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[ [ "Title page", ".", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" ], 
  [ "Copyright", ".-1", [ 0, 0, 1 ], 41, 2, "copyright", "X81488B807F2A1CF1" ], 
  [ "Acknowledgements", ".-2", [ 0, 0, 2 ], 49, 2, "acknowledgements", "X82A988D47DFAFCFA" ], 
  [ "Table of Contents", ".-3", [ 0, 0, 3 ], 136, 4, "table of contents", "X8537FEB07AF2BEC8" ], 
  [ "\033[1XIntroduction\033[0X", "1", [ 1, 0, 0 ], 1, 19, "introduction", "X7DFB63A97E67C0A1" ], 
  [ "\033[1XWhat is the role of the \033[5Xhomalg\033[1X package in the \033[5Xhomalg\033[1X project?\033[0X", "1.1", [ 1, 1, 0 ], 4, 19, 
      "what is the role of the homalg package in the homalg project?", "X7F1B40DB7C1395DD" ], 
  [ "\033[1XPhilosophy\033[0X", "1.1-1", [ 1, 1, 1 ], 7, 19, "philosophy", "X873C99678745ABAF" ], 
  [ "\033[1X\033[5Xhomalg\033[1X provides ...\033[0X", "1.1-2", [ 1, 1, 2 ], 20, 19, "homalg provides ...", "X82A79A2A78AED00B" ], 
  [ "\033[1X\033[5Xhomalg\033[1X delegates ...\033[0X", "1.1-3", [ 1, 1, 3 ], 86, 20, "homalg delegates ...", "X856DCAA4846FBB00" ], 
  [ "\033[1XRings supported in a sufficient way\033[0X", "1.1-4", [ 1, 1, 4 ], 146, 21, "rings supported in a sufficient way", 
      "X84913827857A1F7B" ], [ "\033[1XPrincipal limitation\033[0X", "1.1-5", [ 1, 1, 5 ], 154, 21, "principal limitation", 
      "X7C31B1FE786E596E" ], [ "\033[1XThe black box concept\033[0X", "1.1-6", [ 1, 1, 6 ], 171, 22, "the black box concept", 
      "X808E7BA97C5EA311" ], [ "\033[1X\033[5Xhomalg\033[1X's dictionaries (technical)\033[0X", "1.1-7", [ 1, 1, 7 ], 199, 22, 
      "homalgs dictionaries technical", "X795CE4D5866B6F44" ], [ "\033[1XThe advantages of the outsourcing concept\033[0X", "1.1-8", 
      [ 1, 1, 8 ], 223, 22, "the advantages of the outsourcing concept", "X7D7570837C21607A" ], 
  [ "\033[1XDoes this mean that \033[5Xhomalg\033[1X has only algorithms for the generic case?\033[0X", "1.1-9", [ 1, 1, 9 ], 238, 23, 
      "does this mean that homalg has only algorithms for the generic case?", "X85C5BCDF797B7954" ], 
  [ "\033[1XThe principle of least communication (technical)\033[0X", "1.1-10", [ 1, 1, 10 ], 250, 23, 
      "the principle of least communication technical", "X79DFCAF17BD3DDC6" ], 
  [ "\033[1XBuilding upon the \033[5Xhomalg\033[1X package\033[0X", "1.1-11", [ 1, 1, 11 ], 284, 23, "building upon the homalg package", 
      "X78E6DF7E878D754D" ], [ "\033[1XFrequently asked questions\033[0X", "1.1-12", [ 1, 1, 12 ], 320, 24, "frequently asked questions", 
      "X7D51BC7A80D43EA0" ], [ "\033[1XThis manual\033[0X", "1.2", [ 1, 2, 0 ], 345, 24, "this manual", "X78DD800B83ABC621" ], 
  [ "\033[1XInstallation of the \033[5Xhomalg\033[1X Package\033[0X", "2", [ 2, 0, 0 ], 1, 25, "installation of the homalg package", 
      "X855C716578E12A0B" ], [ "\033[1XQuick Start\033[0X", "3", [ 3, 0, 0 ], 1, 26, "quick start", "X7EB860EC84DFC71E" ], 
  [ "\033[1XWhy are all examples in this manual over \342\204\244 or \342\204\244/m\342\204\244?\033[0X", "3.1", [ 3, 1, 0 ], 7, 26, 
      "why are all examples in this manual over a\204\244 or a\204\244 ma\204\244?", "X7A321B4885D1BFC1" ], 
  [ "\033[1X\033[10Xgap> ExamplesForHomalg();\033[1X\033[0X", "3.2", [ 3, 2, 0 ], 24, 26, "gap> examplesforhomalg", "X85872612814D30B4" ], 
  [ "\033[1XA typical example\033[0X", "3.3", [ 3, 3, 0 ], 34, 26, "a typical example", "X7BBB3E988435A713" ], 
  [ "\033[1XHomHom\033[0X", "3.3-1", [ 3, 3, 1 ], 37, 26, "homhom", "X791E21F47805048A" ], 
  [ "\033[1XRings\033[0X", "4", [ 4, 0, 0 ], 1, 32, "rings", "X81897F6082CACB59" ], 
  [ "\033[1XRings: Category and Representations\033[0X", "4.1", [ 4, 1, 0 ], 4, 32, "rings: category and representations", 
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     ], [ "\033[1XRings: Properties\033[0X", "4.3", [ 4, 3, 0 ], 142, 34, "rings: properties", "X7D171A1C797E27C9" ], 
  [ "\033[1XRings: Attributes\033[0X", "4.4", [ 4, 4, 0 ], 513, 40, "rings: attributes", "X867290E7847A5101" ], 
  [ "\033[1XRings: Operations and Functions\033[0X", "4.5", [ 4, 5, 0 ], 680, 43, "rings: operations and functions", "X7DDAB86C7A7FEDA9" ],
  [ "\033[1XRing Maps\033[0X", "5", [ 5, 0, 0 ], 1, 44, "ring maps", "X7B222197819984A6" ], 
  [ "\033[1XRing Maps: Category and Representations\033[0X", "5.1", [ 5, 1, 0 ], 10, 44, "ring maps: category and representations", 
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      "X8717AEFB7BAC63F7" ], [ "\033[1XRing Maps: Properties\033[0X", "5.3", [ 5, 3, 0 ], 55, 45, "ring maps: properties", 
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      "ring maps: operations and functions", "X7C7401BA7E2221CB" ], [ "\033[1XMatrices\033[0X", "6", [ 6, 0, 0 ], 1, 47, "matrices", 
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      "relations: categories and representations", "X87DADB7B7CB126DC" ], 
  [ "\033[1XRelations: Constructors\033[0X", "7.2", [ 7, 2, 0 ], 56, 71, "relations: constructors", "X7CF74FB785F90889" ], 
  [ "\033[1XRelations: Properties\033[0X", "7.3", [ 7, 3, 0 ], 59, 71, "relations: properties", "X859231317954D702" ], 
  [ "\033[1XRelations: Attributes\033[0X", "7.4", [ 7, 4, 0 ], 78, 71, "relations: attributes", "X7EF7BBCA85851EF1" ], 
  [ "\033[1XRelations: Operations and Functions\033[0X", "7.5", [ 7, 5, 0 ], 89, 71, "relations: operations and functions", 
      "X7890B5EA80774AB5" ], [ "\033[1XGenerators\033[0X", "8", [ 8, 0, 0 ], 1, 72, "generators", "X7BD5B55C802805B4" ], 
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      "generators: operations and functions", "X7AC876EC8137AEA4" ], 
  [ "\033[1XModules\033[0X", "9", [ 9, 0, 0 ], 1, 74, "modules", "X8183A6857B0C3633" ], 
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      "modules: operations and functions", "X7DDA6B237C17BDBA" ], 
  [ "\033[1XMaps\033[0X", "10", [ 10, 0, 0 ], 1, 89, "maps", "X7E8438F77ECB778E" ], 
  [ "\033[1XMaps: Categories and Representations\033[0X", "10.1", [ 10, 1, 0 ], 17, 89, "maps: categories and representations", 
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  [ "\033[1XMaps: Attributes\033[0X", "10.4", [ 10, 4, 0 ], 292, 94, "maps: attributes", "X7EA3B91C78E430BB" ], 
  [ "\033[1XMaps: Operations and Functions\033[0X", "10.5", [ 10, 5, 0 ], 383, 95, "maps: operations and functions", "X783E9FF8800609EB" ],
  [ "\033[1XComplexes\033[0X", "11", [ 11, 0, 0 ], 1, 98, "complexes", "X79C388D385DB7CD1" ], 
  [ "\033[1XComplexes: Category and Representations\033[0X", "11.1", [ 11, 1, 0 ], 4, 98, "complexes: category and representations", 
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      "complexes: operations and functions", "X84E12E9C7A60D9BC" ], 
  [ "\033[1XChain Maps\033[0X", "12", [ 12, 0, 0 ], 1, 106, "chain maps", "X85F418EB859E7597" ], 
  [ "\033[1XChainMaps: Categories and Representations\033[0X", "12.1", [ 12, 1, 0 ], 4, 106, "chainmaps: categories and representations", 
      "X7908AEB8851AF1DB" ], [ "\033[1XChain Maps: Constructors\033[0X", "12.2", [ 12, 2, 0 ], 48, 107, "chain maps: constructors", 
      "X788ADE6C84D455B4" ], [ "\033[1XChain Maps: Properties\033[0X", "12.3", [ 12, 3, 0 ], 110, 108, "chain maps: properties", 
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      "chain maps: operations and functions", "X8684197D8481DE87" ], 
  [ "\033[1XBicomplexes\033[0X", "13", [ 13, 0, 0 ], 1, 111, "bicomplexes", "X7CEDAD61826170CF" ], 
  [ "\033[1XBicomplexes: Category and Representations\033[0X", "13.1", [ 13, 1, 0 ], 13, 111, "bicomplexes: category and representations", 
      "X7CBAE2807BD16E7E" ], [ "\033[1XBicomplexes: Constructors\033[0X", "13.2", [ 13, 2, 0 ], 49, 112, "bicomplexes: constructors", 
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      "bicomplexes: operations and functions", "X81357E7A7C6D31F5" ], [ "\033[1XBigraded Objects\033[0X", "14", [ 14, 0, 0 ], 1, 115, 
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      "bigraded objects: operations and functions", "X7A5828337CE2F4F2" ], 
  [ "\033[1XSpectral Sequences\033[0X", "15", [ 15, 0, 0 ], 1, 120, "spectral sequences", "X87330D8C82E71B50" ], 
  [ "\033[1XSpectralSequences: Categorie and Representations\033[0X", "15.1", [ 15, 1, 0 ], 12, 120, 
      "spectralsequences: categorie and representations", "X85E1174B7BDA291E" ], 
  [ "\033[1XSpectral Sequences: Constructors\033[0X", "15.2", [ 15, 2, 0 ], 79, 121, "spectral sequences: constructors", 
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      [ 15, 4, 0 ], 216, 123, "spectral sequences: operations and functions", "X7BD192607D03A699" ], 
  [ "\033[1XFunctors\033[0X", "16", [ 16, 0, 0 ], 1, 125, "functors", "X78D1062D78BE08C1" ], 
  [ "\033[1XFunctors: Category and Representations\033[0X", "16.1", [ 16, 1, 0 ], 57, 126, "functors: category and representations", 
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  [ "\033[1XTool Functors\033[0X", "16.5", [ 16, 5, 0 ], 1464, 150, "tool functors", "X815BF6DA7FD5D44B" ], 
  [ "\033[1XOther Functors\033[0X", "16.6", [ 16, 6, 0 ], 1467, 150, "other functors", "X879135AC8330C509" ], 
  [ "\033[1XFunctors: Operations and Functions\033[0X", "16.7", [ 16, 7, 0 ], 1470, 150, "functors: operations and functions", 
      "X7DACD68E7E5FA324" ], [ "\033[1XExamples\033[0X", "17", [ 17, 0, 0 ], 1, 153, "examples", "X7A489A5D79DA9E5C" ], 
  [ "\033[1XExtExt\033[0X", "17.1", [ 17, 1, 0 ], 4, 153, "extext", "X7BB9DE017ECE6E86" ], 
  [ "\033[1XPurity\033[0X", "17.2", [ 17, 2, 0 ], 86, 154, "purity", "X7EE63228803A04F1" ], 
  [ "\033[1XTorExt-Grothendieck\033[0X", "17.3", [ 17, 3, 0 ], 181, 156, "torext-grothendieck", "X812EF8147AE16E72" ], 
  [ "\033[1XTorExt\033[0X", "17.4", [ 17, 4, 0 ], 261, 158, "torext", "X784BC2567875830B" ], 
  [ "\033[1XDevelopment\033[0X", "a", [ "A", 0, 0 ], 1, 160, "development", "X816F972F826BE589" ], 
  [ "\033[1XWhy was \033[5Xhomalg\033[1X discontinued in \033[5XMaple\033[1X?\033[0X", "a.1", [ "A", 1, 0 ], 4, 160, 
      "why was homalg discontinued in maple?", "X85B7FB29805B14C9" ], [ "\033[1XWhy \033[5XGAP4\033[1X?\033[0X", "a.2", [ "A", 2, 0 ], 19, 
      160, "why gap4?", "X7D2A5B127A68AB58" ], [ "\033[1X\033[5XGAP\033[1X is free and open software\033[0X", "a.2-1", [ "A", 2, 1 ], 22, 
      160, "gap is free and open software", "X8148BBD87B272E84" ], [ "\033[1X\033[5XGAP\033[1X has an area of expertise\033[0X", "a.2-2", 
      [ "A", 2, 2 ], 52, 161, "gap has an area of expertise", "X799403717D4414BA" ], 
  [ "\033[1X\033[5XGAP4\033[1X can communicate\033[0X", "a.2-3", [ "A", 2, 3 ], 78, 161, "gap4 can communicate", "X863002078157C105" ], 
  [ "\033[1X\033[5XGAP4\033[1X is a \033[13Xmathematical\033[1X object-oriented programming language\033[0X", "a.2-4", [ "A", 2, 4 ], 86, 
      161, "gap4 is a mathematical object-oriented programming language", "X78EB6CAE7C7F2F7C" ], 
  [ "\033[1X\033[5XGAP4\033[1X packages are easily extendible\033[0X", "a.2-5", [ "A", 2, 5 ], 126, 162, 
      "gap4 packages are easily extendible", "X7E1B9133835F33FD" ], [ "\033[1XWhy not \033[5XSage\033[1X?\033[0X", "a.3", [ "A", 3, 0 ], 
      140, 162, "why not sage?", "X7F7CF4AE830E312B" ], [ "\033[1XHow does \033[5Xhomalg\033[1X compare to \033[5XSage\033[1X?\033[0X", 
      "a.4", [ "A", 4, 0 ], 151, 162, "how does homalg compare to sage?", "X81A6C501841B20C4" ], 
  [ "\033[1XThey differ in objectives and scale\033[0X", "a.4-1", [ "A", 4, 1 ], 156, 162, "they differ in objectives and scale", 
      "X82A6EC2C850909B1" ], [ "\033[1XThey differ in the programming language\033[0X", "a.4-2", [ "A", 4, 2 ], 167, 162, 
      "they differ in the programming language", "X8346070A86BF5CC5" ], 
  [ "\033[1XThey differ in the way they communicate with the outer world\033[0X", "a.4-3", [ "A", 4, 3 ], 176, 162, 
      "they differ in the way they communicate with the outer world", "X8040F9357F008C1E" ], 
  [ "\033[1XThe Mathematical Idea behind \033[5Xhomalg\033[1X\033[0X", "b", [ "B", 0, 0 ], 1, 164, "the mathematical idea behind homalg", 
      "X7FBD6C8A83D64BE4" ], [ "\033[1XThe Basic Matrix Operations\033[0X", "c", [ "C", 0, 0 ], 1, 165, "the basic matrix operations", 
      "X7CB422647C7DD289" ], [ "\033[1XMain\033[0X", "c.1", [ "C", 1, 0 ], 7, 165, "main", "X810454AB85D336F5" ], 
  [ "\033[1XEffective\033[0X", "c.2", [ "C", 2, 0 ], 22, 165, "effective", "X8435BB2E7A819478" ], 
  [ "\033[1XRelative\033[0X", "c.3", [ "C", 3, 0 ], 33, 165, "relative", "X7B1023F47EAB7A97" ], 
  [ "\033[1XReduced\033[0X", "c.4", [ "C", 4, 0 ], 40, 166, "reduced", "X7A0B865E7E70DB3D" ], 
  [ "\033[1XThe Matrix Tool Operations\033[0X", "d", [ "D", 0, 0 ], 1, 167, "the matrix tool operations", "X7B2993CB7B012115" ], 
  [ "\033[1XThe Tool Operations \033[13Xwithout\033[1X a Fallback Method\033[0X", "d.1", [ "D", 1, 0 ], 8, 167, 
      "the tool operations without a fallback method", "X7988F0AF7D87FD23" ], 
  [ "\033[1XThe Tool Operations with a Fallback Method\033[0X", "d.2", [ "D", 2, 0 ], 324, 173, 
      "the tool operations with a fallback method", "X7912E42C81296637" ], 
  [ "\033[1XLogic Subpackages\033[0X", "e", [ "E", 0, 0 ], 1, 181, "logic subpackages", "X8222352C78A19214" ], 
  [ "\033[1X\033[5XLIRNG\033[1X: Logical Implications for Rings\033[0X", "e.1", [ "E", 1, 0 ], 4, 181, 
      "lirng: logical implications for rings", "X86BB747287348853" ], 
  [ "\033[1X\033[5XLIMAP\033[1X: Logical Implications for Ring Maps\033[0X", "e.2", [ "E", 2, 0 ], 7, 181, 
      "limap: logical implications for ring maps", "X7B2915F1867EE8D0" ], 
  [ "\033[1X\033[5XLIMAT\033[1X: Logical Implications for Matrices\033[0X", "e.3", [ "E", 3, 0 ], 10, 181, 
      "limat: logical implications for matrices", "X799DA94B849ABF1E" ], 
  [ "\033[1X\033[5XCOLEM\033[1X: Clever Operations for Lazy Evaluated Matrices\033[0X", "e.4", [ "E", 4, 0 ], 13, 181, 
      "colem: clever operations for lazy evaluated matrices", "X847B8AB5843231C2" ], 
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  [ "\033[1XThe 5=1+4 split\033[0X", "h.1", [ "H", 1, 0 ], 16, 213, "the 5 1+4 split", "X7AED759D7A410F98" ], 
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  [ "\033[1XBlack boxes\033[0X", "h.1-2", [ "H", 1, 2 ], 37, 213, "black boxes", "X7EE794358500309A" ], 
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  [ "\033[1XOverview of the \033[5Xhomalg\033[1X Package Source Code\033[0X", "i", [ "I", 0, 0 ], 1, 216, 
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  [ "\033[1XThe Low Level Algorithms\033[0X", "i.3", [ "I", 3, 0 ], 70, 217, "the low level algorithms", "X7C4917CE80359953" ], 
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  [ "\033[1XThe subpackage \033[5XResidueClassRingForHomalg\033[1X\033[0X", "i.6", [ "I", 6, 0 ], 147, 219, 
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