour of the moduli of powers", "X78D5DC93845CA6A0" ], [ "\033[1XImages and preimages under the Collatz mapping\033[0X", "5.13", [ 5, 13, 0 ], 1254, 75, "images and preimages under the collatz mapping" , "X855A3CD88459958B" ], [ "\033[1XA group which acts 4-transitively on the positive integers\033[0X" , "5.14", [ 5, 14, 0 ], 1363, 77, "a group which acts 4-transitively on the positive integers", "X7968C1DF7EF0BD8E" ], [ "\033[1XA group which acts 3-transitively, but not 4-transitively on Z\033\ [0X", "5.15", [ 5, 15, 0 ], 1822, 86, "a group which acts 3-transitively but not 4-transitively on z", "X87E7FCE27EACDA38" ], [ "\033[1XGrigorchuk groups\033[0X", "5.16", [ 5, 16, 0 ], 2027, 89, "grigorchuk groups", "X85DD5E9C7878CAE3" ], [ "\033[1XForward orbits of a monoid with 2 generators\033[0X", "5.17", [ 5, 17, 0 ], 2109, 91, "forward orbits of a monoid with 2 generators", "X7DD9502F80364631" ], [ "\033[1XRepresentations of the free group of rank 2\033[0X", "5.18", [ 5, 18, 0 ], 2191, 92, "representations of the free group of rank 2", "X81407BD58648D206" ], [ "\033[1XRepresentations of the modular group PSL(2,Z)\033[0X", "5.19", [ 5, 19, 0 ], 2283, 93, "representations of the modular group psl 2 z", "X85B4B4DA83B09E81" ], [ "\033[1XThe Algorithms Implemented in RCWA\033[0X", "6.", [ 6, 0, 0 ], 1, 95, "the algorithms implemented in rcwa", "X79EA0B717B045756" ], [ "\033[1XInstallation and auxiliary functions\033[0X", "7.", [ 7, 0, 0 ], 1, 106, "installation and auxiliary functions", "X859F6BF88754E5CC" ], [ "\033[1XRequirements\033[0X", "7.1", [ 7, 1, 0 ], 4, 106, "requirements", "X85A08CF187A6D986" ], [ "\033[1XInstallation\033[0X", "7.2", [ 7, 2, 0 ], 16, 106, "installation", "X8360C04082558A12" ], [ "\033[1XThe Info class of the package\033[0X", "7.3", [ 7, 3, 0 ], 24, 106, "the info class of the package", "X7A31FA44791E93C5" ], [ "\033[1XThe testing routine\033[0X", "7.4", [ 7, 4, 0 ], 35, 106, "the testing routine", "X8667D5027AC3DE8E" ], [ "\033[1XBuilding the manual\033[0X", "7.5", [ 7, 5, 0 ], 47, 107, "building the manual", "X854E65D281B80D3B" ], [ "\033[1XLoading and saving bitmap pictures\033[0X", "7.6", [ 7, 6, 0 ], 63, 107, "loading and saving bitmap pictures", "X7C7AB20486E56B83" ], [ "\033[1XRunning demonstrations\033[0X", "7.7", [ 7, 7, 0 ], 97, 107, "running demonstrations", "X85E215DB85F610ED" ], [ "\033[1XSome general utility functions\033[0X", "7.8", [ 7, 8, 0 ], 115, 108, "some general utility functions", "X808A30E37A293D19" ], [ "Bibliography", "bib.", [ "Bib", 0, 0 ], 1, 109, "bibliography", "X7A6F98FD85F02BFE" ], [ "References", "bib.", [ "Bib", 0, 0 ], 1, 109, "references", "X7A6F98FD85F02BFE" ], [ "Index", "ind.", [ "Ind", 0, 0 ], 1, 111, "index", "X83A0356F839C696F" ], [ "Collatz conjecture", "1.1", [ 1, 1, 0 ], 4, 6, "collatz conjecture", "X7BB9BDB5785B8A9A" ], [ "Collatz mapping", "1.1", [ 1, 1, 0 ], 4, 6, "collatz mapping", "X7BB9BDB5785B8A9A" ], [ "rcwa mapping definition", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa mapping definition", "X7F0B50947EEA87F8" ], [ "rcwa group definition", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa group definition", "X7F0B50947EEA87F8" ], [ "modulus definition", "2.1", [ 2, 1, 0 ], 12, 8, "modulus definition", "X7F0B50947EEA87F8" ], [ "rcwa mapping modulus", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa mapping modulus", "X7F0B50947EEA87F8" ], [ "multiplier definition", "2.1", [ 2, 1, 0 ], 12, 8, "multiplier definition", "X7F0B50947EEA87F8" ], [ "rcwa mapping multiplier", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa mapping multiplier", "X7F0B50947EEA87F8" ], [ "divisor definition", "2.1", [ 2, 1, 0 ], 12, 8, "divisor definition", "X7F0B50947EEA87F8" ], [ "rcwa mapping divisor", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa mapping divisor", "X7F0B50947EEA87F8" ], [ "tame rcwa mapping", "2.1", [ 2, 1, 0 ], 12, 8, "tame rcwa mapping", "X7F0B50947EEA87F8" ], [ "tame rcwa group", "2.1", [ 2, 1, 0 ], 12, 8, "tame rcwa group", "X7F0B50947EEA87F8" ], [ "wild rcwa mapping", "2.1", [ 2, 1, 0 ], 12, 8, "wild rcwa mapping", "X7F0B50947EEA87F8" ], [ "wild rcwa group", "2.1", [ 2, 1, 0 ], 12, 8, "wild rcwa group", "X7F0B50947EEA87F8" ], [ "rcwa mapping tame", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa mapping tame", "X7F0B50947EEA87F8" ], [ "rcwa group tame", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa group tame", "X7F0B50947EEA87F8" ], [ "rcwa mapping wild", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa mapping wild", "X7F0B50947EEA87F8" ], [ "rcwa group wild", "2.1", [ 2, 1, 0 ], 12, 8, "rcwa group wild", "X7F0B50947EEA87F8" ], [ "\033[2XClassShift\033[0X (r, m)", "2.2-1", [ 2, 2, 1 ], 114, 10, "classshift r m", "X86B611BD7EED62A1" ], [ "\033[2XClassShift\033[0X (cl)", "2.2-1", [ 2, 2, 1 ], 114, 10, "classshift cl", "X86B611BD7EED62A1" ], [ "\033[2XClassReflection\033[0X (r, m)", "2.2-2", [ 2, 2, 2 ], 140, 10, "classreflection r m", "X7896C5417E3692B4" ], [ "\033[2XClassReflection\033[0X (cl)", "2.2-2", [ 2, 2, 2 ], 140, 10, "classreflection cl", "X7896C5417E3692B4" ], [ "\033[2XClassTransposition\033[0X (r1, m1, r2, m2)", "2.2-3", [ 2, 2, 3 ], 167, 11, "classtransposition r1 m1 r2 m2", "X8716A75F7DD1C46B" ], [ "\033[2XClassTransposition\033[0X (cl1, cl2)", "2.2-3", [ 2, 2, 3 ], 167, 11, "classtransposition cl1 cl2", "X8716A75F7DD1C46B" ], [ "\033[10XTransposedClasses\033[0X of a class transposition", "2.2-3", [ 2, 2, 3 ], 167, 11, "transposedclasses of a class transposition", "X8716A75F7DD1C46B" ], [ "\033[10XSplittedClassTransposition\033[0X for a class transposition and a\ number of factors", "2.2-3", [ 2, 2, 3 ], 167, 11, "splittedclasstransposition for a class transposition and a number of fa\ ctors", "X8716A75F7DD1C46B" ], [ "\033[2XClassRotation\033[0X (r, m, u)", "2.2-4", [ 2, 2, 4 ], 225, 12, "classrotation r m u", "X87EB8C1C87F78A17" ], [ "\033[2XClassRotation\033[0X (cl, u)", "2.2-4", [ 2, 2, 4 ], 225, 12, "classrotation cl u", "X87EB8C1C87F78A17" ], [ "\033[10XRotationFactor\033[0X of a class rotation", "2.2-4", [ 2, 2, 4 ], 225, 12, "rotationfactor of a class rotation", "X87EB8C1C87F78A17" ], [ "\033[10XIsClassShift\033[0X for an rcwa mapping", "2.2-4", [ 2, 2, 4 ], 225, 12, "isclassshift for an rcwa mapping", "X87EB8C1C87F78A17" ], [ "\033[10XIsClassReflection\033[0X for an rcwa mapping", "2.2-4", [ 2, 2, 4 ], 225, 12, "isclassreflection for an rcwa mapping", "X87EB8C1C87F78A17" ], [ "\033[10XIsClassRotation\033[0X for an rcwa mapping", "2.2-4", [ 2, 2, 4 ], 225, 12, "isclassrotation for an rcwa mapping", "X87EB8C1C87F78A17" ], [ "\033[10XIsClassTransposition\033[0X for an rcwa mapping", "2.2-4", [ 2, 2, 4 ], 225, 12, "isclasstransposition for an rcwa mapping", "X87EB8C1C87F78A17" ], [ "\033[10XIsGeneralizedClassTransposition\033[0X for an rcwa mapping", "2.2-4", [ 2, 2, 4 ], 225, 12, "isgeneralizedclasstransposition for an rcwa mapping", "X87EB8C1C87F78A17" ], [ "\033[10XName\033[0X for cs / cr / ct", "2.2-4", [ 2, 2, 4 ], 225, 12, "name for cs cr ct", "X87EB8C1C87F78A17" ], [ "\033[2XRcwaMapping\033[0X (by ring, modulus and list of coefficients)", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping by ring modulus and list of coefficients", "X7D87A85584BA7E48" ], [ "\033[2XRcwaMapping\033[0X (by ring and list of coefficients)", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping by ring and list of coefficients", "X7D87A85584BA7E48" ], [ "\033[2XRcwaMapping\033[0X (by list of coefficients)", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping by list of coefficients", "X7D87A85584BA7E48" ], [ "\033[2XRcwaMapping\033[0X (by permutation and range)", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping by permutation and range", "X7D87A85584BA7E48" ], [ "\033[2XRcwaMapping\033[0X (by modulus and list of values)", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping by modulus and list of values", "X7D87A85584BA7E48" ], [ "\033[2XRcwaMapping\033[0X (by set of noninvertible primes and list of coe\ fficients)", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping by set of noninvertible primes and list of coefficients", "X7D87A85584BA7E48" ], [ "\033[2XRcwaMapping\033[0X (by finite field size, modulus and list of coef\ ficients)", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping by finite field size modulus and list of coefficients", "X7D87A85584BA7E48" ], [ "\033[2XRcwaMapping\033[0X (by two partitions of a ring into residue class\ es)", "2.2-5", [ 2, 2, 5 ], 281, 13, "rcwamapping by two partitions of a ring into residue classes", "X7D87A85584BA7E48" ], [ "\033[2XRcwaMapping\033[0X (by residue class cycles)", "2.2-5", [ 2, 2, 5 ], 281, 13, 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