#SIXFORMAT  GapDocGAP
HELPBOOKINFOSIXTMP := rec(
encoding := "UTF-8",
bookname := "HAPprime Datatypes",
entries :=
[ [ "Title page", "", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" ], 
  [ "Copyright", "-1", [ 0, 0, 1 ], 30, 2, "copyright", "X81488B807F2A1CF1" ],
  [ "Acknowledgements", "-2", [ 0, 0, 2 ], 56, 2, "acknowledgements", 
      "X82A988D47DFAFCFA" ], 
  [ "Table of Contents", "-3", [ 0, 0, 3 ], 62, 3, "table of contents", 
      "X8537FEB07AF2BEC8" ], 
  [ "\033[1XIntroduction\033[0X", "1", [ 1, 0, 0 ], 1, 8, "introduction", 
      "X7DFB63A97E67C0A1" ], 
  [ "\033[1XResolutions\033[0X", "2", [ 2, 0, 0 ], 1, 9, "resolutions", 
      "X7C0B125E7D5415B4" ], 
  [ "\033[1XThe \033[9XHAPResolution\033[1X datatype in \033[5XHAPprime\033[1X\
\033[0X", "2.1", [ 2, 1, 0 ], 14, 9, "the hapresolution datatype in happrime",
      "X86DA1C1B7EDE0DD8" ], 
  [ "\033[1XImplementation: Constructing resolutions\033[0X", "2.2", 
      [ 2, 2, 0 ], 29, 9, "implementation: constructing resolutions", 
      "X7D3C5D987DEB2360" ], 
  [ "\033[1XResolution construction functions\033[0X", "2.3", [ 2, 3, 0 ], 
      81, 10, "resolution construction functions", "X7D61ADD17A4CF194" ], 
  [ "\033[1XResolution data access functions\033[0X", "2.4", [ 2, 4, 0 ], 
      118, 11, "resolution data access functions", "X84AD05E17FA85CB1" ], 
  [ "\033[1XExample: Computing and working with resolutions\033[0X", "2.5", 
      [ 2, 5, 0 ], 175, 12, "example: computing and working with resolutions",
      "X81D7C767813647B3" ], 
  [ "\033[1XMiscellaneous resolution functions\033[0X", "2.6", [ 2, 6, 0 ], 
      256, 13, "miscellaneous resolution functions", "X79487D6C80383A6A" ], 
  [ "\033[1XGraded algebras\033[0X", "3", [ 3, 0, 0 ], 1, 14, 
      "graded algebras", "X8074AAF07A3E7D2C" ], 
  [ "\033[1XGraded algebras in \033[5XHAP\033[1X (and \033[5XHAPprime\033[1X)\
\033[0X", "3.1", [ 3, 1, 0 ], 20, 14, "graded algebras in hap and happrime", 
      "X844F0654822DAFCC" ], 
  [ "\033[1XData access functions\033[0X", "3.2", [ 3, 2, 0 ], 36, 14, 
      "data access functions", "X7DE3278D7E5DEE03" ], 
  [ "\033[1XOther functions\033[0X", "3.3", [ 3, 3, 0 ], 89, 15, 
      "other functions", "X87C3D1B984960984" ], 
  [ "\033[1XExample: Graded algebras and mod-p cohomology rings\033[0X", 
      "3.4", [ 3, 4, 0 ], 106, 16, 
      "example: graded algebras and mod-p cohomology rings", 
      "X790D62E37AA53C39" ], 
  [ "\033[1XPresentations of graded algebras\033[0X", "4", [ 4, 0, 0 ], 1, 
      17, "presentations of graded algebras", "X7CF4153B7903F639" ], 
  [ "\033[1XThe \033[9XGradedAlgebraPresentation\033[1X datatype\033[0X", 
      "4.1", [ 4, 1, 0 ], 15, 17, "the gradedalgebrapresentation datatype", 
      "X7F7903AE8392D54A" ], 
  [ "\033[1XConstruction function\033[0X", "4.2", [ 4, 2, 0 ], 29, 17, 
      "construction function", "X8589CD117D1ECD29" ], 
  [ "\033[1XGradedAlgebraPresentation construction functions\033[0X", 
      "4.2-1", [ 4, 2, 1 ], 32, 17, 
      "gradedalgebrapresentation construction functions", "X84A14CBF7C499665" 
     ], [ "\033[1XData access functions\033[0X", "4.3", [ 4, 3, 0 ], 48, 18, 
      "data access functions", "X7DE3278D7E5DEE03" ], 
  [ "\033[1XExample: Constructing and accessing data of a \033[9XGradedAlgebra\
Presentation\033[1X\033[0X", "4.3-7", [ 4, 3, 7 ], 99, 18, 
      "example: constructing and accessing data of a gradedalgebrapresentation\
", "X7DB98FC5869F4CBC" ], 
  [ "\033[1XOther functions\033[0X", "4.4", [ 4, 4, 0 ], 123, 19, 
      "other functions", "X87C3D1B984960984" ], 
  [ "\033[1XTensorProduct\033[0X", "4.4-1", [ 4, 4, 1 ], 126, 19, 
      "tensorproduct", "X87EB0B4A852CF4C6" ], 
  [ "\033[1XSubspaceDimensionDegree\033[0X", "4.4-6", [ 4, 4, 6 ], 174, 20, 
      "subspacedimensiondegree", "X7EF085B67B846215" ], 
  [ "\033[1XSubspaceBasisRepsByDegree\033[0X", "4.4-7", [ 4, 4, 7 ], 184, 20, 
      "subspacebasisrepsbydegree", "X7834EE487CAA02D4" ], 
  [ "\033[1XExample: Computing the Lyndon-Hoschild-Serre spectral sequence and\
 mod-p\033[0X \033[1Xcohomology ring for a small p-group\033[0X", "4.5", 
      [ 4, 5, 0 ], 268, 21, 
      "example: computing the lyndon-hoschild-serre spectral sequence and mod-\
p cohomology ring for a small p-group", "X87DD66E67D0D5485" ], 
  [ "\033[1XFG-modules\033[0X", "5", [ 5, 0, 0 ], 1, 23, "fg-modules", 
      "X820435E87D83DF34" ], 
  [ "\033[1XThe \033[9XFpGModuleGF\033[1X datatype\033[0X", "5.1", 
      [ 5, 1, 0 ], 8, 23, "the fpgmodulegf datatype", "X85FA0B237AC4A19D" ], 
  [ "\033[1XImplementation details: Block echelon form\033[0X", "5.2", 
      [ 5, 2, 0 ], 71, 24, "implementation details: block echelon form", 
      "X79DF42E686679AFE" ], 
  [ "\033[1XGenerating vectors and their block structure\033[0X", "5.2-1", 
      [ 5, 2, 1 ], 74, 24, "generating vectors and their block structure", 
      "X79DDD8C37A0B8425" ], 
  [ "\033[1XMatrix echelon reduction and head elements\033[0X", "5.2-2", 
      [ 5, 2, 2 ], 101, 24, "matrix echelon reduction and head elements", 
      "X82F0E0067C40FDD5" ], 
  [ "\033[1XEchelon block structure and minimal generators\033[0X", "5.2-3", 
      [ 5, 2, 3 ], 127, 25, "echelon block structure and minimal generators", 
      "X814C05FC87ED4035" ], 
  [ "\033[1XIntersection of two modules\033[0X", "5.2-4", [ 5, 2, 4 ], 223, 
      26, "intersection of two modules", "X86F4852785A509BF" ], 
  [ "\033[1XConstruction functions\033[0X", "5.3", [ 5, 3, 0 ], 277, 27, 
      "construction functions", "X83D8009086035BCB" ], 
  [ "\033[1XFpGModuleGF construction functions\033[0X", "5.3-1", [ 5, 3, 1 ], 
      280, 27, "fpgmodulegf construction functions", "X862AC894821415A4" ], 
  [ "\033[1XExample: Constructing a \033[9XFpGModuleGF\033[1X\033[0X", 
      "5.3-5", [ 5, 3, 5 ], 364, 29, "example: constructing a fpgmodulegf", 
      "X814553E382BC777E" ], 
  [ "\033[1XData access functions\033[0X", "5.4", [ 5, 4, 0 ], 424, 30, 
      "data access functions", "X7DE3278D7E5DEE03" ], 
  [ "\033[1XExample: Accessing data about a \033[9XFpGModuleGF\033[1X\033[0X",
      "5.4-11", [ 5, 4, 11 ], 543, 32, 
      "example: accessing data about a fpgmodulegf", "X7E4C3C5C7CC7B559" ], 
  [ "\033[1XGenerator and vector space functions\033[0X", "5.5", [ 5, 5, 0 ], 
      598, 33, "generator and vector space functions", "X85D634767E456A9D" ], 
  [ "\033[1XMinimalGeneratorsModule\033[0X", "5.5-9", [ 5, 5, 9 ], 710, 34, 
      "minimalgeneratorsmodule", "X81C340AD7EE8FA63" ], 
  [ "\033[1XExample: Generators and basis vectors of a \033[9XFpGModuleGF\033[\
1X\033[0X", "5.5-11", [ 5, 5, 11 ], 749, 35, 
      "example: generators and basis vectors of a fpgmodulegf", 
      "X7F9E3DF87FE60C1A" ], 
  [ "\033[1XBlock echelon functions\033[0X", "5.6", [ 5, 6, 0 ], 823, 36, 
      "block echelon functions", "X7B989D1181EBBBB5" ], 
  [ "\033[1XExample: Converting a \033[9XFpGModuleGF\033[1X to block echelon f\
orm\033[0X", "5.6-3", [ 5, 6, 3 ], 898, 38, 
      "example: converting a fpgmodulegf to block echelon form", 
      "X83306CFA857F177C" ], 
  [ "\033[1XSum and intersection functions\033[0X", "5.7", [ 5, 7, 0 ], 975, 
      39, "sum and intersection functions", "X7B22D74482E6EF40" ], 
  [ "\033[1XDirectSumOfModules\033[0X", "5.7-1", [ 5, 7, 1 ], 978, 39, 
      "directsumofmodules", "X879541298181840D" ], 
  [ "\033[1XExample: Sum and intersection of \033[9XFpGModuleGF\033[1Xs\033[0X\
", "5.7-5", [ 5, 7, 5 ], 1071, 41, 
      "example: sum and intersection of fpgmodulegfs", "X8198B7C986776BA8" ], 
  [ "\033[1XMiscellaneous functions\033[0X", "5.8", [ 5, 8, 0 ], 1141, 42, 
      "miscellaneous functions", "X8308D685809A4E2F" ], 
  [ "\033[1XIsModuleElement\033[0X", "5.8-2", [ 5, 8, 2 ], 1155, 42, 
      "ismoduleelement", "X78EB919D85362902" ], 
  [ "\033[1XRandom Submodule\033[0X", "5.8-5", [ 5, 8, 5 ], 1187, 43, 
      "random submodule", "X84EB237885A48F03" ], 
  [ "\033[1XFG-module homomorphisms\033[0X", "6", [ 6, 0, 0 ], 1, 44, 
      "fg-module homomorphisms", "X82F28552819A6542" ], 
  [ "\033[1XThe \033[9XFpGModuleHomomorphismGF\033[1X datatype\033[0X", 
      "6.1", [ 6, 1, 0 ], 4, 44, "the fpgmodulehomomorphismgf datatype", 
      "X85481E577D3BAB8E" ], 
  [ "\033[1XCalculating the kernel of a FG-module homorphism by splitting into\
 two\033[0X \033[1Xhomomorphisms\033[0X", "6.2", [ 6, 2, 0 ], 24, 44, 
      "calculating the kernel of a fg-module homorphism by splitting into two \
homomorphisms", "X83FF0EBD81A405A9" ], 
  [ "\033[1XCalculating the kernel of a FG-module homorphism by column reducti\
on and\033[0X \033[1Xpartitioning\033[0X", "6.3", [ 6, 3, 0 ], 83, 45, 
      "calculating the kernel of a fg-module homorphism by column reduction an\
d partitioning", "X8356C3B680B7110E" ], 
  [ "\033[1XConstruction functions\033[0X", "6.4", [ 6, 4, 0 ], 145, 46, 
      "construction functions", "X83D8009086035BCB" ], 
  [ "\033[1XFpGModuleHomomorphismGF construction functions\033[0X", "6.4-1", 
      [ 6, 4, 1 ], 148, 46, "fpgmodulehomomorphismgf construction functions", 
      "X8640D133855BB892" ], 
  [ "\033[1XExample: Constructing a \033[9XFpGModuleHomomorphismGF\033[1X\033[\
0X", "6.4-2", [ 6, 4, 2 ], 175, 46, 
      "example: constructing a fpgmodulehomomorphismgf", "X7EA7C568836E9730" ]
    , [ "\033[1XData access functions\033[0X", "6.5", [ 6, 5, 0 ], 192, 47, 
      "data access functions", "X7DE3278D7E5DEE03" ], 
  [ "\033[1XExample: Accessing data about a \033[9XFpGModuleHomomorphismGF\033\
[1X\033[0X", "6.5-7", [ 6, 5, 7 ], 246, 48, 
      "example: accessing data about a fpgmodulehomomorphismgf", 
      "X7C5F52FE80BB871A" ], 
  [ "\033[1XImage and kernel functions\033[0X", "6.6", [ 6, 6, 0 ], 300, 49, 
      "image and kernel functions", "X79444C767921055C" ], 
  [ "\033[1XImageOfModuleHomomorphism\033[0X", "6.6-1", [ 6, 6, 1 ], 303, 49, 
      "imageofmodulehomomorphism", "X8038F50582425ECA" ], 
  [ "\033[1XPreImageRepresentativeOfModuleHomomorphism\033[0X", "6.6-2", 
      [ 6, 6, 2 ], 327, 49, "preimagerepresentativeofmodulehomomorphism", 
      "X850FD5AE80BF6F11" ], 
  [ "\033[1XExample: Kernel and Image of a \033[9XFpGModuleHomomorphismGF\033[\
1X\033[0X", "6.6-4", [ 6, 6, 4 ], 401, 50, 
      "example: kernel and image of a fpgmodulehomomorphismgf", 
      "X795D4069832F15F8" ], 
  [ "\033[1XRing homomorphisms\033[0X", "7", [ 7, 0, 0 ], 1, 52, 
      "ring homomorphisms", "X7E88C32A82E942DA" ], 
  [ "\033[1XThe \033[9XHAPRingHomomorphism\033[1X datatype\033[0X", "7.1", 
      [ 7, 1, 0 ], 12, 52, "the hapringhomomorphism datatype", 
      "X7A0B792785E2AA8A" ], 
  [ "\033[1XImplementation details\033[0X", "7.1-1", [ 7, 1, 1 ], 38, 52, 
      "implementation details", "X7AB84A0B83B2C1F1" ], 
  [ "\033[1XElimination orderings\033[0X", "7.1-2", [ 7, 1, 2 ], 55, 53, 
      "elimination orderings", "X7AB0F3977DC63F54" ], 
  [ "\033[1XConstruction functions\033[0X", "7.2", [ 7, 2, 0 ], 106, 54, 
      "construction functions", "X83D8009086035BCB" ], 
  [ "\033[1XHAPSubringToRingHomomorphism\033[0X", "7.2-2", [ 7, 2, 2 ], 120, 
      54, "hapsubringtoringhomomorphism", "X7A7E46337D6F47B6" ], 
  [ "\033[1XData access functions\033[0X", "7.3", [ 7, 3, 0 ], 216, 55, 
      "data access functions", "X7DE3278D7E5DEE03" ], 
  [ "\033[1XGeneral functions\033[0X", "7.4", [ 7, 4, 0 ], 265, 56, 
      "general functions", "X7B65E0C37AAB6066" ], 
  [ "\033[1XImageOfRingHomomorphism\033[0X", "7.4-1", [ 7, 4, 1 ], 268, 56, 
      "imageofringhomomorphism", "X8680F51E82EA1939" ], 
  [ "\033[1XPreimageOfRingHomomorphism\033[0X", "7.4-2", [ 7, 4, 2 ], 279, 
      57, "preimageofringhomomorphism", "X7B1B2C0980375531" ], 
  [ "\033[1XExample: Constructing and using a \033[9XHAPRingHomomorphism\033[1\
X\033[0X", "7.5", [ 7, 5, 0 ], 291, 57, 
      "example: constructing and using a hapringhomomorphism", 
      "X7A00ADEE8679D3AD" ], 
  [ "\033[1XDerivations\033[0X", "8", [ 8, 0, 0 ], 1, 59, "derivations", 
      "X80C0FB5A7B72B145" ], 
  [ "\033[1XThe \033[9XHAPDerivation\033[1X datatype\033[0X", "8.1", 
      [ 8, 1, 0 ], 17, 59, "the hapderivation datatype", "X86F29D447B67B28F" ]
    , [ "\033[1XComputing the kernel and homology of a derivation\033[0X", 
      "8.2", [ 8, 2, 0 ], 42, 59, 
      "computing the kernel and homology of a derivation", 
      "X85F99EEF86DD595D" ], 
  [ "\033[1XConstruction function\033[0X", "8.3", [ 8, 3, 0 ], 90, 60, 
      "construction function", "X8589CD117D1ECD29" ], 
  [ "\033[1XHAPDerivation construction functions\033[0X", "8.3-1", 
      [ 8, 3, 1 ], 93, 60, "hapderivation construction functions", 
      "X7B8058948424E639" ], 
  [ "\033[1XData access function\033[0X", "8.4", [ 8, 4, 0 ], 108, 60, 
      "data access function", "X789E616983759E10" ], 
  [ "\033[1XExample: Constructing and accessing data of a \033[9XHAPDerivation\
\033[1X\033[0X", "8.4-4", [ 8, 4, 4 ], 137, 61, 
      "example: constructing and accessing data of a hapderivation", 
      "X84A549558235F536" ], 
  [ "\033[1XImage, kernel and homology functions\033[0X", "8.5", [ 8, 5, 0 ], 
      158, 61, "image kernel and homology functions", "X7956001A816B2507" ], 
  [ "\033[1XExample: Homology of a \033[9XHAPDerivation\033[1X\033[0X", 
      "8.5-4", [ 8, 5, 4 ], 212, 62, "example: homology of a hapderivation", 
      "X78B45E8C86F90981" ], 
  [ "\033[1XPoincar\303\251 series\033[0X", "9", [ 9, 0, 0 ], 1, 64, 
      "poincara\251 series", "X7FF2605B79D7B5F8" ], 
  [ "\033[1XComputing the Poincar\303\251 series using spectral sequences\033[\
0X", "9.1", [ 9, 1, 0 ], 15, 64, 
      "computing the poincara\251 series using spectral sequences", 
      "X872F597F7AACA402" ], 
  [ "\033[1XComputing the Poincar\303\251 series using a minimal resolution\
\033[0X", "9.2", [ 9, 2, 0 ], 27, 64, 
      "computing the poincara\251 series using a minimal resolution", 
      "X7978D58181D2725F" ], 
  [ "\033[1XExample Poincar\303\251 series computations\033[0X", "9.3", 
      [ 9, 3, 0 ], 79, 65, "example poincara\251 series computations", 
      "X82A90FCC80BAC1F9" ], 
  [ "\033[1XThe Poincar\303\251 series of groups of order 64 and 128\033[0X", 
      "9.4", [ 9, 4, 0 ], 112, 66, 
      "the poincara\251 series of groups of order 64 and 128", 
      "X84E1A5148674E7E0" ], 
  [ "\033[1XGeneral Functions\033[0X", "10", [ 10, 0, 0 ], 1, 67, 
      "general functions", "X7B65E0C37AAB6066" ], 
  [ "\033[1XMatrices\033[0X", "10.1", [ 10, 1, 0 ], 9, 67, "matrices", 
      "X812CCAB278643A59" ], 
  [ "\033[1XExample: matrices and vector spaces\033[0X", "10.1-5", 
      [ 10, 1, 5 ], 84, 68, "example: matrices and vector spaces", 
      "X8080767383F9EF31" ], 
  [ "\033[1XPolynomials\033[0X", "10.2", [ 10, 2, 0 ], 108, 69, 
      "polynomials", "X826D8334845549EC" ], 
  [ "\033[1XReduceIdeal\033[0X", "10.2-6", [ 10, 2, 6 ], 163, 69, 
      "reduceideal", "X87DE84AC7B62DC5C" ], 
  [ "\033[1XExample: monomials, polynomials and ring presentations\033[0X", 
      "10.2-8", [ 10, 2, 8 ], 197, 70, 
      "example: monomials polynomials and ring presentations", 
      "X7F8D0B27815DDA6B" ], 
  [ "\033[1XSingular\033[0X", "10.3", [ 10, 3, 0 ], 253, 71, "singular", 
      "X840A7A5D7AE407F2" ], 
  [ "\033[1XGroups\033[0X", "10.4", [ 10, 4, 0 ], 309, 72, "groups", 
      "X8716635F7951801B" ], 
  [ "\033[1XHallSeniorNumber\033[0X", "10.4-1", [ 10, 4, 1 ], 320, 72, 
      "hallseniornumber", "X7FD16926859DD49B" ], 
  [ "Index", "ind", [ "Ind", 0, 0 ], 1, 73, "index", "X83A0356F839C696F" ], 
  [ "\033[2XLengthOneResolutionPrimePowerGroup\033[0X", "2.3-1", [ 2, 3, 1 ], 
      84, 10, "lengthoneresolutionprimepowergroup", "X784BCF7C801B6E8E" ], 
  [ "\033[2XLengthZeroResolutionPrimePowerGroup\033[0X", "2.3-2", 
      [ 2, 3, 2 ], 100, 10, "lengthzeroresolutionprimepowergroup", 
      "X8311B9697B5F7685" ], 
  [ "\033[2XResolutionLength\033[0X", "2.4-1", [ 2, 4, 1 ], 121, 11, 
      "resolutionlength", "X83F7747D8585608C" ], 
  [ "\033[2XResolutionGroup\033[0X", "2.4-2", [ 2, 4, 2 ], 128, 11, 
      "resolutiongroup", "X806048907CE5B7B6" ], 
  [ "\033[2XResolutionFpGModuleGF\033[0X", "2.4-3", [ 2, 4, 3 ], 135, 11, 
      "resolutionfpgmodulegf", "X7FF354AC7EEE2197" ], 
  [ "\033[2XResolutionModuleRank\033[0X", "2.4-4", [ 2, 4, 4 ], 143, 11, 
      "resolutionmodulerank", "X7AFBE74B85AC3D85" ], 
  [ "\033[2XResolutionModuleRanks\033[0X", "2.4-5", [ 2, 4, 5 ], 150, 11, 
      "resolutionmoduleranks", "X7EBA188478844D96" ], 
  [ "\033[2XBoundaryFpGModuleHomomorphismGF\033[0X", "2.4-6", [ 2, 4, 6 ], 
      158, 11, "boundaryfpgmodulehomomorphismgf", "X803528CD872A1F4C" ], 
  [ "\033[2XResolutionsAreEqual\033[0X", "2.4-7", [ 2, 4, 7 ], 167, 11, 
      "resolutionsareequal", "X7FB150F67DAF9059" ], 
  [ "\033[2XBestCentralSubgroupForResolutionFiniteExtension\033[0X", "2.6-1", 
      [ 2, 6, 1 ], 259, 13, "bestcentralsubgroupforresolutionfiniteextension",
      "X7AB2536286A7324D" ], 
  [ "\033[2XModPRingGeneratorDegrees\033[0X", "3.2-1", [ 3, 2, 1 ], 39, 14, 
      "modpringgeneratordegrees", "X78ED069183AD3EEA" ], 
  [ "\033[2XModPRingNiceBasis\033[0X", "3.2-2", [ 3, 2, 2 ], 49, 15, 
      "modpringnicebasis", "X780F21707FB7EFF4" ], 
  [ "\033[2XModPRingNiceBasisAsPolynomials\033[0X", "3.2-3", [ 3, 2, 3 ], 66, 
      15, "modpringnicebasisaspolynomials", "X7F40E8DA7AEC5CDC" ], 
  [ "\033[2XModPRingBasisAsPolynomials\033[0X", "3.2-4", [ 3, 2, 4 ], 78, 15, 
      "modpringbasisaspolynomials", "X7E72445386B555DD" ], 
  [ "\033[2XPresentationOfGradedStructureConstantAlgebra\033[0X", "3.3-1", 
      [ 3, 3, 1 ], 92, 15, "presentationofgradedstructureconstantalgebra", 
      "X79C71A2F878358BB" ], 
  [ "\033[2XGradedAlgebraPresentation\033[0X", "4.2-1", [ 4, 2, 1 ], 32, 17, 
      "gradedalgebrapresentation", "X84A14CBF7C499665" ], 
  [ "\033[2XGradedAlgebraPresentationNC\033[0X", "4.2-1", [ 4, 2, 1 ], 32, 
      17, "gradedalgebrapresentationnc", "X84A14CBF7C499665" ], 
  [ "\033[2XBaseRing\033[0X", "4.3-1", [ 4, 3, 1 ], 51, 18, "basering", 
      "X877889A5792202F7" ], 
  [ "\033[2XCoefficientsRing\033[0X", "4.3-2", [ 4, 3, 2 ], 58, 18, 
      "coefficientsring", "X8235D10781BE8003" ], 
  [ "\033[2XIndeterminatesOfGradedAlgebraPresentation\033[0X", "4.3-3", 
      [ 4, 3, 3 ], 65, 18, "indeterminatesofgradedalgebrapresentation", 
      "X844BB80282EA3EBA" ], 
  [ "\033[2XGeneratorsOfPresentationIdeal\033[0X", "4.3-4", [ 4, 3, 4 ], 72, 
      18, "generatorsofpresentationideal", "X84299C5A7ACD6F71" ], 
  [ "\033[2XPresentationIdeal\033[0X", "4.3-5", [ 4, 3, 5 ], 81, 18, 
      "presentationideal", "X7DABCC1D85B33DAC" ], 
  [ "\033[2XIndeterminateDegrees\033[0X", "4.3-6", [ 4, 3, 6 ], 89, 18, 
      "indeterminatedegrees", "X7BFB8AC97FE6BDD6" ], 
  [ "\033[2XTensorProduct\033[0X (for two algebra presentations)", "4.4-1", 
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