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[ [ "Title page", ".", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" ], 
  [ "Copyright", ".-1", [ 0, 0, 1 ], 41, 2, "copyright", "X81488B807F2A1CF1" ], 
  [ "Table of Contents", ".-2", [ 0, 0, 2 ], 49, 3, "table of contents", "X8537FEB07AF2BEC8" ], 
  [ "\033[1XIntroduction\033[0X", "1", [ 1, 0, 0 ], 1, 11, "introduction", "X7DFB63A97E67C0A1" ], 
  [ "\033[1XWhat is the role of the \033[5XMatricesForHomalg\033[1X package in the \033[5Xhomalg\033[1X project?\033[0X", "1.1", 
      [ 1, 1, 0 ], 4, 11, "what is the role of the matricesforhomalg package in the homalg project?", "X878AE2517B963434" ], 
  [ "\033[1X\033[5XMatricesForHomalg\033[1X provides ...\033[0X", "1.1-1", [ 1, 1, 1 ], 7, 11, "matricesforhomalg provides ...", 
      "X81B1923E82145E72" ], [ "\033[1X\033[5Xhomalg\033[1X delegates ...\033[0X", "1.1-2", [ 1, 1, 2 ], 20, 11, "homalg delegates ...", 
      "X856DCAA4846FBB00" ], [ "\033[1XThe black box concept\033[0X", "1.1-3", [ 1, 1, 3 ], 79, 12, "the black box concept", 
      "X808E7BA97C5EA311" ], [ "\033[1XThis manual\033[0X", "1.2", [ 1, 2, 0 ], 105, 12, "this manual", "X78DD800B83ABC621" ], 
  [ "\033[1XInstallation of the \033[5XMatricesForHomalg\033[1X Package\033[0X", "2", [ 2, 0, 0 ], 1, 13, 
      "installation of the matricesforhomalg package", "X8609DF5282514B96" ], 
  [ "\033[1XRings\033[0X", "3", [ 3, 0, 0 ], 1, 14, "rings", "X81897F6082CACB59" ], 
  [ "\033[1XRings: Category and Representations\033[0X", "3.1", [ 3, 1, 0 ], 4, 14, "rings: category and representations", 
      "X8252B2F483D80E41" ], [ "\033[1XRings: Constructors\033[0X", "3.2", [ 3, 2, 0 ], 68, 15, "rings: constructors", "X7C7962B97E6CDFE2" 
     ], [ "\033[1XRings: Properties\033[0X", "3.3", [ 3, 3, 0 ], 164, 16, "rings: properties", "X7D171A1C797E27C9" ], 
  [ "\033[1XRings: Attributes\033[0X", "3.4", [ 3, 4, 0 ], 535, 23, "rings: attributes", "X867290E7847A5101" ], 
  [ "\033[1XRings: Operations and Functions\033[0X", "3.5", [ 3, 5, 0 ], 709, 26, "rings: operations and functions", "X7DDAB86C7A7FEDA9" ],
  [ "\033[1XRing Maps\033[0X", "4", [ 4, 0, 0 ], 1, 27, "ring maps", "X7B222197819984A6" ], 
  [ "\033[1XRing Maps: Category and Representations\033[0X", "4.1", [ 4, 1, 0 ], 10, 27, "ring maps: category and representations", 
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      "X8717AEFB7BAC63F7" ], [ "\033[1XRing Maps: Properties\033[0X", "4.3", [ 4, 3, 0 ], 55, 28, "ring maps: properties", 
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      "ring maps: operations and functions", "X7C7401BA7E2221CB" ], [ "\033[1XMatrices\033[0X", "5", [ 5, 0, 0 ], 1, 30, "matrices", 
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  [ "\033[1XRing Relations\033[0X", "6", [ 6, 0, 0 ], 1, 53, "ring relations", "X8163F0658017F220" ], 
  [ "\033[1XRing Relations: Categories and Representations\033[0X", "6.1", [ 6, 1, 0 ], 4, 53, 
      "ring relations: categories and representations", "X7EB7C20C78788C69" ], 
  [ "\033[1XRing Relations: Constructors\033[0X", "6.2", [ 6, 2, 0 ], 42, 54, "ring relations: constructors", "X81D1405F81B86E4B" ], 
  [ "\033[1XRing Relations: Properties\033[0X", "6.3", [ 6, 3, 0 ], 45, 54, "ring relations: properties", "X7FFB5DE07BB77319" ], 
  [ "\033[1XRing Relations: Attributes\033[0X", "6.4", [ 6, 4, 0 ], 64, 54, "ring relations: attributes", "X849ED71B8164D1C2" ], 
  [ "\033[1XRing Relations: Operations and Functions\033[0X", "6.5", [ 6, 5, 0 ], 67, 54, "ring relations: operations and functions", 
      "X7ABFB8F982EBD7F8" ], [ "\033[1XThe Basic Matrix Operations\033[0X", "a", [ "A", 0, 0 ], 1, 55, "the basic matrix operations", 
      "X7CB422647C7DD289" ], [ "\033[1XMain\033[0X", "a.1", [ "A", 1, 0 ], 7, 55, "main", "X810454AB85D336F5" ], 
  [ "\033[1XEffective\033[0X", "a.2", [ "A", 2, 0 ], 22, 55, "effective", "X8435BB2E7A819478" ], 
  [ "\033[1XRelative\033[0X", "a.3", [ "A", 3, 0 ], 33, 55, "relative", "X7B1023F47EAB7A97" ], 
  [ "\033[1XReduced\033[0X", "a.4", [ "A", 4, 0 ], 40, 56, "reduced", "X7A0B865E7E70DB3D" ], 
  [ "\033[1XThe Matrix Tool Operations\033[0X", "b", [ "B", 0, 0 ], 1, 57, "the matrix tool operations", "X7B2993CB7B012115" ], 
  [ "\033[1XThe Tool Operations \033[13Xwithout\033[1X a Fallback Method\033[0X", "b.1", [ "B", 1, 0 ], 8, 57, 
      "the tool operations without a fallback method", "X7988F0AF7D87FD23" ], 
  [ "\033[1XThe Tool Operations with a Fallback Method\033[0X", "b.2", [ "B", 2, 0 ], 325, 63, "the tool operations with a fallback method"
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    , [ "\033[1X\033[5XLIRNG\033[1X: Logical Implications for Rings\033[0X", "c.1", [ "C", 1, 0 ], 4, 71, 
      "lirng: logical implications for rings", "X86BB747287348853" ], 
  [ "\033[1X\033[5XLIMAP\033[1X: Logical Implications for Ring Maps\033[0X", "c.2", [ "C", 2, 0 ], 7, 71, 
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  [ "\033[1X\033[5XLIMAT\033[1X: Logical Implications for Matrices\033[0X", "c.3", [ "C", 3, 0 ], 10, 71, 
      "limat: logical implications for matrices", "X799DA94B849ABF1E" ], 
  [ "\033[1X\033[5XCOLEM\033[1X: Clever Operations for Lazy Evaluated Matrices\033[0X", "c.4", [ "C", 4, 0 ], 13, 71, 
      "colem: clever operations for lazy evaluated matrices", "X847B8AB5843231C2" ], 
  [ "\033[1XThe subpackage \033[5XResidueClassRingForHomalg\033[1X as a sample ring package\033[0X", "d", [ "D", 0, 0 ], 1, 86, 
      "the subpackage residueclassringforhomalg as a sample ring package", "X7F3BA9AE7A0D245D" ], 
  [ "\033[1XThe Mandatory Basic Operations\033[0X", "d.1", [ "D", 1, 0 ], 4, 86, "the mandatory basic operations", "X84978AF3878A8375" ], 
  [ "\033[1XThe Mandatory Tool Operations\033[0X", "d.2", [ "D", 2, 0 ], 325, 92, "the mandatory tool operations", "X83E14F457ADC297D" ], 
  [ "\033[1XSome of the Recommended Tool Operations\033[0X", "d.3", [ "D", 3, 0 ], 672, 97, "some of the recommended tool operations", 
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      "debugging matricesforhomalg", "X82D40F3183F4F259" ], [ "\033[1XIncrease the assertion level\033[0X", "e.1", [ "E", 1, 0 ], 7, 99, 
      "increase the assertion level", "X8062637283DD739D" ], [ "\033[1X\033[10XUsing homalgMode\033[1X\033[0X", "e.2", [ "E", 2, 0 ], 113, 
      101, "using homalgmode", "X81D8EB2A7CE587C6" ], 
  [ "\033[1XOverview of the \033[5XMatricesForHomalg\033[1X Package Source Code\033[0X", "f", [ "F", 0, 0 ], 1, 103, 
      "overview of the matricesforhomalg package source code", "X863882737DAD95A3" ], 
  [ "\033[1XRings, Ring Maps, Matrices, Ring Relations\033[0X", "f.1", [ "F", 1, 0 ], 4, 103, "rings ring maps matrices ring relations", 
      "X87E0F36680867FA2" ], [ "\033[1XThe Low Level Algorithms\033[0X", "f.2", [ "F", 2, 0 ], 25, 103, "the low level algorithms", 
      "X7C4917CE80359953" ], [ "\033[1XLogical Implications for \033[5XMatricesForHomalg\033[1X Objects\033[0X", "f.3", [ "F", 3, 0 ], 46, 
      104, "logical implications for matricesforhomalg objects", "X7B2BFFB8876C548C" ], 
  [ "\033[1XThe subpackage \033[5XResidueClassRingForHomalg\033[1X\033[0X", "f.4", [ "F", 4, 0 ], 63, 104, 
      "the subpackage residueclassringforhomalg", "X85A3964E7A98C065" ], 
  [ "\033[1XThe homalgTable for \033[5XGAP4\033[1X built-in rings\033[0X", "f.5", [ "F", 5, 0 ], 83, 105, 
      "the homalgtable for gap4 built-in rings", "X860DCFF383750919" ], [ "Bibliography", "bib", [ "Bib", 0, 0 ], 1, 106, "bibliography", 
      "X7A6F98FD85F02BFE" ], [ "References", "bib", [ "Bib", 0, 0 ], 1, 106, "references", "X7A6F98FD85F02BFE" ], 
  [ "Index", "ind", [ "Ind", 0, 0 ], 1, 107, "index", "X83A0356F839C696F" ], 
  [ "\033[5XMatricesForHomalg\033[0m", ".-2", [ 0, 0, 2 ], 49, 3, "matricesforhomalg", "X8537FEB07AF2BEC8" ], 
  [ "\033[2XIsHomalgRing\033[0X", "3.1-1", [ 3, 1, 1 ], 7, 14, "ishomalgring", "X85E217C67DD633AB" ], 
  [ "\033[2XIsPreHomalgRing\033[0X", "3.1-2", [ 3, 1, 2 ], 21, 14, "isprehomalgring", "X81DC249883163C01" ], 
  [ "\033[2XIsHomalgRingElement\033[0X", "3.1-3", [ 3, 1, 3 ], 39, 14, "ishomalgringelement", "X80A410ED8500DA7E" ], 
  [ "\033[2XIsHomalgInternalRingRep\033[0X", "3.1-4", [ 3, 1, 4 ], 59, 15, "ishomalginternalringrep", "X8097E89E7B6EF731" ], 
  [ "\033[2XHomalgRingOfIntegers\033[0X (constructor for the integers)", "3.2-1", [ 3, 2, 1 ], 84, 15, 
      "homalgringofintegers constructor for the integers", "X78AC74CB802A8A49" ], 
  [ "\033[2XHomalgRingOfIntegers\033[0X (constructor for the residue class rings of the integers)", "3.2-1", [ 3, 2, 1 ], 84, 15, 
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  [ "\033[2XHomalgFieldOfRationals\033[0X (constructor for the field of rationals)", "3.2-2", [ 3, 2, 2 ], 115, 16, 
      "homalgfieldofrationals constructor for the field of rationals", "X7F4829D6808187B3" ], 
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  [ "\033[2XIsRationalsForHomalg\033[0X", "3.3-2", [ 3, 3, 2 ], 199, 17, "isrationalsforhomalg", "X7C337D0F8413FE38" ], 
  [ "\033[2XIsFieldForHomalg\033[0X", "3.3-3", [ 3, 3, 3 ], 206, 17, "isfieldforhomalg", "X86221E0E8416F1CF" ], 
  [ "\033[2XIsDivisionRingForHomalg\033[0X", "3.3-4", [ 3, 3, 4 ], 213, 17, "isdivisionringforhomalg", "X805112347CF99F02" ], 
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