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  1. #############################################################################
  2. ##
  3. #A  init.g                      GAP library                  Martin Schoenert
  4. ##
  5. #A  @(#)$Id: init.g,v 3.24 1993/02/11 17:54:45 martin Rel $
  6. ##
  7. #Y  Copyright 1990-1992,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
  8. ##
  9. ##  This file is read by  GAP  upon startup.  It displays the banner and then
  10. ##  defines all the functions in the library as autoreadable.  Note this file
  11. ##  is automatically generated by 'makeinit', you almost certainly should not
  12. ##  edit it.
  13. ##
  14. #H  $Log: init.g,v $
  15. #H  Revision 3.24  1993/02/11  17:54:45  martin
  16. #H  added 'UnionBlist' etc.
  17. #H
  18. #H  Revision 3.23  1993/02/10  15:18:24  martin
  19. #H  changed 'ReadSys' to 'ReadPath', which returns status
  20. #H
  21. #H  Revision 3.22  1993/02/10  15:06:16  martin
  22. #H  added the new names to the banner
  23. #H
  24. #H  Revision 3.21  1993/02/10  10:14:10  martin
  25. #H  added "permcser", composition series for permutation groups
  26. #H
  27. #H  Revision 3.20  1993/02/04  11:24:28  martin
  28. #H  changed because strings are now lists
  29. #H
  30. #H  Revision 3.19  1993/01/22  14:11:55  martin
  31. #H  added the 3-groups library
  32. #H
  33. #H  Revision 3.18  1993/01/21  08:37:14  martin
  34. #H  added matrix group library
  35. #H
  36. #H  Revision 3.17  1993/01/20  17:49:28  martin
  37. #H  added the table of marks library
  38. #H
  39. #H  Revision 3.16  1993/01/18  19:03:49  martin
  40. #H  added 'AgGroup' for permutation groups and character table computation
  41. #H
  42. #H  Revision 3.15  1992/09/10  10:46:52  martin
  43. #H  added subgroup lattice printing functions
  44. #H
  45. #H  Revision 3.14  1992/08/12  13:30:46  sam
  46. #H  added file 'ctgapmoc.g'
  47. #H
  48. #H  Revision 3.13  1992/08/11  11:02:03  sam
  49. #H  added some functions dealing with library tables
  50. #H
  51. #H  Revision 3.12  1992/07/15  13:38:33  martin
  52. #H  added packages "fpsgpres" and "fptietze"
  53. #H
  54. #H  Revision 3.11  1992/07/14  13:16:10  martin
  55. #H  added package "permprod"
  56. #H
  57. #H  Revision 3.10  1992/06/27  08:07:28  martin
  58. #H  moved 'OnTuples', 'OnSets', etc. into the kernel
  59. #H
  60. #H  Revision 3.9  1992/06/24  16:18:58  goetz
  61. #H  new version of 'ctsymmet.g'.
  62. #H
  63. #H  Revision 3.8  1992/06/04  08:34:50  martin
  64. #H  added "ctlattic", renamed "finpoly" to "polyfin" etc
  65. #H
  66. #H  Revision 3.7  1992/06/03  17:34:33  martin
  67. #H  added "fldpoly", "ratpoly", "recsl", and "chevgrp"
  68. #H
  69. #H  Revision 3.6  1992/05/21  15:35:55  martin
  70. #H  added 'NormedVector'
  71. #H
  72. #H  Revision 3.5  1992/05/08  16:29:43  martin
  73. #H  added the packages for polynomials
  74. #H
  75. #H  Revision 3.4  1992/05/08  16:26:06  martin
  76. #H  added 'VERSION'
  77. #H
  78. #H  Revision 3.3  1992/05/08  16:24:30  martin
  79. #H  fixed 'ReplacedString' to replace the last occurence, not the first
  80. #H
  81. #H  Revision 3.2  1992/05/08  16:23:28  martin
  82. #H  changed the banner to 'Version 3 Release 2'
  83. #H
  84. #H  Revision 3.1  1992/04/07  20:05:03  martin
  85. #H  initial revision under RCS
  86. #H
  87. ##
  88. VERSION := "Version 3 Release 2";
  89.  
  90. if not QUIET and BANNER then
  91. PR := function ( str )  Print("           ",str,"\n");  end;
  92. PR("                                                                  ");
  93. PR("      ########            Lehrstuhl D fuer Mathematik             ");
  94. PR("    ###    ####           RWTH Aachen                             ");
  95. PR("   ##         ##                                                  ");
  96. PR("  ##          #             #######            #########          ");
  97. PR(" ##                        #      ##          ## #     ##         ");
  98. PR(" ##           #           #       ##             #      ##        ");
  99. PR(" ####        ##           ##       #             #      ##        ");
  100. PR("  #####     ###           ##      ##             ##    ##         ");
  101. PR("    ######### #            #########             #######          ");
  102. PR("              #                                  #                ");
  103. PR("             ##           Version 3              #                ");
  104. PR("            ###           Release 2              #                ");
  105. PR("           ## #           10 Feb 93              #                ");
  106. PR("          ##  #                                                   ");
  107. PR("         ##   #  Alice Niemeyer, Werner Nickel,  Martin Schoenert ");
  108. PR("        ##    #  Johannes Meier, Alex Wegner,    Thomas Bischops  ");
  109. PR("       ##     #  Frank Celler,   Juergen Mnich,  Udo Polis        ");
  110. PR("       ###   ##  Thomas Breuer,  Goetz Pfeiffer, Hans U. Besche   ");
  111. PR("        ######   Volkmar Felsch, Heiko Theissen, Alexander Hulpke ");
  112. PR("                 Ansgar Kaup,    Akos Seress                      ");
  113. PR("                                                                  ");
  114. PR("                 For help enter: ?<return>                        ");
  115. fi;
  116.  
  117. ReadIndent := "";
  118.  
  119. if not IsBound( InfoRead1 )  then InfoRead1 := Ignore;  fi;
  120. if not IsBound( InfoRead2 )  then InfoRead2 := Ignore;  fi;
  121.  
  122. ReplacedString := function ( string, old, new )
  123.     local  res, i,  j;
  124.     res := Copy( string );
  125.     if res[Length(res)] <> ';'  then
  126.         Add( res, ';' );
  127.     fi;
  128.     for i  in [1..Length(res)-Length(old)+1]  do
  129.         if res{[i..i+Length(old)-1]} = old  then
  130.             res{[i..i+Length(old)-1]} := new;
  131.         fi;
  132.     od;
  133.     if Length(string) = Length(res)-1  then
  134.         Unbind( res[Length(res)] );
  135.     fi;
  136.     return res;
  137. end;
  138.  
  139. ReadPath := function ( path, name, ext, infomsg )
  140.     local   readIndent, i, k, file, found;
  141.     readIndent := Copy( ReadIndent );
  142.     Append( ReadIndent, "  " );
  143.     InfoRead1( "#I",ReadIndent,infomsg,"( \"", name, "\" )\n" );
  144.     i := 1;
  145.     found := false;
  146.     while not found  and i <= Length(path)+1 do
  147.         k := Position( path, ';', i-1 );
  148.         if k = false  then k := Length(path)+1;  fi;
  149.         file := path{[i..k-1]};  Append( file, name );  Append( file, ext );
  150.         InfoRead2("#I  trying '",file,"'\n");
  151.         found := READ( file );
  152.         i := k + 1;
  153.     od;
  154.     ReadIndent := readIndent;
  155.     if found and ReadIndent = ""  then
  156.         InfoRead1( "#I  ",infomsg,"( \"", name, "\" ) done\n" );
  157.     fi;
  158.     return found;
  159. end;
  160.  
  161. Read := function ( name )
  162.     if not ReadPath( "", name, "", "Read" )  then
  163.      Error("the file '",name,"' must exist and be readable");
  164.     fi;
  165. end;
  166.  
  167. ReadLib := function ( name )
  168.     if not ReadPath( LIBNAME, name, ".g", "ReadLib" )  then
  169.      Error("the library file '",name,"' must exist and be readable");
  170.     fi;
  171. end;
  172.  
  173. GRPNAME := ReplacedString( LIBNAME, "lib/;", "grp/;" );
  174.  
  175. ReadGrp := function ( name )
  176.     if not ReadPath( GRPNAME, name, ".grp", "ReadGrp" )  then
  177.      Error("the group library file '",name,"' must exist and be readable");
  178.     fi;
  179. end;
  180.  
  181. TWONAME := ReplacedString( LIBNAME, "lib/;", "two/;" );
  182.  
  183. ReadTwo := function ( name )
  184.     if not ReadPath( TWONAME, name, ".grp", "ReadTwo" )  then
  185.      Error("the 2-group library file '",name,"' must exist and be readable");
  186.     fi;
  187. end;
  188.  
  189. THRNAME := ReplacedString( LIBNAME, "lib/;", "thr/;" );
  190.  
  191. ReadThr := function ( name )
  192.     if not ReadPath( THRNAME, name, ".grp", "ReadThr" )  then
  193.      Error("the 3-group library file '",name,"' must exist and be readable");
  194.     fi;
  195. end;
  196.  
  197. TBLNAME := ReplacedString( LIBNAME, "lib/;", "tbl/;" );
  198.  
  199. ReadTbl := function ( name )
  200.     if not ReadPath( TBLNAME, name, ".tbl", "ReadTbl" )  then
  201.      Error("the character table file '",name,"' must exist and be readable");
  202.     fi;
  203. end;
  204.  
  205. TOMNAME := ReplacedString( LIBNAME, "lib/;", "tom/;" );
  206.  
  207. ReadTom := function ( name )
  208.     if not ReadPath( TOMNAME, name, ".tom", "ReadTom" )  then
  209.      Error("the table of marks file '",name,"' must exist and be readable");
  210.     fi;
  211. end;
  212.  
  213.  
  214. AUTO( ReadLib( "abattoir" ),
  215.   LengthString, SubString, ConcatenationString, FpGroup, Edit, ProductPol,
  216.   ValuePol, MergedRecord, IsIdentical, UnionBlist, IntersectionBlist,
  217.   DifferenceBlist, SetPrintLevel, Save, SetPkgname, PKGNAME, LOADED_PACKAGES,
  218.   ReadPkg, ExecPkg, LoadPackage, RequirePackage );
  219.  
  220. AUTO( ReadLib( "agcent" ),
  221.   cs_ag_time, cs_ag_trivial_cnt, cs_ag_general_cnt, ec_ag_time,
  222.   ec_ag_central_cnt, ec_ag_non_central_cnt, cen_ag_time, cen_ag_central_cnt,
  223.   cen_ag_non_central_cnt, MainEntryCSAgGroup, CentralCaseCentAgGroup,
  224.   GeneralCaseCentAgGroup, MainEntryCentAgGroup, CentralCaseECAgWords,
  225.   GeneralCaseECAgWords, MainEntryECAgWords, MainEntryACAgWords );
  226.  
  227. AUTO( ReadLib( "agclass" ),
  228.   ecs_ag_time, ecs_ag_centrality_cnt, ecs_ag_central_cnt,
  229.   ecs_ag_non_central_cnt, ncs_ag_time, ncs_ag_central_cnt,
  230.   ncs_ag_non_central_cnt, scs_ag_time, scs_ag_central_cnt,
  231.   scs_ag_non_central_cnt, InHomSolutions, CommutatorGauss,
  232.   CorrectedStabilizer, AffineOrbitsAgGroup, MinimalVectorAgOrbit,
  233.   CentralCaseECSAgGroup, GeneralCaseECSAgGroup, MainEntryECSAgGroup,
  234.   FusionsECSAgGroup, Fusions2ECSAgGroup, SubEntryNECSAgGroup,
  235.   MainEntryNECSAgGroup, SubEntrySECSAgGroup, MainEntrySECSAgGroup,
  236.   NumberConjugacyClasses, StructureConjugacyClasses, ConjugacyClassAgGroupOps );
  237.  
  238. AUTO( ReadLib( "agcomple" ),
  239.   BaseSteinitz, AffineBlocksCO, NextCentralizerCO, NextCocyclesCO,
  240.   NextCentralCO, NextNormalCO, NextComplementsCO, ComplementsCO,
  241.   ComplementsCO2, Complementclasses, Complement );
  242.  
  243. AUTO( ReadLib( "agcoset" ),
  244.   RightCosetAgGroupOps, LeftCosetAgGroupOps, AGDoubleCosets, FactorAgSubgroup,
  245.   ElementVector, MainEntryCCEAgGroup, GenRelOrdersAgGroup );
  246.  
  247. AUTO( ReadLib( "agctbl" ),
  248.   AgGroupClassMatrixColumn, IdentificationAgGroup, InitAgConjugacyTest );
  249.  
  250. AUTO( ReadLib( "aggroup" ),
  251.   AgGroupOps, AgSubgroup, ChangeCollector, RefinedAgSeries, SiftedAgWord,
  252.   Exponents, FactorArgOps, FactorArg, AgGroupPcp, MatGroupAgGroup,
  253.   PermGroupAgGroup, AgGroupFpGroup, DirectProductAgGroupOps,
  254.   SemidirectMatProduct, CollectorlessFactorGroup, CanonicalAgWord7,
  255.   CanonicalAgWord4, CanonicalAgWord5, CanonicalAgWord6a, CanonicalAgWord6b,
  256.   CayleyInputAgGroup, GapInputAgGroup, SogosInputAgGroup, CGSInputAgGroup,
  257.   MergeOperationsEntries );
  258.  
  259. AUTO( ReadLib( "aghall" ),
  260.   GS_LIMIT, ConjugatingWordGS, ConjugatingWordCN, ComplementConjugatingAgWord,
  261.   CoprimeComplement, HallEAS, HallComposition, HallSubgroup,
  262.   HallConjugatingAgWord, SylowSystem, SylowComplements );
  263.  
  264. AUTO( ReadLib( "aghomomo" ),
  265.   AbstractIgs, HomomorphicIgs, KernelHomomorphismAgGroupPermGroup,
  266.   KernelHomomorphismAgGroupAgGroup, AgGroupHomomorphismOps,
  267.   AgGroupHomomorphismByImagesOps, CompositionHomomorphismOps,
  268.   CompositionFactorGroup, HomomorphismsSeries, IsomorphismAgGroup );
  269.  
  270. AUTO( ReadLib( "aginters" ),
  271.   GS_SIZE, ExtendedIntersectionSumAgGroup, SumFactorizationFunctionAgGroup,
  272.   GlasbyCover, GlasbyShift, GlasbyStabilizer, GlasbyIntersection,
  273.   IntersectionSumAgGroup, SumAgGroup );
  274.  
  275. AUTO( ReadLib( "agnorm" ),
  276.   NormalizeIgsMod, NormalizeIgsModLess, StabilizerOp1, StabilizerOp2,
  277.   Stabilizer1NO, Stabilizer2NO, StabilizerNO, GlasbyNO, AbstractBaseMat,
  278.   CoboundsNO, LinearNO, NormalizerNO );
  279.  
  280. AUTO( ReadLib( "agprops" ),
  281.   IsAgGroup, IsElementAgSeries, IsConsistent, IsElementaryAbelianAgSeries,
  282.   PiPowerSubgroupAgGroup, IsPNilpotent, FactorsAgGroup, MaximalElement,
  283.   SmallGeneratingSetAgGroup );
  284.  
  285. AUTO( ReadLib( "agsubgrp" ),
  286.   MergedIgs, MergedCgs, Igs, Cgs, IsNormalized, Normalized, Normalize,
  287.   CopyAgGroup, PRump, CompositionSubgroup, AddElementaryAbelianSeries,
  288.   MeltElementaryAbelianSeriesAgGroup, ElementaryAbelianSeriesThrough,
  289.   RefinedSubnormalSeries, AgOrbitStabilizer, LinearOperation, AffineOperation );
  290.  
  291. AUTO( ReadLib( "agwords" ),
  292.   WordList, LetterInt, AgWords, AgWordsOps, CanonicalAgWord, CentralWeight,
  293.   CompositionLength, Depth, LeadingExponent, RelativeOrder, FactorGroupAgWord,
  294.   FactorGroupAgWordOps );
  295.  
  296. AUTO( ReadLib( "cdaggrp" ),
  297.   con_col_list, f2_orbit_priv, f2_orbits_priv, ls_orbit_priv, ls_orbits_priv,
  298.   omega_1_priv, kernel_priv_ag_char, ProjectiveCharDegAgGroup, CharDegAgGroup,
  299.   char_sec_prev, char_sec, CharTableSSGroup );
  300.  
  301. AUTO( ReadLib( "chevgrp" ),
  302.   ChevA, ChevB, ChevC, ChevD, ChevG, ChevF, ChevE, Chev2A, Chev2B, Chev2D,
  303.   Chev3D, Chev2G, Chev2F, Chev2E );
  304.  
  305. AUTO( ReadLib( "combinat" ),
  306.   Factorial, Binomial, Bell, Stirling1, Stirling2, CombinationsA,
  307.   CombinationsK, Combinations, NrCombinationsK, NrCombinations, ArrangementsA,
  308.   ArrangementsK, Arrangements, NrArrangementsA, NrArrangementsK,
  309.   NrArrangements, UnorderedTuplesK, UnorderedTuples, NrUnorderedTuples,
  310.   TuplesK, Tuples, NrTuples, PermutationsListK, PermutationsList,
  311.   NrPermutationsList, DerangementsK, Derangements, NrDerangementsK,
  312.   NrDerangements, Permanent2, Permanent, PartitionsSetA, PartitionsSetK,
  313.   PartitionsSet, NrPartitionsSet, PartitionsA, PartitionsK, Partitions,
  314.   NrPartitions, OrderedPartitionsA, OrderedPartitionsK, OrderedPartitions,
  315.   NrOrderedPartitions, RestrictedPartitionsA, RestrictedPartitionsK,
  316.   RestrictedPartitions, NrRestrictedPartitionsK, NrRestrictedPartitions,
  317.   SignPartition, AssociatedPartition, PowerPartition, PartitionTuples, Lucas,
  318.   Fibonacci, Bernoulli2, Bernoulli );
  319.  
  320. AUTO( ReadLib( "ctautoms" ),
  321.   FamiliesOfRows, MatAutomorphismsFamily, MatAutomorphisms,
  322.   TableAutomorphisms, TransformingPermutationFamily, TransformingPermutations,
  323.   TransformingPermutationsCharTables );
  324.  
  325. AUTO( ReadLib( "ctbasic" ),
  326.   IsCharTable, CharTableOps, BrauerTableOps, KernelChar, InitClassesCharTable,
  327.   InverseClassesCharTable, PrintToCAS, TestCharTable, ClassNamesCharTable,
  328.   CharTable, DisplayCharTable, ClassMultCoeffCharTable,
  329.   ClassStructureCharTable, MatClassMultCoeffsCharTable, RealClassesCharTable,
  330.   ClassOrbitCharTable, NrPolyhedralSubgroups, ClassRootsCharTable,
  331.   SortCharactersCharTable, SortClassesCharTable, SortCharTable );
  332.  
  333. AUTO( ReadLib( "ctcharac" ),
  334.   ScalarProduct, MatScalarProducts, InverseMatMod, PadicCoefficients,
  335.   LinearIndependentColumns, DecompositionInt, IntegralizedMat, Decomposition,
  336.   Tensored, Reduced, ReducedOrdinary, Symmetrisations, Symmetrizations,
  337.   SymmetricParts, AntiSymmetricParts, MinusCharacter, RefinedSymmetrisations,
  338.   OrthogonalComponents, SymplecticComponents, PrimeBlocks, Eigenvalues,
  339.   IrreducibleDifferences );
  340.  
  341. AUTO( ReadLib( "ctfilter" ),
  342.   StepModGauss, ModGauss, ContainedDecomposables, ContainedCharacters );
  343.  
  344. AUTO( ReadLib( "ctgapmoc" ),
  345.   FieldInfo, Subfields, MAKElb11, StructureConstants, PowerInfo, ScanMOC,
  346.   MOCChars, GAPChars, MOCTableOps, MOCTable, MOCTable0, MOCTableP, PrintToMOC );
  347.  
  348. AUTO( ReadLib( "ctgeneri" ),
  349.   CharTableRegular, CharTableDirectProduct, CharTableFactorGroup,
  350.   CharTableNormalSubgroup, CharTableSplitClasses, CharTableCollapsedClasses,
  351.   CharTableIsoclinic, CharTableQuaternionic, GEN_Q_P, PrimeBase,
  352.   CharTableSpecialized );
  353.  
  354. AUTO( ReadLib( "ctlattic" ),
  355.   LLL, LLLReducedGramMat, ShortestVectors, Extract, Decreased,
  356.   OrthogonalEmbeddings, OrthogonalEmbeddingsSpecialDimension, DnLattice,
  357.   DnLatticeIterative );
  358.  
  359. AUTO( ReadLib( "ctmapcon" ),
  360.   CharString, UpdateMap, NonnegIntScalarProducts, IntScalarProducts,
  361.   ContainedSpecialVectors, ContainedPossibleCharacters,
  362.   ContainedPossibleVirtualCharacters, InitFusion, CheckPermChar, ImproveMaps,
  363.   CommutativeDiagram, CheckFixedPoints, TransferDiagram, TestConsistencyMaps,
  364.   InitPowermap, Congruences, ConsiderKernels, ConsiderSmallerPowermaps,
  365.   PowermapsAllowedBySymmetrisations, Powermap, ConsiderTableAutomorphisms,
  366.   OrbitFusions, OrbitPowermaps, RepresentativesFusions,
  367.   RepresentativesPowermaps, FusionsAllowedByRestrictions, SubgroupFusions );
  368.  
  369. AUTO( ReadLib( "ctmapusi" ),
  370.   InverseMap, CompositionMaps, ProjectionMap, Indeterminateness,
  371.   PrintAmbiguity, Parametrized, ContainedMaps, Indirected, GetFusionMap,
  372.   StoreFusion, ElementOrdersPowermap, Restricted, Inflated, Induced,
  373.   CollapsedMat, Powmap, InducedCyclic, Power, Indicator );
  374.  
  375. AUTO( ReadLib( "ctpermch" ),
  376.   SubClass, TestPerm1, TestPerm2, TestPerm3, Inequalities, Permut, PermBounds,
  377.   PermComb, PermCandidates, PermCandidatesFaithful, PermChars, PermCharInfo );
  378.  
  379. AUTO( ReadLib( "ctpgrp" ),
  380.   RepresentationsPGroup, MatRepresentationsPGroup, CharTablePGroup,
  381.   FusionConjugacyClasses, SupersolvableResiduumAgGroup, SupersolvableResiduum );
  382.  
  383. AUTO( ReadLib( "ctsymmet" ),
  384.   BetaSet, CentralizerWreath, PowerWreath, InductionScheme,
  385.   MatCharsWreathSymmetric, CharValueSymmetric, CharTableSymmetric,
  386.   CharTableAlternating, CharValueWeylB, CharTableWeylB, CharTableWeylD,
  387.   CharValueWreathSymmetric, CharTableWreathSymmetric );
  388.  
  389. AUTO( ReadLib( "cyclotom" ),
  390.   IntCyc, RoundCyc, CoeffsCyc, CycList, Atlas1, EB, EC, ED, EE, EF, EG, EH,
  391.   NK, Atlas2, EY, EX, EW, EV, EU, ET, ES, EM, EL, EK, EJ, ER, EI, StarCyc,
  392.   Quadratic, GeneratorsPrimeResidues, GaloisMat, RationalizedMat );
  393.  
  394. AUTO( ReadLib( "domain" ),
  395.   IsDomain, Domain, DomainOps, Elements, IsFinite, Size, IsSubset,
  396.   Intersection, IntersectionSet, Union, UnionSet, CartesianProduct,
  397.   Difference, Representative, Random, DefineName );
  398.  
  399. AUTO( ReadLib( "field" ),
  400.   IsField, FieldOps, GaloisGroup, Conjugates, Norm, Trace, CharPol, MinPol,
  401.   FieldElementsOps, FieldElements, Field, DefaultField, IsFieldHomomorphism,
  402.   KernelFieldHomomorphism, FieldHomomorphismOps,
  403.   CompositionFieldHomomorphismOps, IdentityFieldHomomorphismOps );
  404.  
  405. AUTO( ReadLib( "finfield" ),
  406.   IsFiniteField, FiniteFieldOps, OrderFFE, IntFFE, GF, FiniteField,
  407.   GaloisField, FiniteFieldElementsOps, FiniteFieldElements, IsBaseFF,
  408.   IsFrobeniusAutomorphism, FrobeniusAutomorphism, FrobeniusAutomorphismI,
  409.   FrobeniusAutomorphismOps );
  410.  
  411. AUTO( ReadLib( "fpgrp" ),
  412.   FreeGroup, Words, WordsOps, IsFpGroup, FpGroupOps, CyclicPermutationsWords,
  413.   RelatorRepresentatives, RelsSortedByStartGen, CosetTableFpGroup,
  414.   GeneratorsCosetTable, OperationCosetsFpGroup,
  415.   FpGroupHomomorphismByImagesOps, LowIndexSubgroupsFpGroup );
  416.  
  417. AUTO( ReadLib( "fpsgpres" ),
  418.   AugmentedCosetTableMtc, AugmentedCosetTableRrs, CanonicalRelator,
  419.   PresentationAugmentedCosetTable, PresentationNormalClosureRrs,
  420.   PresentationNormalClosure, PresentationSubgroupMtc, PresentationSubgroupRrs,
  421.   PresentationSubgroup, ReducedRrsWord, RenumberTree, RewriteSubgroupRelators,
  422.   SpanningTree );
  423.  
  424. AUTO( ReadLib( "fptietze" ),
  425.   TZ_NUMGENS, TZ_NUMRELS, TZ_TOTAL, TZ_GENERATORS, TZ_INVERSES, TZ_RELATORS,
  426.   TZ_LENGTHS, TZ_FLAGS, TZ_MODIFIED, TZ_NUMREDUNDS, TZ_STATUS,
  427.   TZ_LENGTHTIETZE, TR_TREELENGTH, TR_PRIMARY, TR_TREENUMS, TR_TREEPOINTERS,
  428.   TR_TREELAST, PresentationOps, AddGenerator, AddRelator, DecodeTree,
  429.   FpGroupPresentation, PresentationFpGroup, RemoveRelator, SimplifiedFpGroup,
  430.   TzCheckRecord, TzEliminate, TzEliminateFromTree, TzEliminateGen,
  431.   TzEliminateGen1, TzEliminateGens, TzFindCyclicJoins, TzGeneratorExponents,
  432.   TzGo, SimplifyPresentation, TzGoGo, TzHandleLength1Or2Relators,
  433.   TzMostFrequentPairs, TzNewGenerator, TzPrint, TzPrintGenerators,
  434.   TzPrintLengths, TzOptionNames, TzRecordOps, TzPrintOptions, TzPrintPairs,
  435.   TzPrintPresentation, TzPrintRelators, TzPrintStatus, TzRecoverFromFile,
  436.   TzRemoveGenerators, TzSearch, TzSearchEqual, TzSort, TzSubstitute,
  437.   TzSubstituteCyclicJoins );
  438.  
  439. AUTO( ReadLib( "gaussian" ),
  440.   IsGaussInt, GaussianIntegersOps, GaussianIntegers, TwoSquares,
  441.   GaussianIntegersAsAdditiveGroupOps, IsGaussRat, GaussianRationalsOps,
  442.   GaussianRationals, GaussianRationalsAsRingOps );
  443.  
  444. AUTO( ReadLib( "group" ),
  445.   GroupString, GroupOps, Group, AsGroup, IsGroup, IsParent, Parent,
  446.   MaintainedGroupInfo, Subgroup, AsSubgroup, Centralizer, Centre, Closure,
  447.   CommutatorFactorGroup, CommutatorSubgroup, Core, DerivedSubgroup,
  448.   FittingSubgroup, FrattiniSubgroup, NormalClosure, NormalIntersection,
  449.   Normalizer, PCore, Radical, SylowSubgroup, TrivialSubgroup, DerivedSeries,
  450.   ElementaryAbelianSeries, CompositionSeries, LowerCentralSeries,
  451.   NormalSubgroups, PCentralSeries, SubnormalSeries, UpperCentralSeries,
  452.   IsAbelian, IsCentral, IsConjugate, IsCyclic, IsElementaryAbelian,
  453.   IsNilpotent, IsNormal, IsPerfect, IsSimple, IsSolvable, IsSubgroup,
  454.   IsSubnormal, IsTrivial, AbelianInvariants, Exponent, Index,
  455.   SmallestGenerators, IsConjugacyClass, ConjugacyClass,
  456.   ConjugacyClassGroupOps, ConjugacyClasses, ConjugateSubgroup,
  457.   ConjugateSubgroups, AbstractElementsGroup, Factorization, AgGroup,
  458.   PermGroup );
  459.  
  460. AUTO( ReadLib( "grpcoset" ),
  461.   IsRightCoset, IsCoset, RightCoset, Coset, RightCosetGroupOps, RightCosets,
  462.   Cosets, IsLeftCoset, LeftCoset, LeftCosetGroupOps, LeftCosets,
  463.   IsDoubleCoset, DoubleCoset, DoubleCosetGroupOps, DoubleCosets,
  464.   CalcDoubleCosets, AscendingChain, RefinedChain, Extension,
  465.   CanonicalRightTransversal, CanonicalCosetElement, OnCanonicalCosetElements,
  466.   PermutationCharacter, IsFactorGroupElement, FactorGroupElement,
  467.   FactorGroupElementOps, FactorGroupElements, FactorGroupElementsOps,
  468.   FactorGroup, NaturalHomomorphism, NaturalHomomorphismOps, FactorGroupOps );
  469.  
  470. AUTO( ReadLib( "grpctbl" ),
  471.   USECTPGROUP, IsLargeGroup, CharTableDixonSchneider, DixonRecord,
  472.   DixonRecordOps, DixonInit, RegisterNewCharacter, DixontinI, SortDixonRecord,
  473.   DixonSplit, OrbitSplit, CombinatoricSplit, SplitCharacters,
  474.   IncludeIrreducibles, DxLinearCharacters, ClassComparison, DxCalcPowerMap,
  475.   DxPowerClass, SplitStep, SplitTwoSpace, DxLiftCharacter,
  476.   GeneratePrimeCyclotomic, ModProduct, ModularCharacterDegree,
  477.   DegreeCandidates, FrobSchurInd, BestSplittingMatrix, SplitDegree,
  478.   CharacterMorphismGroup, AsCharacterMorphismFunction,
  479.   CharacterMorphismOrbits, GaloisOrbits, RootsOfPol, ModRoots,
  480.   ModularValuePol, BMminpol, KrylovSequence, Eigenbase, ActiveCols, PadicInt,
  481.   ClassElementLargeGroup, ClassElementSmallGroup, DoubleCentralizerOrbit,
  482.   StandardClassMatrixColumn, IdentificationGenericGroup,
  483.   AbelianNormalSubgroups );
  484.  
  485. AUTO( ReadLib( "grpelms" ),
  486.   IsGroupElement, GroupElements, GroupElementsOps, GroupElementOps, Order );
  487.  
  488. AUTO( ReadLib( "grphomom" ),
  489.   IsGroupHomomorphism, KernelGroupHomomorphism, GroupHomomorphismOps,
  490.   CompositionGroupHomomorphismOps, IdentityGroupHomomorphismOps,
  491.   ConjugationGroupHomomorphism, ConjugationGroupHomomorphismOps,
  492.   InnerAutomorphism, GroupHomomorphismByImages, GroupHomomorphismByImagesOps );
  493.  
  494. AUTO( ReadLib( "grpprods" ),
  495.   IsDirectProductElement, DirectProductElement, DirectProductElementOps,
  496.   IsDirectProduct, DirectProduct, DirectProductOps, EmbeddingDirectProductOps,
  497.   ProjectionDirectProductOps, SubdirectProduct, SubdirectProductOps,
  498.   IsSemidirectProductElement, SemidirectProductElement,
  499.   SemidirectProductElementOps, IsSemidirectProduct, SemidirectProduct,
  500.   SemidirectProductOps, EmbeddingSemidirectProductOps,
  501.   ProjectionSemidirectProductOps, IsWreathProductElement,
  502.   WreathProductElement, WreathProductElementOps, IsWreathProduct,
  503.   WreathProduct, WreathProductOps );
  504.  
  505. AUTO( ReadLib( "integer" ),
  506.   IntegersOps, Integers, NrBitsInt, Primes, Primes2, TraceModQF, IsPrimeInt,
  507.   IsPrimePowerInt, NextPrimeInt, PrevPrimeInt, FactorsRho, FactorsInt,
  508.   DivisorsSmall, DivisorsInt, Sigma, Tau, MoebiusMu, PowerModInt, LcmInt,
  509.   Gcdex, Int, AbsInt, SignInt, ChineseRem, LogInt, RootInt, SmallestRootInt,
  510.   IntegersAsAdditiveGroupOps );
  511.  
  512. AUTO( ReadLib( "lattgrp" ),
  513.   LatticeBreak, Zuppos, ZuppoBlist, GeneratorZuppos, GeneratorZuppoBlist,
  514.   ConjugateZuppos, ConjugateZuppoBlist, SetLatticeStatus, IsLattice,
  515.   IsSubgroupLattice, Lattice, StopLattice, ClearLatticeQueue,
  516.   RightTransversal, PerfectSubgroups, IsConjugacyClassSubgroups,
  517.   ConjugacyClassSubgroups, ConjugacyClassesSubgroups,
  518.   ConjugacyClassSubgroupsGroupOps, SubgroupLatticeOps,
  519.   PrintClassSubgroupLattice, PrintGroupSubgroupLattice,
  520.   PrintMaxSubgroupLattice, PrintMinSubgroupLattice, MinMaxLatticeRelation,
  521.   FreePerfectGroupsCatalogue );
  522.  
  523. AUTO( ReadLib( "lattperf" ),
  524.   PerfectGroupsCatalogue );
  525.  
  526. AUTO( ReadLib( "list" ),
  527.   List, Apply, Concatenation, Flat, Reversed, Sublist, Filtered, Number,
  528.   Collected, Equivalenceclasses, ForAll, ForAny, First, PositionProperty,
  529.   Cartesian2, Cartesian, Sort, SortParallel, Sortex, Permuted, PositionSorted,
  530.   Product, Sum, Iterated, Maximum, Minimum, R_N, RandomList, RandomSeed );
  531.  
  532. AUTO( ReadLib( "mapping" ),
  533.   IsGeneralMapping, IsMapping, IsInjective, IsSurjective, IsBijection,
  534.   IsBijective, IsHomomorphism, IsMonomorphism, IsEpimorphism, IsIsomorphism,
  535.   IsEndomorphism, IsAutomorphism, Image, Images, ImagesRepresentative,
  536.   PreImage, PreImages, PreImagesRepresentative, CompositionMapping,
  537.   IdentityMapping, InverseMapping, PowerMapping, Kernel, MappingOps,
  538.   CompositionMappingOps, InverseMappingOps, MappingByFunction,
  539.   MappingByFunctionOps, Embedding, Projection, Mappings, MappingsOps );
  540.  
  541. AUTO( ReadLib( "matgrp" ),
  542.   IsMatGroup, MatGroupOps, RightCosetMatGroupOps, MatGroup, RandomMatGroup,
  543.   Transposed, InvariantSubspace, IsInvariantSubspace, IrreducibilityTest,
  544.   AbsoluteIrreducibilityTest, CompositionFactors, EquivalenceTest,
  545.   AddNextMatrixFunction, NextMatrix, SmallCorankMatrixRecord,
  546.   RandomMatrixRecord, Fingerprint, ClassicNextMatrix,
  547.   ExtendedClassicNextMatrix, NextMatrix1, NextMatrix2, NextMatrix3 );
  548.  
  549. AUTO( ReadLib( "matring" ),
  550.   IsMatrixRing, MatrixRingOps );
  551.  
  552. AUTO( ReadLib( "matrix" ),
  553.   MatricesOps, Matrices, DimensionsMat, IdentityMat, NullMat, RandomMat,
  554.   RandomInvertableMat, RandomUnimodularMat, TransposedMat, KroneckerProduct,
  555.   OrderMatLimit, OrderMat, TraceMat, RankMat, DeterminantMat, TriangulizeMat,
  556.   BaseMat, NullspaceMat, DiagonalizeMat, ElementaryDivisorsMat, SolutionMat,
  557.   FieldMatrices, FieldMatricesOps, MinimalPolynomial,
  558.   CharacteristicPolynomial, FiniteFieldMatrices, FiniteFieldMatricesOps );
  559.  
  560. AUTO( ReadLib( "module" ),
  561.   ModuleOps, Module, IsModule );
  562.  
  563. AUTO( ReadLib( "numfield" ),
  564.   IsNumberField, IsCyclotomicField, NumberFieldOps, IsNFAutomorphism,
  565.   NFAutomorphism, NFAutomorphismOps, OrderCyc, NormalBaseNumberField,
  566.   ZumbroichBase, LenstraBase, NF, NumberField, CyclotomicFieldOps, CF,
  567.   CyclotomicField, NumberRingOps, NumberRing, CyclotomicRing, CyclotomicsOps,
  568.   Cyclotomics );
  569.  
  570. AUTO( ReadLib( "numtheor" ),
  571.   PrimeResiduesSmall, PrimeResidues, Phi, Lambda, OrderMod,
  572.   IsPrimitiveRootMod, PrimitiveRootMod, Jacobi, Legendre, RootModPrime,
  573.   RootModPrimePower, RootMod, RootsUnityModPrime, RootsUnityModPrimePower,
  574.   RootsUnityMod, LogMod, IsResidueClass, ResidueClass, ResidueClassOps,
  575.   ResidueClasses, ResidueClassesOps, ResidueClassGroupOps,
  576.   PrimeResidueClassGroup );
  577.  
  578. AUTO( ReadLib( "onecohom" ),
  579.   OCAgGroupOps, OCPermGroupOps, OneCoboundariesOC, ConjugatingWordOC,
  580.   EquationMatrixOC, SmallEquationMatrixOC, EquationVectorOC,
  581.   SmallEquationVectorOC, OneCocyclesOC, OneCoboundaries, OneCocycles,
  582.   PPrimeSetsOC );
  583.  
  584. AUTO( ReadLib( "operatio" ),
  585.   OnRightCosets, OnLeftCosets, OnLines, Cycle, CycleLength, Cycles,
  586.   CycleLengths, Permutation, IsFixpoint, IsFixpointFree, DegreeOperation,
  587.   IsTransitive, Transitivity, IsRegular, IsSemiRegular, Orbit, OrbitLength,
  588.   Orbits, OrbitLengths, Operation, OperationHomomorphism,
  589.   OperationHomomorphismOps, Blocks, MaximalBlocks, IsPrimitive, Stabilizer,
  590.   RepresentativeOperation, RepresentativesOperation, IsEquivalentOperation );
  591.  
  592. AUTO( ReadLib( "permag" ),
  593.   MaximalBlocksPGroup, OrderFactorGroupElement, InsertStabChain,
  594.   ClosureNormalizingElementPermGroup, ExtendElementaryAbelianSeriesPermGroup,
  595.   BaseStrongSubnormalGeneratingSetPPermGroup, ExponentsPermSolvablePermGroup,
  596.   PcPresentationPermGroup, CompositionSeriesSolvablePermGroup,
  597.   SubnormalSeriesPPermGroup, CentralCompositionSeriesPPermGroup );
  598.  
  599. AUTO( ReadLib( "permcose" ),
  600.   RightCosetPermGroupOps, PermRefinedChain, MainEntryCCEPermGroup );
  601.  
  602. AUTO( ReadLib( "permcser" ),
  603.   CompositionSeriesPermGroup, NonPerfectCSPG, PerfectCSPG, CasesCSPG,
  604.   FindNormalCSPG, NinKernelCSPG, RegularNinKernelCSPG, NormalizerStabCSPG,
  605.   TransStabCSPG, PullbackKernelCSPG, PullbackCSPG, CosetRepAsWord,
  606.   ImageInWord, SiftAsWord, InverseAsWord, RandomElmAsWord,
  607.   CentralizerNormalCSPG, CentralizerNormalTransCSPG, CentralizerTransSymmCSPG,
  608.   IntersectionNormalClosurePermGroup, ActionAbelianCSPG, ImageOnAbelianCSPG );
  609.  
  610. AUTO( ReadLib( "permctbl" ),
  611.   IdentificationPermGroup, RationalIdentificationPermGroup, FingerprintPerm );
  612.  
  613. AUTO( ReadLib( "permgrp" ),
  614.   IsPermGroup, PermGroupOps, SC_level, ReduceStabChain, ExtendStabChain,
  615.   MakeStabChain, MakeStabChainStrongGenerators, MakeStabChainRandom,
  616.   ListStabChain, ConjugacyClassPermGroupOps );
  617.  
  618. AUTO( ReadLib( "permhomo" ),
  619.   PermGroupHomomorphismByImagesOps, TransConstHomomorphismOps,
  620.   BlocksHomomorphismOps );
  621.  
  622. AUTO( ReadLib( "permnorm" ),
  623.   SortedOrbitsButler, SortedOrbitsPermGroup, BaseForNormalizerPermGroup,
  624.   SigmaSets );
  625.  
  626. AUTO( ReadLib( "permprod" ),
  627.   DirectProductPermGroupOps, EmbeddingDirectProductPermGroupOps,
  628.   ProjectionDirectProductPermGroupOps );
  629.  
  630. AUTO( ReadLib( "permutat" ),
  631.   PermutationsOps, Permutations, CycleStructurePerm, SmallestMovedPointPerm,
  632.   ListPerm, MappingPermListList, RestrictedPerm );
  633.  
  634. AUTO( ReadLib( "polyfin" ),
  635.   FiniteFieldPolynomialRingOps, FiniteFieldLaurentPolynomials,
  636.   FiniteFieldLaurentPolynomialsOps, FiniteFieldPolynomials,
  637.   FiniteFieldPolynomialsOps, FiniteFieldPolynomialOps, PrimePowersInt,
  638.   ProductPP, LcmPP, OrderKnownDividendList );
  639.  
  640. AUTO( ReadLib( "polyfld" ),
  641.   FieldPolynomialRingOps, FieldLaurentPolynomialRingOps );
  642.  
  643. AUTO( ReadLib( "polynom" ),
  644.   Polynomial, IsPolynomial, CompanionMatrix, EmbeddedPolynomial, RandomPol,
  645.   Value, Indeterminate, X, LaurentPolynomialRing, IsLaurentPolynomialRing,
  646.   LaurentPolynomialRingOps, Derivative, PolynomialRing, IsPolynomialRing,
  647.   PolynomialRingOps, LaurentPolynomials, LaurentPolynomialsOps, Polynomials,
  648.   PolynomialsOps, PolynomialOps, Degree, LeadingCoefficient,
  649.   DisplayPolynomial );
  650.  
  651. AUTO( ReadLib( "polyrat" ),
  652.   RationalsPolynomialOps, RationalsPolynomials, RationalsPolynomialsOps,
  653.   LandauMignotteBoundGcd, LandauMignotteBound );
  654.  
  655. AUTO( ReadLib( "pq" ),
  656.   PQpOps, PQp, SavePQp, InitPQp, AddGeneratorsPQp, DefineGeneratorsPQp,
  657.   TailsPQp, EchelonizePQp, ConsistencyPQp, ElimTailsPQp, LiftHomomorphismPQp,
  658.   CleanUpPQp, FirstClassPQp, PQuotient, pQuotient, PrimeQuotient,
  659.   NextClassPQp, Weight );
  660.  
  661. AUTO( ReadLib( "rational" ),
  662.   RationalsOps, Rationals, RationalsAsRingOps );
  663.  
  664. AUTO( ReadLib( "recsl" ),
  665.   RecSL, PossibleBlockSizes, SporadicGroupsInfo, RecognizeSL );
  666.  
  667. AUTO( ReadLib( "ring" ),
  668.   IsRing, RingOps, IsCommutativeRing, IsIntegralRing,
  669.   IsUniqueFactorizationRing, IsEuclideanRing, Quotient, IsUnit, Units,
  670.   IsAssociated, StandardAssociate, Associates, IsIrreducible, IsPrime,
  671.   Factors, EuclideanDegree, Mod, QuotientMod, PowerMod, Gcd,
  672.   GcdRepresentation, Lcm, RingElementsOps, RingElements, Ring, DefaultRing,
  673.   AsRing );
  674.  
  675. AUTO( ReadLib( "rowmodul" ),
  676.   RowModuleOps, RowModule, IsRowModule, Submodule, Representation,
  677.   ProperSubmodule );
  678.  
  679. AUTO( ReadLib( "rowspace" ),
  680.   IntegerTable, RowSpace, IsRowSpace, RowSpaceOps, BaseTypeRowSpace,
  681.   SiftedVector, ModspaceOps );
  682.  
  683. AUTO( ReadLib( "string" ),
  684.   StringInt, StringRat, StringCyc, StringFFE, StringPerm, StringAgWord,
  685.   StringBool, StringList, StringRec, String, PrintArray, PrintRecIgnore,
  686.   PrintRecIndent, RecordOps, PrintRec, DaysInYear, DaysInMonth, DMYDay,
  687.   DayDMY, NameWeekDay, WeekDay, NameMonth, StringDate, HMSMSec, SecHMSM,
  688.   StringTime, StringPP, Ordinal );
  689.  
  690. AUTO( ReadLib( "tom" ),
  691.   IsTom, TableOfMarks, Marks, NrSubs, WeightsTom, TomMat, MatTom,
  692.   DecomposedFixedPointVector, TestRow, TestTom, DisplayTom, NormalizerTom,
  693.   IntersectionsTom, IsCyclicTom, PermCharsTom, FusionCharTableTom, MoebiusTom,
  694.   CyclicExtensionsTom, IdempotentsTom, ClassTypesTom, ClassNamesTom,
  695.   TomCyclic, TomDihedral, TomFrobenius );
  696.  
  697. AUTO( ReadLib( "vecspace" ),
  698.   VectorSpace, IsVectorSpace, VectorSpaceOps, IsSubspace, Base, AddBase,
  699.   Dimension, Information, Coefficients, LinearCombination, Enumeration,
  700.   LineEnumeration, NormedVector );
  701.  
  702. AUTO( ReadGrp( "basic" ),
  703.   CyclicGroup, AbelianGroup, ElementaryAbelianGroup, DihedralGroup,
  704.   PolyhedralGroup, AlternatingGroup, SymmetricGroup, GeneralLinearGroup,
  705.   SpecialLinearGroup, SymplecticGroup, GeneralUnitaryGroup,
  706.   SpecialUnitaryGroup );
  707.  
  708. AUTO( ReadGrp( "matgrp" ),
  709.   MatGroupLib, SpecialLinearMatGroup, GeneralLinearMatGroup,
  710.   SymplecticMatGroup, GeneralUnitaryMatGroup, SpecialUnitaryMatGroup );
  711.  
  712. AUTO( ReadGrp( "permgrp" ),
  713.   PermGroupLib, CyclicPermGroup, AbelianPermGroup, ElementaryAbelianPermGroup,
  714.   DihedralPermGroup, PolyhedralPermGroup, AlternatingPermGroup,
  715.   AlternatingPermGroupOps, SymmetricPermGroup, SymmetricPermGroupOps );
  716.  
  717. AUTO( ReadGrp( "primitiv" ),
  718.   PGGens, FAC, PGTable, PG, PrimitiveGroup, AllPrimitiveGroups,
  719.   OnePrimitiveGroup );
  720.  
  721. AUTO( ReadGrp( "solvable" ),
  722.   AGTable, AGGroup, SolvableGroup, IsNontrivialDirectProduct,
  723.   AllSolvableGroups, OneSolvableGroup );
  724.  
  725. AUTO( ReadTwo( "twogp" ),
  726.   TGParts, TGLoad, TGGroup, TwoGroup, Rank, pClass, AllTwoGroups, OneTwoGroup );
  727.  
  728. AUTO( ReadThr( "thrgp" ),
  729.   ThGParts, ThGLoad, ThGGroup, ThreeGroup, AllThreeGroups, OneThreeGroup );
  730.  
  731. AUTO( ReadTbl( "ctprimar" ),
  732.   GALOIS, TENSOR, MBT, EvalChars, LowercaseString, FirstNameCharTable,
  733.   FileNameCharTable, PrintText, BlanklessPrint, ShrinkChars, PrintToLib,
  734.   ConstructMixed, ConstructProj, BrauerTree, DecMat, BasicSetBrauerTree,
  735.   AddDecMats, PartsBrauerTableName, BrauerTable, CharTableLibrary,
  736.   NotifyCharTable, NotifyCharTableName, MakeLIBLIST );
  737.  
  738. AUTO( ReadTom( "tmprimar" ),
  739.   TOM, TOMLIST, TomLibrary );
  740.  
  741.