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531\makelabel{ref:Backtrack}{43.12}{X86C78160854C7F30} 532\makelabel{ref:Working with large degree permutation groups}{43.13}{X78A68F5A80ADD1B6} 533\makelabel{ref:Matrix Groups}{44}{X7CF51CB48610A07D} 534\makelabel{ref:IsMatrixGroup (Filter)}{44.1}{X86CEA60E7C04744C} 535\makelabel{ref:Attributes and Properties for Matrix Groups}{44.2}{X7FD808E386FAF9B0} 536\makelabel{ref:Actions of Matrix Groups}{44.3}{X7F4B0B397AAC7659} 537\makelabel{ref:GL and SL}{44.4}{X7934EED77891BE6B} 538\makelabel{ref:Invariant Forms}{44.5}{X7CA4097C79F5BD90} 539\makelabel{ref:Matrix Groups in Characteristic 0}{44.6}{X7FB0138F79E8C5E7} 540\makelabel{ref:Acting OnRight and OnLeft}{44.7}{X868288377CFA8D1B} 541\makelabel{ref:Polycyclic Groups}{45}{X86007B0083F60470} 542\makelabel{ref:Polycyclic Generating Systems}{45.1}{X7F18A01785DBAC4E} 543\makelabel{ref:Computing a Pcgs}{45.2}{X87F7E31879AFA06C} 544\makelabel{ref:Defining a Pcgs Yourself}{45.3}{X7CAAD6D2838354D9} 545\makelabel{ref:Elementary Operations for a 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1442\makelabel{ref:Spreadsheet}{10.11}{X848DD7DC79363341} 1443\makelabel{ref:Excel}{10.11}{X848DD7DC79363341} 1444\makelabel{ref:ReadCSV}{10.11.1}{X86FDC1EF82CAD2DA} 1445\makelabel{ref:PrintCSV}{10.11.2}{X8779DAC585E05A47} 1446\makelabel{ref:Process}{11.1.1}{X7B09033178D1107A} 1447\makelabel{ref:Exec}{11.1.2}{X81402C91833986FC} 1448\makelabel{ref:IsObject}{12.1.1}{X7B130AC98415CAFB} 1449\makelabel{ref:elements definition}{12.2}{X780C66027A49D110} 1450\makelabel{ref:IsIdenticalObj}{12.5.1}{X7961183378DFB902} 1451\makelabel{ref:IsNotIdenticalObj}{12.5.2}{X811976EC78EC5E29} 1452\makelabel{ref:IsCopyable}{12.6.1}{X811EFD727EBD1ADC} 1453\makelabel{ref:IsMutable}{12.6.2}{X7999AD1D7A4F1F46} 1454\makelabel{ref:Immutable}{12.6.3}{X7F0ABF2C870B0CBB} 1455\makelabel{ref:MakeImmutable}{12.6.4}{X80CE136D804097C7} 1456\makelabel{ref:Copy}{12.7}{X786B942B82D684BD} 1457\makelabel{ref:copy an object}{12.7}{X786B942B82D684BD} 1458\makelabel{ref:clone an object}{12.7}{X786B942B82D684BD} 1459\makelabel{ref:ShallowCopy}{12.7.1}{X846BC7107C352031} 1460\makelabel{ref:StructuralCopy}{12.7.2}{X7C1E70587EBDD2CB} 1461\makelabel{ref:SetName}{12.8.1}{X85D6D47B83BD02A1} 1462\makelabel{ref:Name}{12.8.2}{X7F14EF9D81432113} 1463\makelabel{ref:InfoText}{12.8.3}{X871562FD7F982C12} 1464\makelabel{ref:IsInternallyConsistent}{12.8.4}{X7F6C5C3287E8B816} 1465\makelabel{ref:MemoryUsage}{12.8.5}{X7F4D216B7DF7BE9D} 1466\makelabel{ref:FamilyObj}{13.1.1}{X7CF70EAC84284919} 1467\makelabel{ref:NewFamily}{13.1.2}{X7FB4123E7E22137D} 1468\makelabel{ref:and for filters}{13.2}{X84EFA4C07D4277BB} 1469\makelabel{ref:RankFilter}{13.2.1}{X82E62B997C05E05E} 1470\makelabel{ref:NamesFilter}{13.2.2}{X7A78ECC67E2C9D78} 1471\makelabel{ref:FilterByName}{13.2.3}{X7F6645D87DD26CF0} 1472\makelabel{ref:ShowImpliedFilters}{13.2.4}{X7F9568A67F3840DE} 1473\makelabel{ref:FiltersType}{13.2.5}{X836FAA18861BE387} 1474\makelabel{ref:FiltersObj}{13.2.5}{X836FAA18861BE387} 1475\makelabel{ref:IsCategory}{13.3.1}{X792A23BF82BDF66B} 1476\makelabel{ref:CategoriesOfObject}{13.3.2}{X85C6EB707A406A5A} 1477\makelabel{ref:CategoryByName}{13.3.3}{X85D07C3E7F4D4043} 1478\makelabel{ref:NewCategory}{13.3.4}{X87F68F887B44DBBD} 1479\makelabel{ref:DeclareCategory}{13.3.5}{X879DE2A17A6C6E92} 1480\makelabel{ref:CategoryFamily}{13.3.6}{X787BACEE7937EF01} 1481\makelabel{ref:IsInternalRep}{13.4.1}{X805F1C3B7C730062} 1482\makelabel{ref:IsDataObjectRep}{13.4.1}{X805F1C3B7C730062} 1483\makelabel{ref:IsPositionalObjectRep}{13.4.1}{X805F1C3B7C730062} 1484\makelabel{ref:IsComponentObjectRep}{13.4.1}{X805F1C3B7C730062} 1485\makelabel{ref:IsRepresentation}{13.4.2}{X86D42C7783ACA5F4} 1486\makelabel{ref:RepresentationsOfObject}{13.4.3}{X7BBE93BE7977750F} 1487\makelabel{ref:NewRepresentation}{13.4.4}{X7CC8106F809E15CF} 1488\makelabel{ref:DeclareRepresentation}{13.4.5}{X7C81FB2682AE54CD} 1489\makelabel{ref:IsAttribute}{13.5.1}{X7973C8F4782D15A1} 1490\makelabel{ref:KnownAttributesOfObject}{13.5.2}{X7F7960338163AA88} 1491\makelabel{ref:NewAttribute}{13.5.3}{X7B9654807858A3B0} 1492\makelabel{ref:DeclareAttribute}{13.5.4}{X7A00FC8A7A677A56} 1493\makelabel{ref:IsAttributeStoringRep}{13.5.5}{X7A951C33839AF2C1} 1494\makelabel{ref:system getter}{13.5.5}{X7A951C33839AF2C1} 1495\makelabel{ref:system setter}{13.5.5}{X7A951C33839AF2C1} 1496\makelabel{ref:setter}{13.6}{X79DE5208877AE42A} 1497\makelabel{ref:tester}{13.6}{X79DE5208877AE42A} 1498\makelabel{ref:Tester}{13.6.1}{X87D5B5AC7DAF932D} 1499\makelabel{ref:Setter}{13.6.2}{X7FD8952C841D2B1F} 1500\makelabel{ref:AttributeValueNotSet}{13.6.3}{X8529F8A17884A32C} 1501\makelabel{ref:InfoAttributes}{13.6.4}{X79120CE37BB69D11} 1502\makelabel{ref:DisableAttributeValueStoring}{13.6.5}{X7851E2DB79656DB0} 1503\makelabel{ref:EnableAttributeValueStoring}{13.6.6}{X7E5DACBE7A9A9AD1} 1504\makelabel{ref:IsProperty}{13.7.1}{X81F1C3EE83003FA0} 1505\makelabel{ref:KnownPropertiesOfObject}{13.7.2}{X7E51C08286E03E7F} 1506\makelabel{ref:KnownTruePropertiesOfObject}{13.7.3}{X86711BC77B62EB02} 1507\makelabel{ref:NewProperty}{13.7.4}{X7F2D6FD979FE23DD} 1508\makelabel{ref:DeclareProperty}{13.7.5}{X7F4602F082682A04} 1509\makelabel{ref:NewFilter}{13.8.1}{X821635DA7821ED74} 1510\makelabel{ref:DeclareFilter}{13.8.2}{X846EA18A7D36626C} 1511\makelabel{ref:SetFilterObj}{13.8.3}{X7C92D53E7920CE02} 1512\makelabel{ref:ResetFilterObj}{13.8.4}{X8117FD03870FB02E} 1513\makelabel{ref:TypeObj}{13.9.1}{X7D3E6B6482BE5B16} 1514\makelabel{ref:DataType}{13.9.2}{X85A60A7F8083C1C4} 1515\makelabel{ref:NewType}{13.9.3}{X7CE39E9478AEC826} 1516\makelabel{ref:small integer}{14}{X853DF11B80068ED5} 1517\makelabel{ref:immediate integer}{14}{X853DF11B80068ED5} 1518\makelabel{ref:INTOBJMIN}{14}{X853DF11B80068ED5} 1519\makelabel{ref:INTOBJMAX}{14}{X853DF11B80068ED5} 1520\makelabel{ref:Integers global variable}{14.1.1}{X7E20D82B79DE5129} 1521\makelabel{ref:PositiveIntegers}{14.1.1}{X7E20D82B79DE5129} 1522\makelabel{ref:NonnegativeIntegers}{14.1.1}{X7E20D82B79DE5129} 1523\makelabel{ref:IsIntegers}{14.1.2}{X818683B17F8C97F3} 1524\makelabel{ref:IsPositiveIntegers}{14.1.2}{X818683B17F8C97F3} 1525\makelabel{ref:IsNonnegativeIntegers}{14.1.2}{X818683B17F8C97F3} 1526\makelabel{ref:IsInt}{14.2.1}{X87AEADF07DC8303B} 1527\makelabel{ref:IsPosInt}{14.2.2}{X82A854757DFA9C76} 1528\makelabel{ref:Int}{14.2.3}{X87CA734380B5F68C} 1529\makelabel{ref:IsEvenInt}{14.2.4}{X87DD1EEE7EF18036} 1530\makelabel{ref:IsOddInt}{14.2.5}{X8621BA927CD12EFB} 1531\makelabel{ref:AbsInt}{14.2.6}{X782095927FB9F1DB} 1532\makelabel{ref:absolute value of an integer}{14.2.6}{X782095927FB9F1DB} 1533\makelabel{ref:SignInt}{14.2.7}{X842614817FE48D62} 1534\makelabel{ref:sign of an integer}{14.2.7}{X842614817FE48D62} 1535\makelabel{ref:LogInt}{14.2.8}{X8197C4E882BAF14E} 1536\makelabel{ref:RootInt}{14.2.9}{X83D9B5C87EEA2A77} 1537\makelabel{ref:root of an integer}{14.2.9}{X83D9B5C87EEA2A77} 1538\makelabel{ref:square root of an integer}{14.2.9}{X83D9B5C87EEA2A77} 1539\makelabel{ref:SmallestRootInt}{14.2.10}{X7F98A0CE7B9FD366} 1540\makelabel{ref:root of an integer, smallest}{14.2.10}{X7F98A0CE7B9FD366} 1541\makelabel{ref:ListOfDigits}{14.2.11}{X862D1BD786EFFDA9} 1542\makelabel{ref:Random for integers}{14.2.12}{X8185784B7E228DEA} 1543\makelabel{ref:QuoInt}{14.3.1}{X849D0F807F697D35} 1544\makelabel{ref:integer part of a quotient}{14.3.1}{X849D0F807F697D35} 1545\makelabel{ref:BestQuoInt}{14.3.2}{X795170A385AC8FEE} 1546\makelabel{ref:RemInt}{14.3.3}{X805ADD5A826D844D} 1547\makelabel{ref:remainder of a quotient}{14.3.3}{X805ADD5A826D844D} 1548\makelabel{ref:GcdInt}{14.3.4}{X7A4FEFCA8128E3C3} 1549\makelabel{ref:Gcdex}{14.3.5}{X8775930486BD0C5B} 1550\makelabel{ref:LcmInt}{14.3.6}{X7B33143E78A8DDE3} 1551\makelabel{ref:CoefficientsQadic}{14.3.7}{X79B466E984CD52D4} 1552\makelabel{ref:CoefficientsMultiadic}{14.3.8}{X83124F86839DC7E6} 1553\makelabel{ref:ChineseRem}{14.3.9}{X84A1900E82902B5F} 1554\makelabel{ref:Chinese remainder}{14.3.9}{X84A1900E82902B5F} 1555\makelabel{ref:PowerModInt}{14.3.10}{X7E404B1183DBC82A} 1556\makelabel{ref:Primes}{14.4.1}{X86F5E4CD82FEB9F4} 1557\makelabel{ref:IsPrimeInt}{14.4.2}{X78FDA4437EDCA70C} 1558\makelabel{ref:IsProbablyPrimeInt}{14.4.2}{X78FDA4437EDCA70C} 1559\makelabel{ref:PrimalityProof}{14.4.3}{X7CD977B17B4A7A4B} 1560\makelabel{ref:IsPrimePowerInt}{14.4.4}{X8443125D7FD6F2A6} 1561\makelabel{ref:NextPrimeInt}{14.4.5}{X78744C367A94C69F} 1562\makelabel{ref:PrevPrimeInt}{14.4.6}{X819060E17E83728A} 1563\makelabel{ref:FactorsInt}{14.4.7}{X82C989DB84744B36} 1564\makelabel{ref:FactorsInt using pollard's rho}{14.4.7}{X82C989DB84744B36} 1565\makelabel{ref:PrimeDivisors}{14.4.8}{X80E7A5D381C64CC9} 1566\makelabel{ref:PartialFactorization}{14.4.9}{X786FF92C7C54BF97} 1567\makelabel{ref:PrintFactorsInt}{14.4.10}{X803D431087B6FF28} 1568\makelabel{ref:PrimePowersInt}{14.4.11}{X82148B347E294C87} 1569\makelabel{ref:DivisorsInt}{14.4.12}{X809E0E1B83AF7695} 1570\makelabel{ref:divisors of an integer}{14.4.12}{X809E0E1B83AF7695} 1571\makelabel{ref:mod residue class rings}{14.5}{X864BF040862409FC} 1572\makelabel{ref:modulo residue class rings}{14.5}{X864BF040862409FC} 1573\makelabel{ref:ZmodnZ}{14.5.2}{X79CE76AD82B3E2B2} 1574\makelabel{ref:ZmodpZ}{14.5.2}{X79CE76AD82B3E2B2} 1575\makelabel{ref:ZmodpZNC}{14.5.2}{X79CE76AD82B3E2B2} 1576\makelabel{ref:mod Integers}{14.5.2}{X79CE76AD82B3E2B2} 1577\makelabel{ref:ZmodnZObj for a residue class family and integer}{14.5.3}{X838F36507D985EDA} 1578\makelabel{ref:ZmodnZObj for two integers}{14.5.3}{X838F36507D985EDA} 1579\makelabel{ref:IsZmodnZObj}{14.5.4}{X7D0107DD79753901} 1580\makelabel{ref:IsZmodnZObjNonprime}{14.5.4}{X7D0107DD79753901} 1581\makelabel{ref:IsZmodpZObj}{14.5.4}{X7D0107DD79753901} 1582\makelabel{ref:IsZmodpZObjSmall}{14.5.4}{X7D0107DD79753901} 1583\makelabel{ref:IsZmodpZObjLarge}{14.5.4}{X7D0107DD79753901} 1584\makelabel{ref:CheckDigitISBN}{14.6.1}{X82BABA8F868BD425} 1585\makelabel{ref:CheckDigitISBN13}{14.6.1}{X82BABA8F868BD425} 1586\makelabel{ref:CheckDigitPostalMoneyOrder}{14.6.1}{X82BABA8F868BD425} 1587\makelabel{ref:CheckDigitUPC}{14.6.1}{X82BABA8F868BD425} 1588\makelabel{ref:CheckDigitTestFunction}{14.6.2}{X85F1A6A5870485B9} 1589\makelabel{ref:IsRandomSource}{14.7.1}{X82E31A697E389F1D} 1590\makelabel{ref:Random for random source and list}{14.7.2}{X821004F286282D49} 1591\makelabel{ref:Random for random source and collection}{14.7.2}{X821004F286282D49} 1592\makelabel{ref:Random for random source and two integers}{14.7.2}{X821004F286282D49} 1593\makelabel{ref:State}{14.7.3}{X819E3E3080297347} 1594\makelabel{ref:Reset}{14.7.3}{X819E3E3080297347} 1595\makelabel{ref:Init}{14.7.3}{X819E3E3080297347} 1596\makelabel{ref:IsMersenneTwister}{14.7.4}{X7F772E2686B35865} 1597\makelabel{ref:IsGAPRandomSource}{14.7.4}{X7F772E2686B35865} 1598\makelabel{ref:IsGlobalRandomSource}{14.7.4}{X7F772E2686B35865} 1599\makelabel{ref:GlobalMersenneTwister}{14.7.4}{X7F772E2686B35865} 1600\makelabel{ref:GlobalRandomSource}{14.7.4}{X7F772E2686B35865} 1601\makelabel{ref:RandomSource}{14.7.5}{X7CB0B5BC82F8FD8F} 1602\makelabel{ref:MakeBitfields}{14.8.1}{X85C7BD9E7FCC6C10} 1603\makelabel{ref:BuildBitfields}{14.8.2}{X8068CE3781F4003C} 1604\makelabel{ref:prime residue group}{15}{X7FB995737B7ED8A2} 1605\makelabel{ref:InfoNumtheor}{15.1.1}{X796F0DFE7D5D211C} 1606\makelabel{ref:prime residue group}{15.2}{X823386567DAC22E6} 1607\makelabel{ref:PrimeResidues}{15.2.1}{X7FA3F5347B7004BA} 1608\makelabel{ref:Phi}{15.2.2}{X85A0C67982D9057A} 1609\makelabel{ref:order of the prime residue group}{15.2.2}{X85A0C67982D9057A} 1610\makelabel{ref:prime residue group order}{15.2.2}{X85A0C67982D9057A} 1611\makelabel{ref:Euler's totient function}{15.2.2}{X85A0C67982D9057A} 1612\makelabel{ref:Lambda}{15.2.3}{X85296F3087611B03} 1613\makelabel{ref:Carmichael's lambda function}{15.2.3}{X85296F3087611B03} 1614\makelabel{ref:prime residue group exponent}{15.2.3}{X85296F3087611B03} 1615\makelabel{ref:exponent of the prime residue group}{15.2.3}{X85296F3087611B03} 1616\makelabel{ref:GeneratorsPrimeResidues}{15.2.4}{X7D191CF67E5018BE} 1617\makelabel{ref:OrderMod}{15.3.1}{X82373F3D8277EE9E} 1618\makelabel{ref:multiplicative order of an integer}{15.3.1}{X82373F3D8277EE9E} 1619\makelabel{ref:LogMod}{15.3.2}{X81AD9C7779A7BA89} 1620\makelabel{ref:LogModShanks}{15.3.2}{X81AD9C7779A7BA89} 1621\makelabel{ref:logarithm discrete}{15.3.2}{X81AD9C7779A7BA89} 1622\makelabel{ref:PrimitiveRootMod}{15.3.3}{X82440BB9812FF148} 1623\makelabel{ref:primitive root modulo an integer}{15.3.3}{X82440BB9812FF148} 1624\makelabel{ref:prime residue group generator}{15.3.3}{X82440BB9812FF148} 1625\makelabel{ref:generator of the prime residue group}{15.3.3}{X82440BB9812FF148} 1626\makelabel{ref:IsPrimitiveRootMod}{15.3.4}{X790466C07BD90E20} 1627\makelabel{ref:test for a primitive root}{15.3.4}{X790466C07BD90E20} 1628\makelabel{ref:prime residue group generator}{15.3.4}{X790466C07BD90E20} 1629\makelabel{ref:generator of the prime residue group}{15.3.4}{X790466C07BD90E20} 1630\makelabel{ref:Jacobi}{15.4.1}{X83449DBC80495971} 1631\makelabel{ref:quadratic residue}{15.4.1}{X83449DBC80495971} 1632\makelabel{ref:residue quadratic}{15.4.1}{X83449DBC80495971} 1633\makelabel{ref:Legendre}{15.4.2}{X81464ABF7F10E544} 1634\makelabel{ref:quadratic residue}{15.4.2}{X81464ABF7F10E544} 1635\makelabel{ref:residue quadratic}{15.4.2}{X81464ABF7F10E544} 1636\makelabel{ref:RootMod}{15.4.3}{X83E3ED577B7A04ED} 1637\makelabel{ref:quadratic residue}{15.4.3}{X83E3ED577B7A04ED} 1638\makelabel{ref:residue quadratic}{15.4.3}{X83E3ED577B7A04ED} 1639\makelabel{ref:root of an integer modulo another}{15.4.3}{X83E3ED577B7A04ED} 1640\makelabel{ref:RootsMod}{15.4.4}{X84D3F03B862841F8} 1641\makelabel{ref:RootsUnityMod}{15.4.5}{X81F856E682A8ECBA} 1642\makelabel{ref:modular roots}{15.4.5}{X81F856E682A8ECBA} 1643\makelabel{ref:root of 1 modulo an integer}{15.4.5}{X81F856E682A8ECBA} 1644\makelabel{ref:Sigma}{15.5.1}{X823707DF821E79A0} 1645\makelabel{ref:Tau}{15.5.2}{X798C62847EE0372E} 1646\makelabel{ref:MoebiusMu}{15.5.3}{X79C1DA36827C2959} 1647\makelabel{ref:ContinuedFractionExpansionOfRoot}{15.6.1}{X874C161B83416092} 1648\makelabel{ref:ContinuedFractionApproximationOfRoot}{15.6.2}{X8059667580A039A6} 1649\makelabel{ref:PValuation}{15.7.1}{X8243EAA586D78ED4} 1650\makelabel{ref:TwoSquares}{15.7.2}{X85E1EFC484F648A4} 1651\makelabel{ref:representation as a sum of two squares}{15.7.2}{X85E1EFC484F648A4} 1652\makelabel{ref:Factorial}{16.1.1}{X87665F748594BF29} 1653\makelabel{ref:Binomial}{16.1.2}{X7A9AF5F58682819D} 1654\makelabel{ref:coefficient binomial}{16.1.2}{X7A9AF5F58682819D} 1655\makelabel{ref:number binomial}{16.1.2}{X7A9AF5F58682819D} 1656\makelabel{ref:Bell}{16.1.3}{X7DC5667580522BDA} 1657\makelabel{ref:number Bell}{16.1.3}{X7DC5667580522BDA} 1658\makelabel{ref:Bernoulli}{16.1.4}{X792FF6EA786A5C2B} 1659\makelabel{ref:sequence Bernoulli}{16.1.4}{X792FF6EA786A5C2B} 1660\makelabel{ref:Stirling1}{16.1.5}{X85037456785BB33C} 1661\makelabel{ref:Stirling number of the first kind}{16.1.5}{X85037456785BB33C} 1662\makelabel{ref:number Stirling, of the first kind}{16.1.5}{X85037456785BB33C} 1663\makelabel{ref:Stirling2}{16.1.6}{X7C93E14D7BC360F0} 1664\makelabel{ref:Stirling number of the second kind}{16.1.6}{X7C93E14D7BC360F0} 1665\makelabel{ref:number Stirling, of the second kind}{16.1.6}{X7C93E14D7BC360F0} 1666\makelabel{ref:Combinations}{16.2.1}{X8770F16D794C0ADB} 1667\makelabel{ref:power set}{16.2.1}{X8770F16D794C0ADB} 1668\makelabel{ref:subsets}{16.2.1}{X8770F16D794C0ADB} 1669\makelabel{ref:IteratorOfCombinations}{16.2.2}{X78DD5C0D81057540} 1670\makelabel{ref:EnumeratorOfCombinations}{16.2.2}{X78DD5C0D81057540} 1671\makelabel{ref:NrCombinations}{16.2.3}{X82A6E98C85714FD0} 1672\makelabel{ref:Arrangements}{16.2.4}{X7837B3357C7566C8} 1673\makelabel{ref:NrArrangements}{16.2.5}{X7DE1ABD47D19F140} 1674\makelabel{ref:UnorderedTuples}{16.2.6}{X81601C6786120DDC} 1675\makelabel{ref:NrUnorderedTuples}{16.2.7}{X7959281584C42C52} 1676\makelabel{ref:Tuples}{16.2.8}{X86A3CA0F7CC8C320} 1677\makelabel{ref:EnumeratorOfTuples}{16.2.9}{X7BA135297E8DA819} 1678\makelabel{ref:IteratorOfTuples}{16.2.10}{X86416A31807B0086} 1679\makelabel{ref:NrTuples}{16.2.11}{X85E18A9A87FD4CA2} 1680\makelabel{ref:PermutationsList}{16.2.12}{X7B0143FB83F359B7} 1681\makelabel{ref:NrPermutationsList}{16.2.13}{X8629A2908050EB3A} 1682\makelabel{ref:Derangements}{16.2.14}{X79C159507B2BF1C9} 1683\makelabel{ref:NrDerangements}{16.2.15}{X7C1741B181A9AB9C} 1684\makelabel{ref:PartitionsSet}{16.2.16}{X7A13D8DC8204525F} 1685\makelabel{ref:NrPartitionsSet}{16.2.17}{X7BCD7FC2876386F1} 1686\makelabel{ref:Partitions}{16.2.18}{X84A6D15F8107008B} 1687\makelabel{ref:IteratorOfPartitions}{16.2.19}{X8793AEBD7E529E1D} 1688\makelabel{ref:NrPartitions}{16.2.20}{X86933C4F795C4EBD} 1689\makelabel{ref:OrderedPartitions}{16.2.21}{X820DF201871F2723} 1690\makelabel{ref:partitions ordered, of an integer}{16.2.21}{X820DF201871F2723} 1691\makelabel{ref:partitions improper, of an integer}{16.2.21}{X820DF201871F2723} 1692\makelabel{ref:NrOrderedPartitions}{16.2.22}{X80BB9F4982CA1E8B} 1693\makelabel{ref:PartitionsGreatestLE}{16.2.23}{X8009520C82942461} 1694\makelabel{ref:PartitionsGreatestEQ}{16.2.24}{X7CB8D4FF8592A9BB} 1695\makelabel{ref:RestrictedPartitions}{16.2.25}{X7A70D4F3809494E7} 1696\makelabel{ref:partitions restricted, of an integer}{16.2.25}{X7A70D4F3809494E7} 1697\makelabel{ref:NrRestrictedPartitions}{16.2.26}{X800B43838742FBF4} 1698\makelabel{ref:SignPartition}{16.2.27}{X7F4EDCCA780B469D} 1699\makelabel{ref:AssociatedPartition}{16.2.28}{X7DB9BEB6856EC03D} 1700\makelabel{ref:PowerPartition}{16.2.29}{X7A95D8A6820363A8} 1701\makelabel{ref:symmetric group power map}{16.2.29}{X7A95D8A6820363A8} 1702\makelabel{ref:PartitionTuples}{16.2.30}{X877D997B7F66A119} 1703\makelabel{ref:NrPartitionTuples}{16.2.31}{X7F44AD098561DE32} 1704\makelabel{ref:BetaSet}{16.2.32}{X8796C1D783ED9CB4} 1705\makelabel{ref:Fibonacci}{16.3.1}{X85AE1D70803A886C} 1706\makelabel{ref:sequence Fibonacci}{16.3.1}{X85AE1D70803A886C} 1707\makelabel{ref:Lucas}{16.3.2}{X7830A03181D67192} 1708\makelabel{ref:sequence Lucas}{16.3.2}{X7830A03181D67192} 1709\makelabel{ref:Permanent}{16.4.1}{X7F0942DD83BBAB7A} 1710\makelabel{ref:Rationals}{17.1.1}{X7B6029D18570C08A} 1711\makelabel{ref:IsRationals}{17.1.1}{X7B6029D18570C08A} 1712\makelabel{ref:IsRat}{17.2.1}{X7ED018F5794935F7} 1713\makelabel{ref:test for a rational}{17.2.1}{X7ED018F5794935F7} 1714\makelabel{ref:IsPosRat}{17.2.2}{X7BD6E170840F045D} 1715\makelabel{ref:IsNegRat}{17.2.3}{X81179AC87AC951A8} 1716\makelabel{ref:NumeratorRat}{17.2.4}{X7D830E7482E7F528} 1717\makelabel{ref:numerator of a rational}{17.2.4}{X7D830E7482E7F528} 1718\makelabel{ref:DenominatorRat}{17.2.5}{X81F6B5877A81E727} 1719\makelabel{ref:denominator of a rational}{17.2.5}{X81F6B5877A81E727} 1720\makelabel{ref:Rat}{17.2.6}{X7EB4C646806A2BDE} 1721\makelabel{ref:Random for rationals}{17.2.7}{X7C8F8693825C28A4} 1722\makelabel{ref:type cyclotomic}{18}{X7DFC03C187DE4841} 1723\makelabel{ref:irrationalities}{18}{X7DFC03C187DE4841} 1724\makelabel{ref:cyclotomic field elements}{18}{X7DFC03C187DE4841} 1725\makelabel{ref:E}{18.1.1}{X8631458886314588} 1726\makelabel{ref:roots of unity}{18.1.1}{X8631458886314588} 1727\makelabel{ref:Cyclotomics}{18.1.2}{X863D1E017BC9EB7F} 1728\makelabel{ref:IsCyclotomic}{18.1.3}{X841C425281A6F775} 1729\makelabel{ref:IsCyc}{18.1.3}{X841C425281A6F775} 1730\makelabel{ref:CyclotomicsFamily}{18.1.3}{X841C425281A6F775} 1731\makelabel{ref:IsIntegralCyclotomic}{18.1.4}{X869750DA81EA0E67} 1732\makelabel{ref:Int for a cyclotomic}{18.1.5}{X7DD6B95F79321D23} 1733\makelabel{ref:String for a cyclotomic}{18.1.6}{X7CBA6CB678E2B143} 1734\makelabel{ref:Conductor for a cyclotomic}{18.1.7}{X815D6EC57CBA9827} 1735\makelabel{ref:Conductor for a collection of cyclotomics}{18.1.7}{X815D6EC57CBA9827} 1736\makelabel{ref:AbsoluteValue}{18.1.8}{X81DD58BB81FB3426} 1737\makelabel{ref:RoundCyc}{18.1.9}{X7808ECF37AA9004D} 1738\makelabel{ref:CoeffsCyc}{18.1.10}{X7AE2933985BE4C3E} 1739\makelabel{ref:coefficients for cyclotomics}{18.1.10}{X7AE2933985BE4C3E} 1740\makelabel{ref:DenominatorCyc}{18.1.11}{X803478CA7D2D830F} 1741\makelabel{ref:ExtRepOfObj for a cyclotomic}{18.1.12}{X785F2CAB805DE1BE} 1742\makelabel{ref:DescriptionOfRootOfUnity}{18.1.13}{X7DDD51B983D5BC44} 1743\makelabel{ref:logarithm of a root of unity}{18.1.13}{X7DDD51B983D5BC44} 1744\makelabel{ref:IsGaussInt}{18.1.14}{X8712419182ECD8DD} 1745\makelabel{ref:IsGaussRat}{18.1.15}{X7E6CF4947D0A56F7} 1746\makelabel{ref:DefaultField for cyclotomics}{18.1.16}{X7FE3D5637B5485D0} 1747\makelabel{ref:IsInfinity}{18.2.1}{X8511B8DF83324C27} 1748\makelabel{ref:IsNegInfinity}{18.2.1}{X8511B8DF83324C27} 1749\makelabel{ref:infinity}{18.2.1}{X8511B8DF83324C27} 1750\makelabel{ref:-infinity}{18.2.1}{X8511B8DF83324C27} 1751\makelabel{ref:operators for cyclotomics}{18.3}{X7F66A62384329705} 1752\makelabel{ref:atomic irrationalities}{18.4}{X7B242083873DD74F} 1753\makelabel{ref:EB}{18.4.1}{X8414ED887AF36359} 1754\makelabel{ref:EC}{18.4.1}{X8414ED887AF36359} 1755\makelabel{ref:ED}{18.4.1}{X8414ED887AF36359} 1756\makelabel{ref:EE}{18.4.1}{X8414ED887AF36359} 1757\makelabel{ref:EF}{18.4.1}{X8414ED887AF36359} 1758\makelabel{ref:EG}{18.4.1}{X8414ED887AF36359} 1759\makelabel{ref:EH}{18.4.1}{X8414ED887AF36359} 1760\makelabel{ref:bN (irrational value)}{18.4.1}{X8414ED887AF36359} 1761\makelabel{ref:cN (irrational value)}{18.4.1}{X8414ED887AF36359} 1762\makelabel{ref:dN (irrational value)}{18.4.1}{X8414ED887AF36359} 1763\makelabel{ref:eN (irrational value)}{18.4.1}{X8414ED887AF36359} 1764\makelabel{ref:fN (irrational value)}{18.4.1}{X8414ED887AF36359} 1765\makelabel{ref:gN (irrational value)}{18.4.1}{X8414ED887AF36359} 1766\makelabel{ref:hN (irrational value)}{18.4.1}{X8414ED887AF36359} 1767\makelabel{ref:EI}{18.4.2}{X813CF4327C4B4D29} 1768\makelabel{ref:ER}{18.4.2}{X813CF4327C4B4D29} 1769\makelabel{ref:iN (irrational value)}{18.4.2}{X813CF4327C4B4D29} 1770\makelabel{ref:rN (irrational value)}{18.4.2}{X813CF4327C4B4D29} 1771\makelabel{ref:EY}{18.4.3}{X8672D7F986CBA116} 1772\makelabel{ref:EX}{18.4.3}{X8672D7F986CBA116} 1773\makelabel{ref:EW}{18.4.3}{X8672D7F986CBA116} 1774\makelabel{ref:EV}{18.4.3}{X8672D7F986CBA116} 1775\makelabel{ref:EU}{18.4.3}{X8672D7F986CBA116} 1776\makelabel{ref:ET}{18.4.3}{X8672D7F986CBA116} 1777\makelabel{ref:ES}{18.4.3}{X8672D7F986CBA116} 1778\makelabel{ref:sN (irrational value)}{18.4.3}{X8672D7F986CBA116} 1779\makelabel{ref:tN (irrational value)}{18.4.3}{X8672D7F986CBA116} 1780\makelabel{ref:uN (irrational value)}{18.4.3}{X8672D7F986CBA116} 1781\makelabel{ref:vN (irrational value)}{18.4.3}{X8672D7F986CBA116} 1782\makelabel{ref:wN (irrational value)}{18.4.3}{X8672D7F986CBA116} 1783\makelabel{ref:xN (irrational value)}{18.4.3}{X8672D7F986CBA116} 1784\makelabel{ref:yN (irrational value)}{18.4.3}{X8672D7F986CBA116} 1785\makelabel{ref:EM}{18.4.4}{X7E5985FC846C5201} 1786\makelabel{ref:EL}{18.4.4}{X7E5985FC846C5201} 1787\makelabel{ref:EK}{18.4.4}{X7E5985FC846C5201} 1788\makelabel{ref:EJ}{18.4.4}{X7E5985FC846C5201} 1789\makelabel{ref:jN (irrational value)}{18.4.4}{X7E5985FC846C5201} 1790\makelabel{ref:kN (irrational value)}{18.4.4}{X7E5985FC846C5201} 1791\makelabel{ref:lN (irrational value)}{18.4.4}{X7E5985FC846C5201} 1792\makelabel{ref:mN (irrational value)}{18.4.4}{X7E5985FC846C5201} 1793\makelabel{ref:NK}{18.4.5}{X844F0EBF849EDEB3} 1794\makelabel{ref:AtlasIrrationality}{18.4.6}{X812E334E7A869D33} 1795\makelabel{ref:GaloisCyc for a cyclotomic}{18.5.1}{X79EE9097783128C4} 1796\makelabel{ref:GaloisCyc for a list of cyclotomics}{18.5.1}{X79EE9097783128C4} 1797\makelabel{ref:ComplexConjugate}{18.5.2}{X7BE001A0811CD599} 1798\makelabel{ref:RealPart}{18.5.2}{X7BE001A0811CD599} 1799\makelabel{ref:ImaginaryPart}{18.5.2}{X7BE001A0811CD599} 1800\makelabel{ref:StarCyc}{18.5.3}{X7E361C057E97CA66} 1801\makelabel{ref:Quadratic}{18.5.4}{X84438F867B0CC299} 1802\makelabel{ref:GaloisMat}{18.5.5}{X7DDDEC3F80543B7D} 1803\makelabel{ref:RationalizedMat}{18.5.6}{X7BB9F5957AA8C082} 1804\makelabel{ref:SetCyclotomicsLimit}{18.6.1}{X7D3028777DE39709} 1805\makelabel{ref:GetCyclotomicsLimit}{18.6.1}{X7D3028777DE39709} 1806\makelabel{ref:Float}{19.2.1}{X86D5EA93813FB6C4} 1807\makelabel{ref:NewFloat}{19.2.1}{X86D5EA93813FB6C4} 1808\makelabel{ref:MakeFloat}{19.2.1}{X86D5EA93813FB6C4} 1809\makelabel{ref:Rat for floats}{19.2.2}{X7BCD34DC7B5A0521} 1810\makelabel{ref:Cyc for floats}{19.2.3}{X7D1EAE11844625F4} 1811\makelabel{ref:SetFloats}{19.2.4}{X7A962B0983FA66E8} 1812\makelabel{ref:FLOAT constants}{19.2.5}{X819050BF8403806E} 1813\makelabel{ref:EqFloat}{19.2.6}{X7BD96E0585D5A1EE} 1814\makelabel{ref:PrecisionFloat}{19.2.7}{X7B3133497DDE839B} 1815\makelabel{ref:SignBit}{19.2.8}{X801753137949DD78} 1816\makelabel{ref:SignFloat}{19.2.8}{X801753137949DD78} 1817\makelabel{ref:IsPInfinity}{19.2.9}{X7E03FDEE824D1E8E} 1818\makelabel{ref:IsNInfinity}{19.2.9}{X7E03FDEE824D1E8E} 1819\makelabel{ref:IsXInfinity}{19.2.9}{X7E03FDEE824D1E8E} 1820\makelabel{ref:IsFinite for floats}{19.2.9}{X7E03FDEE824D1E8E} 1821\makelabel{ref:IsNaN}{19.2.9}{X7E03FDEE824D1E8E} 1822\makelabel{ref:Cos}{19.2.10}{X8151581186F75BA3} 1823\makelabel{ref:Sin}{19.2.10}{X8151581186F75BA3} 1824\makelabel{ref:Tan}{19.2.10}{X8151581186F75BA3} 1825\makelabel{ref:Sec}{19.2.10}{X8151581186F75BA3} 1826\makelabel{ref:Csc}{19.2.10}{X8151581186F75BA3} 1827\makelabel{ref:Cot}{19.2.10}{X8151581186F75BA3} 1828\makelabel{ref:Asin}{19.2.10}{X8151581186F75BA3} 1829\makelabel{ref:Acos}{19.2.10}{X8151581186F75BA3} 1830\makelabel{ref:Atan}{19.2.10}{X8151581186F75BA3} 1831\makelabel{ref:Cosh}{19.2.10}{X8151581186F75BA3} 1832\makelabel{ref:Sinh}{19.2.10}{X8151581186F75BA3} 1833\makelabel{ref:Tanh}{19.2.10}{X8151581186F75BA3} 1834\makelabel{ref:Sech}{19.2.10}{X8151581186F75BA3} 1835\makelabel{ref:Csch}{19.2.10}{X8151581186F75BA3} 1836\makelabel{ref:Coth}{19.2.10}{X8151581186F75BA3} 1837\makelabel{ref:Asinh}{19.2.10}{X8151581186F75BA3} 1838\makelabel{ref:Acosh}{19.2.10}{X8151581186F75BA3} 1839\makelabel{ref:Atanh}{19.2.10}{X8151581186F75BA3} 1840\makelabel{ref:Log}{19.2.10}{X8151581186F75BA3} 1841\makelabel{ref:Log2}{19.2.10}{X8151581186F75BA3} 1842\makelabel{ref:Log10}{19.2.10}{X8151581186F75BA3} 1843\makelabel{ref:Log1p}{19.2.10}{X8151581186F75BA3} 1844\makelabel{ref:Exp}{19.2.10}{X8151581186F75BA3} 1845\makelabel{ref:Exp2}{19.2.10}{X8151581186F75BA3} 1846\makelabel{ref:Exp10}{19.2.10}{X8151581186F75BA3} 1847\makelabel{ref:Expm1}{19.2.10}{X8151581186F75BA3} 1848\makelabel{ref:CubeRoot}{19.2.10}{X8151581186F75BA3} 1849\makelabel{ref:Square}{19.2.10}{X8151581186F75BA3} 1850\makelabel{ref:Ceil}{19.2.10}{X8151581186F75BA3} 1851\makelabel{ref:Floor}{19.2.10}{X8151581186F75BA3} 1852\makelabel{ref:Round}{19.2.10}{X8151581186F75BA3} 1853\makelabel{ref:Trunc}{19.2.10}{X8151581186F75BA3} 1854\makelabel{ref:Atan2}{19.2.10}{X8151581186F75BA3} 1855\makelabel{ref:FrExp}{19.2.10}{X8151581186F75BA3} 1856\makelabel{ref:LdExp}{19.2.10}{X8151581186F75BA3} 1857\makelabel{ref:AbsoluteValue for floats}{19.2.10}{X8151581186F75BA3} 1858\makelabel{ref:Norm for floats}{19.2.10}{X8151581186F75BA3} 1859\makelabel{ref:Hypothenuse}{19.2.10}{X8151581186F75BA3} 1860\makelabel{ref:Frac}{19.2.10}{X8151581186F75BA3} 1861\makelabel{ref:SinCos}{19.2.10}{X8151581186F75BA3} 1862\makelabel{ref:Erf}{19.2.10}{X8151581186F75BA3} 1863\makelabel{ref:Zeta}{19.2.10}{X8151581186F75BA3} 1864\makelabel{ref:Gamma}{19.2.10}{X8151581186F75BA3} 1865\makelabel{ref:Argument for complex floats}{19.4.1}{X7B0269D983F96677} 1866\makelabel{ref:Sup}{19.5.1}{X7C34D1D185802F2F} 1867\makelabel{ref:Inf}{19.5.2}{X78F1E457814FD1FD} 1868\makelabel{ref:Mid}{19.5.3}{X829581A485F55996} 1869\makelabel{ref:AbsoluteDiameter}{19.5.4}{X7FE540B387B0012C} 1870\makelabel{ref:Diameter}{19.5.4}{X7FE540B387B0012C} 1871\makelabel{ref:RelativeDiameter}{19.5.5}{X7CA771757F441592} 1872\makelabel{ref:IsDisjoint}{19.5.6}{X86D22AE57E2D84B2} 1873\makelabel{ref:IsSubset for interval floats}{19.5.7}{X7A5E0C3E79837EB8} 1874\makelabel{ref:IncreaseInterval}{19.5.8}{X85191E1679936CE9} 1875\makelabel{ref:BlowupInterval}{19.5.9}{X879EE14282DD1539} 1876\makelabel{ref:BisectInterval}{19.5.10}{X7EC15DAE7CBBB42E} 1877\makelabel{ref:type boolean}{20}{X787B4AB77A2F5E14} 1878\makelabel{ref:logical}{20}{X787B4AB77A2F5E14} 1879\makelabel{ref:IsBool}{20.1.1}{X7D58580284CF7894} 1880\makelabel{ref:fail}{20.2.1}{X8294AAC9860E87E5} 1881\makelabel{ref:comparisons of booleans}{20.3}{X862F17B68465B399} 1882\makelabel{ref:equality of booleans}{20.3.1}{X79305F9780394190} 1883\makelabel{ref:inequality of booleans}{20.3.1}{X79305F9780394190} 1884\makelabel{ref:ordering booleans}{20.3.2}{X7FEF019482AF5923} 1885\makelabel{ref:operations for booleans}{20.4}{X79AD41A185FD7213} 1886\makelabel{ref:logical operations}{20.4}{X79AD41A185FD7213} 1887\makelabel{ref:Logical disjunction}{20.4.1}{X7DFE7E518088AA89} 1888\makelabel{ref:or}{20.4.1}{X7DFE7E518088AA89} 1889\makelabel{ref:Logical conjunction}{20.4.2}{X7A64D25F804973CD} 1890\makelabel{ref:and}{20.4.2}{X7A64D25F804973CD} 1891\makelabel{ref:and for filters}{20.4.2}{X7A64D25F804973CD} 1892\makelabel{ref:Logical negation}{20.4.3}{X84F5034185D7EC3C} 1893\makelabel{ref:not}{20.4.3}{X84F5034185D7EC3C} 1894\makelabel{ref:Sets}{21}{X7B256AE5780F140A} 1895\makelabel{ref:IsList}{21.1.1}{X7C4CC4EA8299701E} 1896\makelabel{ref:IsDenseList}{21.1.2}{X870AA9D8798C93DD} 1897\makelabel{ref:IsHomogeneousList}{21.1.3}{X7C71596C82B6EF35} 1898\makelabel{ref:IsTable}{21.1.4}{X80872FAF80EB5DF9} 1899\makelabel{ref:IsRectangularTable}{21.1.5}{X79581E0387F7F7A9} 1900\makelabel{ref:IsConstantTimeAccessList}{21.1.6}{X7C84E16A85C99C8C} 1901\makelabel{ref:list element operation}{21.2}{X7B202D147A5C2884} 1902\makelabel{ref:list boundedness test operation}{21.2}{X7B202D147A5C2884} 1903\makelabel{ref:list assignment operation}{21.2}{X7B202D147A5C2884} 1904\makelabel{ref:list unbind operation}{21.2}{X7B202D147A5C2884} 1905\makelabel{ref:accessing list elements}{21.3}{X7921047F83F5FA28} 1906\makelabel{ref:list element access}{21.3}{X7921047F83F5FA28} 1907\makelabel{ref:sublist}{21.3}{X7921047F83F5FA28} 1908\makelabel{ref:sublist access}{21.3}{X7921047F83F5FA28} 1909\makelabel{ref:sublist operation}{21.3}{X7921047F83F5FA28} 1910\makelabel{ref:assignment to a list}{21.4}{X8611EF768210625B} 1911\makelabel{ref:list element assignment}{21.4}{X8611EF768210625B} 1912\makelabel{ref:sublist assignment}{21.4}{X8611EF768210625B} 1913\makelabel{ref:sublist assignment operation}{21.4}{X8611EF768210625B} 1914\makelabel{ref:Add}{21.4.2}{X795EC9D67E34DAB0} 1915\makelabel{ref:Remove}{21.4.3}{X7E98B11B79BA9167} 1916\makelabel{ref:CopyListEntries}{21.4.4}{X79D7E96F80A2D7C0} 1917\makelabel{ref:Append}{21.4.5}{X79E31DB27C82D6E1} 1918\makelabel{ref:IsBound for a list index}{21.5.1}{X79EC565A7DCEC938} 1919\makelabel{ref:GetWithDefault}{21.5.2}{X866F45D3797FDA00} 1920\makelabel{ref:Unbind unbind a list entry}{21.5.3}{X78B72FDF7BD63C0B} 1921\makelabel{ref:ShallowCopy for lists}{21.7}{X7ED7C0738495556F} 1922\makelabel{ref:StructuralCopy for lists}{21.7}{X7ED7C0738495556F} 1923\makelabel{ref:in for lists}{21.8.1}{X7B914A287F88ED0A} 1924\makelabel{ref:element test for lists}{21.8.1}{X7B914A287F88ED0A} 1925\makelabel{ref:EmptyPlist}{21.9.1}{X78BF67A5802E93AD} 1926\makelabel{ref:ShrinkAllocationPlist}{21.9.1}{X78BF67A5802E93AD} 1927\makelabel{ref:comparisons of lists}{21.10}{X8016D50F85147A77} 1928\makelabel{ref:list equal comparison}{21.10}{X8016D50F85147A77} 1929\makelabel{ref:list smaller comparison}{21.10}{X8016D50F85147A77} 1930\makelabel{ref:operators for lists}{21.11}{X845EEAF083D43CCE} 1931\makelabel{ref:IsGeneralizedRowVector}{21.12.1}{X87ABCEE9809585A0} 1932\makelabel{ref:IsMultiplicativeGeneralizedRowVector}{21.12.2}{X7FBCA5B58308C158} 1933\makelabel{ref:IsListDefault}{21.12.3}{X7BAD12E67BFC90DE} 1934\makelabel{ref:NestingDepthA}{21.12.4}{X8428E77B86722D52} 1935\makelabel{ref:NestingDepthM}{21.12.5}{X84B383B97FD986CD} 1936\makelabel{ref:addition list and non-list}{21.13.3}{X842D123E7EE5E3DB} 1937\makelabel{ref:list and non-list difference}{21.13.4}{X7C3DC8BE78DEECDE} 1938\makelabel{ref:list and non-list product}{21.14.3}{X84FDB95179BFE4CD} 1939\makelabel{ref:list and non-list quotient}{21.14.4}{X82EA2A5B786181C7} 1940\makelabel{ref:list and non-list mod}{21.14.5}{X7A0FD70C80B95C00} 1941\makelabel{ref:mod lists}{21.14.5}{X7A0FD70C80B95C00} 1942\makelabel{ref:list and non-list left quotient}{21.14.6}{X84BB2DFB8432A1A4} 1943\makelabel{ref:ListWithIdenticalEntries}{21.15.1}{X80FDB1457FF582E7} 1944\makelabel{ref:Position}{21.16.1}{X79975EC6783B4293} 1945\makelabel{ref:Positions}{21.16.2}{X7FA9648883AE1B88} 1946\makelabel{ref:PositionsOp}{21.16.2}{X7FA9648883AE1B88} 1947\makelabel{ref:PositionCanonical}{21.16.3}{X7B4B10AE81602D4E} 1948\makelabel{ref:PositionNthOccurrence}{21.16.4}{X7D2B25B484591506} 1949\makelabel{ref:PositionSorted}{21.16.5}{X7A122E848464E534} 1950\makelabel{ref:PositionSortedOp}{21.16.5}{X7A122E848464E534} 1951\makelabel{ref:PositionSortedBy}{21.16.6}{X820BA44D85930EBF} 1952\makelabel{ref:PositionSortedByOp}{21.16.6}{X820BA44D85930EBF} 1953\makelabel{ref:PositionSet}{21.16.7}{X78BFE9D78347C0DA} 1954\makelabel{ref:PositionMaximum}{21.16.8}{X7FD9C1D37F300206} 1955\makelabel{ref:PositionMinimum}{21.16.8}{X7FD9C1D37F300206} 1956\makelabel{ref:PositionProperty}{21.16.9}{X7E6C763A82C6153B} 1957\makelabel{ref:PositionsProperty}{21.16.10}{X7DA94D278304EC3D} 1958\makelabel{ref:PositionBound}{21.16.11}{X86C9E5C3863B3C03} 1959\makelabel{ref:PositionsBound}{21.16.12}{X819F71047AABEA2F} 1960\makelabel{ref:PositionNot}{21.16.13}{X865EF45D87ED1384} 1961\makelabel{ref:PositionNonZero}{21.16.14}{X7F42E5AD87EC9D5A} 1962\makelabel{ref:PositionSublist}{21.16.15}{X87A8C62A867D6DA4} 1963\makelabel{ref:IsMatchingSublist}{21.17.1}{X83F8EC7C7BF27EFC} 1964\makelabel{ref:IsDuplicateFree}{21.17.2}{X7FA892828252BB3B} 1965\makelabel{ref:IsDuplicateFreeList}{21.17.2}{X7FA892828252BB3B} 1966\makelabel{ref:duplicate free}{21.17.2}{X7FA892828252BB3B} 1967\makelabel{ref:IsSortedList}{21.17.3}{X7BAA9B0E81D4A884} 1968\makelabel{ref:list sorted}{21.17.3}{X7BAA9B0E81D4A884} 1969\makelabel{ref:IsSSortedList}{21.17.4}{X80CDAF45782E8DCB} 1970\makelabel{ref:IsSet}{21.17.4}{X80CDAF45782E8DCB} 1971\makelabel{ref:strictly sorted list}{21.17.4}{X80CDAF45782E8DCB} 1972\makelabel{ref:Length}{21.17.5}{X780769238600AFD1} 1973\makelabel{ref:ConstantTimeAccessList}{21.17.6}{X7B55FB967CDEF468} 1974\makelabel{ref:Sort}{21.18.1}{X7FE4975F8166884D} 1975\makelabel{ref:SortBy}{21.18.1}{X7FE4975F8166884D} 1976\makelabel{ref:StableSort}{21.18.1}{X7FE4975F8166884D} 1977\makelabel{ref:StableSortBy}{21.18.1}{X7FE4975F8166884D} 1978\makelabel{ref:SortParallel}{21.18.2}{X791F2B2C7E9B9A46} 1979\makelabel{ref:StableSortParallel}{21.18.2}{X791F2B2C7E9B9A46} 1980\makelabel{ref:Sortex}{21.18.3}{X87287FCA81E2B06A} 1981\makelabel{ref:SortingPerm}{21.18.4}{X800209E881E7CECB} 1982\makelabel{ref:sets}{21.19}{X80ABC25582343910} 1983\makelabel{ref:multisets}{21.19}{X80ABC25582343910} 1984\makelabel{ref:IsEqualSet}{21.19.2}{X7B4C0FEE7CDF6F2A} 1985\makelabel{ref:test for set equality}{21.19.2}{X7B4C0FEE7CDF6F2A} 1986\makelabel{ref:IsSubsetSet}{21.19.3}{X79B940567A849216} 1987\makelabel{ref:AddSet}{21.19.4}{X832C23CC7FCD8892} 1988\makelabel{ref:add an element to a set}{21.19.4}{X832C23CC7FCD8892} 1989\makelabel{ref:RemoveSet}{21.19.5}{X7FCA282E789A4F4B} 1990\makelabel{ref:remove an element from a set}{21.19.5}{X7FCA282E789A4F4B} 1991\makelabel{ref:UniteSet}{21.19.6}{X7B3469CD7EFC1A87} 1992\makelabel{ref:union of sets}{21.19.6}{X7B3469CD7EFC1A87} 1993\makelabel{ref:IntersectSet}{21.19.7}{X8473AA657FEC3D4D} 1994\makelabel{ref:intersection of sets}{21.19.7}{X8473AA657FEC3D4D} 1995\makelabel{ref:SubtractSet}{21.19.8}{X80B427537EB07D09} 1996\makelabel{ref:subtract a set from another}{21.19.8}{X80B427537EB07D09} 1997\makelabel{ref:concatenation of lists}{21.20}{X7DF510F7848CBBFD} 1998\makelabel{ref:Concatenation for several lists}{21.20.1}{X840C55A77D1BB2E1} 1999\makelabel{ref:Concatenation for a list of lists}{21.20.1}{X840C55A77D1BB2E1} 2000\makelabel{ref:Compacted}{21.20.2}{X7CB0A6AF87C7FAF7} 2001\makelabel{ref:Collected}{21.20.3}{X7ECE9056792F28BA} 2002\makelabel{ref:DuplicateFreeList}{21.20.4}{X8727F2928467C2F9} 2003\makelabel{ref:Unique}{21.20.4}{X8727F2928467C2F9} 2004\makelabel{ref:AsDuplicateFreeList}{21.20.5}{X7F5D4DD87E4378AC} 2005\makelabel{ref:Flat}{21.20.6}{X7FA272D984EF82ED} 2006\makelabel{ref:Reversed}{21.20.7}{X7C4FDB007C3F54A1} 2007\makelabel{ref:Shuffle}{21.20.8}{X8057372F83374193} 2008\makelabel{ref:IsLexicographicallyLess}{21.20.9}{X7BA5EF2181DD78D7} 2009\makelabel{ref:Apply}{21.20.10}{X8075FBDE7B81B4C8} 2010\makelabel{ref:Perform}{21.20.11}{X7EF6E2BC81DBF6FB} 2011\makelabel{ref:PermListList}{21.20.12}{X8763882A7D65F979} 2012\makelabel{ref:Maximum for various objects}{21.20.13}{X82CE0DE8828E4303} 2013\makelabel{ref:Maximum for a list}{21.20.13}{X82CE0DE8828E4303} 2014\makelabel{ref:Minimum for various objects}{21.20.14}{X82F133EC7F89665F} 2015\makelabel{ref:Minimum for a list}{21.20.14}{X82F133EC7F89665F} 2016\makelabel{ref:MaximumList}{21.20.15}{X842851EB7E0969F7} 2017\makelabel{ref:MinimumList}{21.20.15}{X842851EB7E0969F7} 2018\makelabel{ref:Cartesian for various objects}{21.20.16}{X7E1593B979BDF2CD} 2019\makelabel{ref:Cartesian for a list}{21.20.16}{X7E1593B979BDF2CD} 2020\makelabel{ref:IteratorOfCartesianProduct for several lists}{21.20.17}{X7E76F5A782184823} 2021\makelabel{ref:IteratorOfCartesianProduct for a list of lists}{21.20.17}{X7E76F5A782184823} 2022\makelabel{ref:Permuted}{21.20.18}{X7B5A19098406347A} 2023\makelabel{ref:List for a list (and a function)}{21.20.19}{X86CB7DCE8510F977} 2024\makelabel{ref:Filtered}{21.20.20}{X7C86D7F7795125F0} 2025\makelabel{ref:Number}{21.20.21}{X8179B13D80E935FC} 2026\makelabel{ref:First}{21.20.22}{X82801DFA84E11272} 2027\makelabel{ref:ForAll}{21.20.23}{X7F06961278166671} 2028\makelabel{ref:ForAny}{21.20.24}{X7AF82E747A8BDA75} 2029\makelabel{ref:Product}{21.20.25}{X7E5C72F27B657948} 2030\makelabel{ref:Sum}{21.20.26}{X7A04B71C84CFCC2D} 2031\makelabel{ref:Iterated}{21.20.27}{X834E4DF57F3A20F0} 2032\makelabel{ref:ListN}{21.20.28}{X7D150C2881881139} 2033\makelabel{ref:ListX}{21.21.1}{X8258477D7F72171B} 2034\makelabel{ref:SetX}{21.21.2}{X7AC321B87A2DCAF5} 2035\makelabel{ref:SumX}{21.21.3}{X82B1411E7FBE925F} 2036\makelabel{ref:ProductX}{21.21.4}{X7FB318B47D8783DA} 2037\makelabel{ref:range}{21.22}{X79596BDE7CAF8491} 2038\makelabel{ref:IsRange}{21.22.1}{X86DDC2FF7A50FBEE} 2039\makelabel{ref:IsRangeRep}{21.22.2}{X83896BC481536B07} 2040\makelabel{ref:ConvertToRangeRep}{21.22.3}{X7D22B2298167A58F} 2041\makelabel{ref:IsQuickPositionList}{21.23.1}{X7BB462C17962647F} 2042\makelabel{ref:IsPlistRep}{21.24.1}{X87BA4EBF80F16B72} 2043\makelabel{ref:IsBlist}{22.1.1}{X7BE078187A08DCEA} 2044\makelabel{ref:BlistList}{22.2.1}{X7C597B2D87CA2E6E} 2045\makelabel{ref:ListBlist}{22.2.2}{X874BEF63785AB439} 2046\makelabel{ref:SizeBlist}{22.2.3}{X85AD5EF77EFD7451} 2047\makelabel{ref:IsSubsetBlist}{22.2.4}{X7BA42D03796ED4B3} 2048\makelabel{ref:UnionBlist for various boolean lists}{22.3.1}{X7970BD3883C42D91} 2049\makelabel{ref:UnionBlist for a list}{22.3.1}{X7970BD3883C42D91} 2050\makelabel{ref:IntersectionBlist for various boolean lists}{22.3.2}{X86E1F8DE85E1EE1E} 2051\makelabel{ref:IntersectionBlist for a list}{22.3.2}{X86E1F8DE85E1EE1E} 2052\makelabel{ref:DifferenceBlist}{22.3.3}{X7D6FC2C58725708C} 2053\makelabel{ref:UniteBlist}{22.4.1}{X79815EB77CC8A389} 2054\makelabel{ref:UniteBlistList}{22.4.2}{X7C86C8D3853BE5EB} 2055\makelabel{ref:IntersectBlist}{22.4.3}{X84EB70D37EB275DF} 2056\makelabel{ref:SubtractBlist}{22.4.4}{X7AA138407D5A3BAC} 2057\makelabel{ref:FlipBlist}{22.4.5}{X7F14FF35786DAEF3} 2058\makelabel{ref:SetAllBlist}{22.4.6}{X7E9F6C197A79098F} 2059\makelabel{ref:ClearAllBlist}{22.4.7}{X87ED45A88688AE8E} 2060\makelabel{ref:IsBlistRep}{22.5.1}{X8453ADDA810B4C03} 2061\makelabel{ref:ConvertToBlistRep}{22.5.1}{X8453ADDA810B4C03} 2062\makelabel{ref:IsRowVector}{23.1.1}{X7DFB22A07836A7A9} 2063\makelabel{ref:addition vectors}{23.2}{X85516C3179C229DB} 2064\makelabel{ref:addition vector and scalar}{23.2}{X85516C3179C229DB} 2065\makelabel{ref:subtraction vectors}{23.2}{X85516C3179C229DB} 2066\makelabel{ref:subtraction scalar and vector}{23.2}{X85516C3179C229DB} 2067\makelabel{ref:subtraction vector and scalar}{23.2}{X85516C3179C229DB} 2068\makelabel{ref:multiplication scalar and vector}{23.2}{X85516C3179C229DB} 2069\makelabel{ref:multiplication vector and scalar}{23.2}{X85516C3179C229DB} 2070\makelabel{ref:multiplication vectors}{23.2}{X85516C3179C229DB} 2071\makelabel{ref:NormedRowVector}{23.2.1}{X785DC60D8482695D} 2072\makelabel{ref:ConvertToVectorRep for a list (and a field)}{23.3.1}{X810E46927F9E8F75} 2073\makelabel{ref:ConvertToVectorRep for a list (and a prime power)}{23.3.1}{X810E46927F9E8F75} 2074\makelabel{ref:ConvertToVectorRepNC for a list (and a field)}{23.3.1}{X810E46927F9E8F75} 2075\makelabel{ref:ConvertToVectorRepNC for a list (and a prime power)}{23.3.1}{X810E46927F9E8F75} 2076\makelabel{ref:ImmutableVector}{23.3.2}{X83D8F5BB80089279} 2077\makelabel{ref:NumberFFVector}{23.3.3}{X872E17FF829DB50F} 2078\makelabel{ref:AddRowVector}{23.4.1}{X78E6897186F482F6} 2079\makelabel{ref:AddCoeffs}{23.4.2}{X7854B2B67E3FE2CA} 2080\makelabel{ref:MultVector}{23.4.3}{X7BEF28C981C42E16} 2081\makelabel{ref:MultVectorLeft}{23.4.3}{X7BEF28C981C42E16} 2082\makelabel{ref:CoeffsMod}{23.4.4}{X8264B3EE7D56EEDD} 2083\makelabel{ref:LeftShiftRowVector}{23.5.1}{X80465E9B7A38C176} 2084\makelabel{ref:RightShiftRowVector}{23.5.2}{X822CCA4781D5C5EC} 2085\makelabel{ref:ShrinkRowVector}{23.5.3}{X78951C0E86D857B5} 2086\makelabel{ref:RemoveOuterCoeffs}{23.5.4}{X85796B6079581023} 2087\makelabel{ref:WeightVecFFE}{23.6.1}{X7C9F4D657F9BA5A1} 2088\makelabel{ref:DistanceVecFFE}{23.6.2}{X85AA5C6587559C1C} 2089\makelabel{ref:DistancesDistributionVecFFEsVecFFE}{23.6.3}{X7F2F630984A9D3D6} 2090\makelabel{ref:DistancesDistributionMatFFEVecFFE}{23.6.4}{X85135CEB86E61D49} 2091\makelabel{ref:AClosestVectorCombinationsMatFFEVecFFE}{23.6.5}{X82E5987E81487D18} 2092\makelabel{ref:AClosestVectorCombinationsMatFFEVecFFECoords}{23.6.5}{X82E5987E81487D18} 2093\makelabel{ref:CosetLeadersMatFFE}{23.6.6}{X7C88671678A2BEB4} 2094\makelabel{ref:ValuePol}{23.7.1}{X84DE99D57C29D47F} 2095\makelabel{ref:ProductCoeffs}{23.7.2}{X8328088C807AFFAF} 2096\makelabel{ref:ReduceCoeffs}{23.7.3}{X87248AA27F05BDCC} 2097\makelabel{ref:ReduceCoeffsMod}{23.7.4}{X7F74B1637CB13B7B} 2098\makelabel{ref:PowerModCoeffs}{23.7.5}{X825F8F357FB1BF56} 2099\makelabel{ref:ShiftedCoeffs}{23.7.6}{X833EF7AE80CE8B3C} 2100\makelabel{ref:InfoMatrix}{24.1.1}{X78EC82D27B4191DA} 2101\makelabel{ref:IsMatrix}{24.2.1}{X7E1AE46B862B185F} 2102\makelabel{ref:IsOrdinaryMatrix}{24.2.2}{X7CF42B8A845BC6A9} 2103\makelabel{ref:IsLieMatrix}{24.2.3}{X86EC33E17DD12D0E} 2104\makelabel{ref:addition matrices}{24.3}{X7899335779A39A95} 2105\makelabel{ref:addition scalar and matrix}{24.3}{X7899335779A39A95} 2106\makelabel{ref:addition matrix and scalar}{24.3}{X7899335779A39A95} 2107\makelabel{ref:subtraction matrices}{24.3}{X7899335779A39A95} 2108\makelabel{ref:subtraction scalar and matrix}{24.3}{X7899335779A39A95} 2109\makelabel{ref:subtraction matrix and scalar}{24.3}{X7899335779A39A95} 2110\makelabel{ref:multiplication scalar and matrix}{24.3}{X7899335779A39A95} 2111\makelabel{ref:multiplication matrix and scalar}{24.3}{X7899335779A39A95} 2112\makelabel{ref:multiplication vector and matrix}{24.3}{X7899335779A39A95} 2113\makelabel{ref:multiplication matrix and vector}{24.3}{X7899335779A39A95} 2114\makelabel{ref:multiplication matrices}{24.3}{X7899335779A39A95} 2115\makelabel{ref:inverse matrix}{24.3}{X7899335779A39A95} 2116\makelabel{ref:quotient matrices}{24.3}{X7899335779A39A95} 2117\makelabel{ref:quotient scalar and matrix}{24.3}{X7899335779A39A95} 2118\makelabel{ref:quotient matrix and scalar}{24.3}{X7899335779A39A95} 2119\makelabel{ref:quotient vector and matrix}{24.3}{X7899335779A39A95} 2120\makelabel{ref:power matrix}{24.3}{X7899335779A39A95} 2121\makelabel{ref:conjugate matrix}{24.3}{X7899335779A39A95} 2122\makelabel{ref:image vector under matrix}{24.3}{X7899335779A39A95} 2123\makelabel{ref:matrices commutator}{24.3}{X7899335779A39A95} 2124\makelabel{ref:addition scalar and matrix list}{24.3}{X7899335779A39A95} 2125\makelabel{ref:addition scalar and matrix list}{24.3}{X7899335779A39A95} 2126\makelabel{ref:subtraction scalar and matrix list}{24.3}{X7899335779A39A95} 2127\makelabel{ref:subtraction scalar and matrix list}{24.3}{X7899335779A39A95} 2128\makelabel{ref:multiplication scalar and matrix list}{24.3}{X7899335779A39A95} 2129\makelabel{ref:multiplication scalar and matrix list}{24.3}{X7899335779A39A95} 2130\makelabel{ref:quotient scalar and matrix list}{24.3}{X7899335779A39A95} 2131\makelabel{ref:multiplication matrix and matrix list}{24.3}{X7899335779A39A95} 2132\makelabel{ref:multiplication matrix and matrix list}{24.3}{X7899335779A39A95} 2133\makelabel{ref:quotient matrix and matrix list}{24.3}{X7899335779A39A95} 2134\makelabel{ref:multiplication vector and matrix list}{24.3}{X7899335779A39A95} 2135\makelabel{ref:DimensionsMat}{24.4.1}{X83A9DC2085D3A972} 2136\makelabel{ref:DefaultFieldOfMatrix}{24.4.2}{X80AE547B8095A5CB} 2137\makelabel{ref:TraceMat}{24.4.3}{X793D5E87870FFBCD} 2138\makelabel{ref:Trace of a matrix}{24.4.3}{X793D5E87870FFBCD} 2139\makelabel{ref:DeterminantMat}{24.4.4}{X83045F6F82C180E1} 2140\makelabel{ref:Determinant}{24.4.4}{X83045F6F82C180E1} 2141\makelabel{ref:DeterminantMatDestructive}{24.4.5}{X84277D21848B7B7F} 2142\makelabel{ref:DeterminantMatDivFree}{24.4.6}{X7EEA7E7A7F6BE6F3} 2143\makelabel{ref:IsEmptyMatrix for matrices}{24.4.7}{X8740D4D47D7ECD4A} 2144\makelabel{ref:IsMonomialMatrix}{24.4.8}{X848B80437CE65FF3} 2145\makelabel{ref:IsDiagonalMatrix}{24.4.9}{X7EEC8E768178696E} 2146\makelabel{ref:IsDiagonalMat}{24.4.9}{X7EEC8E768178696E} 2147\makelabel{ref:IsUpperTriangularMatrix}{24.4.10}{X8740E71C799C0BCC} 2148\makelabel{ref:IsUpperTriangularMat}{24.4.10}{X8740E71C799C0BCC} 2149\makelabel{ref:IsLowerTriangularMatrix}{24.4.11}{X853A5B988306DBFE} 2150\makelabel{ref:IsLowerTriangularMat}{24.4.11}{X853A5B988306DBFE} 2151\makelabel{ref:IdentityMat}{24.5.1}{X7DB902CE848D1524} 2152\makelabel{ref:NullMat}{24.5.2}{X86D343A77D9B3D4D} 2153\makelabel{ref:EmptyMatrix}{24.5.3}{X8508A7EA812BA0CC} 2154\makelabel{ref:DiagonalMat}{24.5.4}{X81042E7A7F247ADE} 2155\makelabel{ref:PermutationMat}{24.5.5}{X806C62A67A7D5379} 2156\makelabel{ref:TransposedMatImmutable}{24.5.6}{X7C52A38C79C36C35} 2157\makelabel{ref:TransposedMatAttr}{24.5.6}{X7C52A38C79C36C35} 2158\makelabel{ref:TransposedMat}{24.5.6}{X7C52A38C79C36C35} 2159\makelabel{ref:TransposedMatMutable}{24.5.6}{X7C52A38C79C36C35} 2160\makelabel{ref:TransposedMatOp}{24.5.6}{X7C52A38C79C36C35} 2161\makelabel{ref:TransposedMatDestructive}{24.5.7}{X7DBB40847E2B6252} 2162\makelabel{ref:KroneckerProduct}{24.5.8}{X8634C79E7DB22934} 2163\makelabel{ref:ReflectionMat}{24.5.9}{X845EC4D18054D140} 2164\makelabel{ref:PrintArray}{24.5.10}{X7DEBC9967DFDFC18} 2165\makelabel{ref:RandomMat}{24.6.1}{X7F957F0280A87961} 2166\makelabel{ref:RandomInvertibleMat}{24.6.2}{X7C939B4A7EDF015D} 2167\makelabel{ref:RandomUnimodularMat}{24.6.3}{X84743732846ACB44} 2168\makelabel{ref:Gaussian algorithm}{24.7}{X85485DCE809E323A} 2169\makelabel{ref:RankMat}{24.7.1}{X7B21AE7987D4FB31} 2170\makelabel{ref:TriangulizedMat}{24.7.2}{X7BA26C3387AB434E} 2171\makelabel{ref:RREF}{24.7.2}{X7BA26C3387AB434E} 2172\makelabel{ref:TriangulizeMat}{24.7.3}{X8384CA8E7B3850D3} 2173\makelabel{ref:NullspaceMat}{24.7.4}{X7DA0D5887DB12DC4} 2174\makelabel{ref:TriangulizedNullspaceMat}{24.7.4}{X7DA0D5887DB12DC4} 2175\makelabel{ref:kernel of a matrix}{24.7.4}{X7DA0D5887DB12DC4} 2176\makelabel{ref:NullspaceMatDestructive}{24.7.5}{X87684B0F7AB7B7DB} 2177\makelabel{ref:TriangulizedNullspaceMatDestructive}{24.7.5}{X87684B0F7AB7B7DB} 2178\makelabel{ref:SolutionMat}{24.7.6}{X838A519C7CD2969E} 2179\makelabel{ref:SolutionMatDestructive}{24.7.7}{X7A7880D27CE7C1FE} 2180\makelabel{ref:BaseFixedSpace}{24.7.8}{X7AB5AC547809F999} 2181\makelabel{ref:GeneralisedEigenvalues}{24.8.1}{X7A2462CC7B0C9D66} 2182\makelabel{ref:GeneralizedEigenvalues}{24.8.1}{X7A2462CC7B0C9D66} 2183\makelabel{ref:GeneralisedEigenspaces}{24.8.2}{X845CA0457D65876D} 2184\makelabel{ref:GeneralizedEigenspaces}{24.8.2}{X845CA0457D65876D} 2185\makelabel{ref:Eigenvalues}{24.8.3}{X8413C6FB7CEE9D59} 2186\makelabel{ref:Eigenspaces}{24.8.4}{X7A6B047281B52FD7} 2187\makelabel{ref:Eigenvectors}{24.8.5}{X8506584579D4EA18} 2188\makelabel{ref:ElementaryDivisorsMat}{24.9.1}{X7AC4D74F81908109} 2189\makelabel{ref:ElementaryDivisorsMatDestructive}{24.9.1}{X7AC4D74F81908109} 2190\makelabel{ref:ElementaryDivisorsTransformationsMat}{24.9.2}{X7AA1C9047B102204} 2191\makelabel{ref:ElementaryDivisorsTransformationsMatDestructive}{24.9.2}{X7AA1C9047B102204} 2192\makelabel{ref:DiagonalizeMat}{24.9.3}{X85819D3F7A582180} 2193\makelabel{ref:SemiEchelonMat}{24.10.1}{X7D5D6BD07B7E981B} 2194\makelabel{ref:SemiEchelonMatDestructive}{24.10.2}{X8251F6F57D346385} 2195\makelabel{ref:SemiEchelonMatTransformation}{24.10.3}{X7EFD1DB5861A54F0} 2196\makelabel{ref:SemiEchelonMats}{24.10.4}{X827D7971800DB661} 2197\makelabel{ref:SemiEchelonMatsDestructive}{24.10.5}{X808F493B839BC7A6} 2198\makelabel{ref:BaseMat}{24.11.1}{X7AD6B5F5794D9E46} 2199\makelabel{ref:BaseMatDestructive}{24.11.2}{X78B094597E382A5F} 2200\makelabel{ref:BaseOrthogonalSpaceMat}{24.11.3}{X78B94EFF87A455BE} 2201\makelabel{ref:SumIntersectionMat}{24.11.4}{X7AFF8BCF80C88B45} 2202\makelabel{ref:BaseSteinitzVectors}{24.11.5}{X8245D54F7AC532EB} 2203\makelabel{ref:DiagonalOfMatrix}{24.12.1}{X7A9139D686ACB7D8} 2204\makelabel{ref:DiagonalOfMat}{24.12.1}{X7A9139D686ACB7D8} 2205\makelabel{ref:UpperSubdiagonal}{24.12.2}{X84A78C057F9DAE5E} 2206\makelabel{ref:DepthOfUpperTriangularMatrix}{24.12.3}{X84D74DEA798A9094} 2207\makelabel{ref:CharacteristicPolynomial}{24.13.1}{X87FA0A727CDB060B} 2208\makelabel{ref:RationalCanonicalFormTransform}{24.13.2}{X7B52560C792C1A0F} 2209\makelabel{ref:Frobenius Normal Form}{24.13.2}{X7B52560C792C1A0F} 2210\makelabel{ref:JordanDecomposition}{24.13.3}{X83F55D4E79BA5D1B} 2211\makelabel{ref:BlownUpMat}{24.13.4}{X85923C107A4569D0} 2212\makelabel{ref:BlownUpVector}{24.13.5}{X82AC277D84EC5749} 2213\makelabel{ref:CompanionMat}{24.13.6}{X85A1026D7CB6ABAC} 2214\makelabel{ref:ImmutableMatrix}{24.14.1}{X7DED2522828B6C30} 2215\makelabel{ref:ConvertToMatrixRep for a list (and a field)}{24.14.2}{X8587A62F818AA0D6} 2216\makelabel{ref:ConvertToMatrixRep for a list (and a prime power)}{24.14.2}{X8587A62F818AA0D6} 2217\makelabel{ref:ConvertToMatrixRepNC for a list (and a field)}{24.14.2}{X8587A62F818AA0D6} 2218\makelabel{ref:ConvertToMatrixRepNC for a list (and a prime power)}{24.14.2}{X8587A62F818AA0D6} 2219\makelabel{ref:ProjectiveOrder}{24.14.3}{X84A76F7A7B4166BC} 2220\makelabel{ref:SimultaneousEigenvalues}{24.14.4}{X847ADC6779E33A1C} 2221\makelabel{ref:InverseMatMod}{24.15.1}{X7D8D1E0E83C7F872} 2222\makelabel{ref:BasisNullspaceModN}{24.15.2}{X7D7DF873826A7C20} 2223\makelabel{ref:NullspaceModQ}{24.15.3}{X86AE919983B242E2} 2224\makelabel{ref:NullspaceModN}{24.15.3}{X86AE919983B242E2} 2225\makelabel{ref:PRODGF2MATGF2MATSIMPLE}{24.16.1}{X7C0C26027FAE0C83} 2226\makelabel{ref:PRODGF2MATGF2MATADVANCED}{24.16.2}{X81965B7D7F45E088} 2227\makelabel{ref:IsBlockMatrixRep}{24.17}{X7F8A71F38201A250} 2228\makelabel{ref:AsBlockMatrix}{24.17.1}{X7D675B3C79CF8871} 2229\makelabel{ref:BlockMatrix}{24.17.2}{X8633538685551E7A} 2230\makelabel{ref:MatrixByBlockMatrix}{24.17.3}{X83FAF4158180041F} 2231\makelabel{ref:SimplexMethod}{24.18.1}{X845D5F8D7D905CB8} 2232\makelabel{ref:NullspaceIntMat}{25.1.1}{X792315717F5B0294} 2233\makelabel{ref:SolutionIntMat}{25.1.2}{X7D749F317DBD1E69} 2234\makelabel{ref:SolutionNullspaceIntMat}{25.1.3}{X82CECB6E7D515CD2} 2235\makelabel{ref:BaseIntMat}{25.1.4}{X7F66E8EA7D1AA2C1} 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2428\makelabel{ref:IsFinite}{30.4.2}{X808A4061809A6E67} 2429\makelabel{ref:finiteness test for a list or collection}{30.4.2}{X808A4061809A6E67} 2430\makelabel{ref:IsTrivial}{30.4.3}{X7E3402D6799D3C24} 2431\makelabel{ref:IsNonTrivial}{30.4.4}{X7F192373850B85B9} 2432\makelabel{ref:IsWholeFamily}{30.4.5}{X78EF6A137E8F66B0} 2433\makelabel{ref:Size}{30.4.6}{X858ADA3B7A684421} 2434\makelabel{ref:size of a list or collection}{30.4.6}{X858ADA3B7A684421} 2435\makelabel{ref:order of a list, collection or domain}{30.4.6}{X858ADA3B7A684421} 2436\makelabel{ref:Representative}{30.4.7}{X865507568182424E} 2437\makelabel{ref:RepresentativeSmallest}{30.4.8}{X8026085680270D37} 2438\makelabel{ref:representative of a list or collection}{30.4.8}{X8026085680270D37} 2439\makelabel{ref:IsSubset}{30.5.1}{X79CA175481F8105F} 2440\makelabel{ref:subset test for collections}{30.5.1}{X79CA175481F8105F} 2441\makelabel{ref:Intersection for various collections}{30.5.2}{X851069107CACF98E} 2442\makelabel{ref:Intersection 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2473\makelabel{ref:AsStruct}{31.4}{X7EA77DE17DD8A231} 2474\makelabel{ref:IsomorphismRepStruct}{31.5}{X860FCCBE7A41412F} 2475\makelabel{ref:IsStruct}{31.6}{X7D72F11B82F4A036} 2476\makelabel{ref:Parent}{31.7.1}{X7BC856CC7F116BB0} 2477\makelabel{ref:SetParent}{31.7.1}{X7BC856CC7F116BB0} 2478\makelabel{ref:HasParent}{31.7.1}{X7BC856CC7F116BB0} 2479\makelabel{ref:Subdomains}{31.8}{X7B58FDEF80338DD6} 2480\makelabel{ref:Substruct}{31.8}{X7B58FDEF80338DD6} 2481\makelabel{ref:SubstructNC}{31.8}{X7B58FDEF80338DD6} 2482\makelabel{ref:AsSubstruct}{31.8}{X7B58FDEF80338DD6} 2483\makelabel{ref:IsSubstruct}{31.8}{X7B58FDEF80338DD6} 2484\makelabel{ref:IsGeneralizedDomain}{31.9.1}{X86B4AC017FAF4D12} 2485\makelabel{ref:IsDomain}{31.9.1}{X86B4AC017FAF4D12} 2486\makelabel{ref:GeneratorsOfDomain}{31.9.2}{X7E353DD1838AB223} 2487\makelabel{ref:Domain}{31.9.3}{X826A21287FD3ACC0} 2488\makelabel{ref:DomainByGenerators}{31.9.3}{X826A21287FD3ACC0} 2489\makelabel{ref:Characteristic}{31.10.1}{X81278E53800BF64D} 2490\makelabel{ref:OneImmutable}{31.10.2}{X8046262384895B2A} 2491\makelabel{ref:OneAttr}{31.10.2}{X8046262384895B2A} 2492\makelabel{ref:One}{31.10.2}{X8046262384895B2A} 2493\makelabel{ref:Identity}{31.10.2}{X8046262384895B2A} 2494\makelabel{ref:OneMutable}{31.10.2}{X8046262384895B2A} 2495\makelabel{ref:OneOp}{31.10.2}{X8046262384895B2A} 2496\makelabel{ref:OneSameMutability}{31.10.2}{X8046262384895B2A} 2497\makelabel{ref:OneSM}{31.10.2}{X8046262384895B2A} 2498\makelabel{ref:ZeroImmutable}{31.10.3}{X8040AC7A79FFC442} 2499\makelabel{ref:ZeroAttr}{31.10.3}{X8040AC7A79FFC442} 2500\makelabel{ref:Zero}{31.10.3}{X8040AC7A79FFC442} 2501\makelabel{ref:ZeroMutable}{31.10.3}{X8040AC7A79FFC442} 2502\makelabel{ref:ZeroOp}{31.10.3}{X8040AC7A79FFC442} 2503\makelabel{ref:ZeroSameMutability}{31.10.3}{X8040AC7A79FFC442} 2504\makelabel{ref:ZeroSM}{31.10.3}{X8040AC7A79FFC442} 2505\makelabel{ref:MultiplicativeZeroOp}{31.10.4}{X86DEB543824C40EB} 2506\makelabel{ref:IsOne}{31.10.5}{X814D78347858EC13} 2507\makelabel{ref:IsZero}{31.10.6}{X82BDA47282F9BBA7} 2508\makelabel{ref:IsIdempotent}{31.10.7}{X7CB5896082D29173} 2509\makelabel{ref:InverseImmutable}{31.10.8}{X78EE524E83624057} 2510\makelabel{ref:InverseAttr}{31.10.8}{X78EE524E83624057} 2511\makelabel{ref:Inverse}{31.10.8}{X78EE524E83624057} 2512\makelabel{ref:InverseMutable}{31.10.8}{X78EE524E83624057} 2513\makelabel{ref:InverseOp}{31.10.8}{X78EE524E83624057} 2514\makelabel{ref:InverseSameMutability}{31.10.8}{X78EE524E83624057} 2515\makelabel{ref:InverseSM}{31.10.8}{X78EE524E83624057} 2516\makelabel{ref:AdditiveInverseImmutable}{31.10.9}{X84BB723C81D55D63} 2517\makelabel{ref:AdditiveInverseAttr}{31.10.9}{X84BB723C81D55D63} 2518\makelabel{ref:AdditiveInverse}{31.10.9}{X84BB723C81D55D63} 2519\makelabel{ref:AdditiveInverseMutable}{31.10.9}{X84BB723C81D55D63} 2520\makelabel{ref:AdditiveInverseOp}{31.10.9}{X84BB723C81D55D63} 2521\makelabel{ref:AdditiveInverseSameMutability}{31.10.9}{X84BB723C81D55D63} 2522\makelabel{ref:AdditiveInverseSM}{31.10.9}{X84BB723C81D55D63} 2523\makelabel{ref:Order}{31.10.10}{X84F59A2687C62763} 2524\makelabel{ref:equality operation}{31.11.1}{X7EF67D047F03CA6F} 2525\makelabel{ref:comparison operation}{31.11.1}{X7EF67D047F03CA6F} 2526\makelabel{ref:CanEasilyCompareElements}{31.11.2}{X7EFE013B8634D214} 2527\makelabel{ref:CanEasilyCompareElementsFamily}{31.11.2}{X7EFE013B8634D214} 2528\makelabel{ref:CanEasilySortElements}{31.11.2}{X7EFE013B8634D214} 2529\makelabel{ref:CanEasilySortElementsFamily}{31.11.2}{X7EFE013B8634D214} 2530\makelabel{ref:addition operation}{31.12.1}{X8481C9B97B214C23} 2531\makelabel{ref:multiplication operation}{31.12.1}{X8481C9B97B214C23} 2532\makelabel{ref:division operation}{31.12.1}{X8481C9B97B214C23} 2533\makelabel{ref:exponentiation operation}{31.12.1}{X8481C9B97B214C23} 2534\makelabel{ref:remainder operation}{31.12.1}{X8481C9B97B214C23} 2535\makelabel{ref:LeftQuotient}{31.12.2}{X7A37082878DB3930} 2536\makelabel{ref:Comm}{31.12.3}{X80761843831B468E} 2537\makelabel{ref:LieBracket}{31.12.4}{X86A62A937A42B82E} 2538\makelabel{ref:Sqrt}{31.12.5}{X7E8F1FB87C229BB0} 2539\makelabel{ref:UseSubsetRelation}{31.13.1}{X7C03098C838ADE40} 2540\makelabel{ref:UseFactorRelation}{31.13.2}{X78039B628262BFA8} 2541\makelabel{ref:UseIsomorphismRelation}{31.13.3}{X839BE6467E8474D9} 2542\makelabel{ref:InstallSubsetMaintenance}{31.13.4}{X863C35007C7AA914} 2543\makelabel{ref:InstallFactorMaintenance}{31.13.5}{X7BB7EE5078EF6F47} 2544\makelabel{ref:InstallIsomorphismMaintenance}{31.13.6}{X79F97F0F78D89186} 2545\makelabel{ref:IsExtAElement}{31.14.1}{X7FBD4F65861C2DF2} 2546\makelabel{ref:IsNearAdditiveElement}{31.14.2}{X7F346AA47AEC39AB} 2547\makelabel{ref:IsAdditiveElement}{31.14.3}{X78D042B486E1D7F7} 2548\makelabel{ref:IsNearAdditiveElementWithZero}{31.14.4}{X7CE2353F836F6E0A} 2549\makelabel{ref:IsAdditiveElementWithZero}{31.14.5}{X87F3552A789C572D} 2550\makelabel{ref:IsNearAdditiveElementWithInverse}{31.14.6}{X84B0929982B51CB4} 2551\makelabel{ref:IsAdditiveElementWithInverse}{31.14.7}{X7C0E4AE883947778} 2552\makelabel{ref:IsExtLElement}{31.14.8}{X860D1E387DD5CCCF} 2553\makelabel{ref:IsExtRElement}{31.14.9}{X809E0C097E480AF1} 2554\makelabel{ref:IsMultiplicativeElement}{31.14.10}{X797D3B2A7A2B2F53} 2555\makelabel{ref:IsMultiplicativeElementWithOne}{31.14.11}{X82BC294F7D388AE8} 2556\makelabel{ref:IsMultiplicativeElementWithZero}{31.14.12}{X8703BFC2841BBD63} 2557\makelabel{ref:IsMultiplicativeElementWithInverse}{31.14.13}{X7FDB14E57814FA3B} 2558\makelabel{ref:IsVector}{31.14.14}{X802F34F280B29DF4} 2559\makelabel{ref:IsNearRingElement}{31.14.15}{X799AEDE180C31276} 2560\makelabel{ref:IsRingElement}{31.14.16}{X84BF40CA86C07361} 2561\makelabel{ref:IsNearRingElementWithOne}{31.14.17}{X7C724689784EEF3D} 2562\makelabel{ref:IsRingElementWithOne}{31.14.18}{X875B67208017608E} 2563\makelabel{ref:IsNearRingElementWithInverse}{31.14.19}{X80CD04ED85B6B2F9} 2564\makelabel{ref:IsRingElementWithInverse}{31.14.20}{X8113834E84FD0435} 2565\makelabel{ref:IsScalar}{31.14.20}{X8113834E84FD0435} 2566\makelabel{ref:IsAssociativeElement}{31.15.1}{X7979AFAA80FF795A} 2567\makelabel{ref:IsAssociativeElementCollection}{31.15.1}{X7979AFAA80FF795A} 2568\makelabel{ref:IsAssociativeElementCollColl}{31.15.1}{X7979AFAA80FF795A} 2569\makelabel{ref:IsAdditivelyCommutativeElement}{31.15.2}{X78A286418205CE44} 2570\makelabel{ref:IsAdditivelyCommutativeElementCollection}{31.15.2}{X78A286418205CE44} 2571\makelabel{ref:IsAdditivelyCommutativeElementCollColl}{31.15.2}{X78A286418205CE44} 2572\makelabel{ref:IsAdditivelyCommutativeElementFamily}{31.15.2}{X78A286418205CE44} 2573\makelabel{ref:IsCommutativeElement}{31.15.3}{X8137FA8D86714AC0} 2574\makelabel{ref:IsCommutativeElementCollection}{31.15.3}{X8137FA8D86714AC0} 2575\makelabel{ref:IsCommutativeElementCollColl}{31.15.3}{X8137FA8D86714AC0} 2576\makelabel{ref:IsFiniteOrderElement}{31.15.4}{X810D2E5E832594AA} 2577\makelabel{ref:IsFiniteOrderElementCollection}{31.15.4}{X810D2E5E832594AA} 2578\makelabel{ref:IsFiniteOrderElementCollColl}{31.15.4}{X810D2E5E832594AA} 2579\makelabel{ref:IsJacobianElement}{31.15.5}{X796957D0805A0221} 2580\makelabel{ref:IsJacobianElementCollection}{31.15.5}{X796957D0805A0221} 2581\makelabel{ref:IsJacobianElementCollColl}{31.15.5}{X796957D0805A0221} 2582\makelabel{ref:IsRestrictedJacobianElement}{31.15.5}{X796957D0805A0221} 2583\makelabel{ref:IsRestrictedJacobianElementCollection}{31.15.5}{X796957D0805A0221} 2584\makelabel{ref:IsRestrictedJacobianElementCollColl}{31.15.5}{X796957D0805A0221} 2585\makelabel{ref:IsZeroSquaredElement}{31.15.6}{X7844399D7847AB24} 2586\makelabel{ref:IsZeroSquaredElementCollection}{31.15.6}{X7844399D7847AB24} 2587\makelabel{ref:IsZeroSquaredElementCollColl}{31.15.6}{X7844399D7847AB24} 2588\makelabel{ref:functions as in mathematics}{32}{X7C9734B880042C73} 2589\makelabel{ref:relations}{32}{X7C9734B880042C73} 2590\makelabel{ref:IsDirectProductElement}{32.1.1}{X87FD9FE787023FF0} 2591\makelabel{ref:DirectProductFamily}{32.1.2}{X78F8A1168280E06D} 2592\makelabel{ref:GeneralMappingByElements}{32.2.1}{X79D0D2F07A14D039} 2593\makelabel{ref:MappingByFunction by function (and inverse function) between two domains}{32.2.2}{X7D55E1977ED70E01} 2594\makelabel{ref:MappingByFunction by function and function that computes one preimage}{32.2.2}{X7D55E1977ED70E01} 2595\makelabel{ref:InverseGeneralMapping}{32.2.3}{X865FC25A87D36F3D} 2596\makelabel{ref:RestrictedInverseGeneralMapping}{32.2.4}{X7BD2D5A87CD6B213} 2597\makelabel{ref:CompositionMapping}{32.2.5}{X7ED1E4E27CCE2DCA} 2598\makelabel{ref:CompositionMapping2}{32.2.6}{X86486B687B7077AC} 2599\makelabel{ref:CompositionMapping2General}{32.2.6}{X86486B687B7077AC} 2600\makelabel{ref:IsCompositionMappingRep}{32.2.7}{X7A926D167C3155F6} 2601\makelabel{ref:ConstituentsCompositionMapping}{32.2.8}{X87775B438008DCA5} 2602\makelabel{ref:ZeroMapping}{32.2.9}{X795FF8DC785F110A} 2603\makelabel{ref:IdentityMapping}{32.2.10}{X7EBAE0368470A603} 2604\makelabel{ref:Embedding for two domains}{32.2.11}{X86452F8587CBAEA0} 2605\makelabel{ref:Embedding for a domain and a positive integer}{32.2.11}{X86452F8587CBAEA0} 2606\makelabel{ref:Projection for two domains}{32.2.12}{X8769E8DA80BC96C1} 2607\makelabel{ref:Projection for a domain and a positive integer}{32.2.12}{X8769E8DA80BC96C1} 2608\makelabel{ref:Projection for a domain}{32.2.12}{X8769E8DA80BC96C1} 2609\makelabel{ref:RestrictedMapping}{32.2.13}{X800014D683A81009} 2610\makelabel{ref:IsTotal}{32.3.1}{X83C7494E828CC9C8} 2611\makelabel{ref:IsSingleValued}{32.3.2}{X86D44C8A78BF1981} 2612\makelabel{ref:IsMapping}{32.3.3}{X7CC95EB282854385} 2613\makelabel{ref:IsInjective}{32.3.4}{X7F065FD7822C0A12} 2614\makelabel{ref:IsSurjective}{32.3.5}{X784ECE847E005B8F} 2615\makelabel{ref:IsBijective}{32.3.6}{X878F56AB7B342767} 2616\makelabel{ref:Range of a general mapping}{32.3.7}{X7B6FD7277CDE9FCB} 2617\makelabel{ref:Source}{32.3.8}{X7DE8173F80E07AB1} 2618\makelabel{ref:UnderlyingRelation}{32.3.9}{X784F871383FB599B} 2619\makelabel{ref:UnderlyingGeneralMapping}{32.3.10}{X786581DE871A47D0} 2620\makelabel{ref:ImagesSource}{32.4.1}{X7D23C1CE863DACD8} 2621\makelabel{ref:ImagesRepresentative}{32.4.2}{X85ADB89B7C8DD7D0} 2622\makelabel{ref:ImagesElm}{32.4.3}{X7D51184B7EE5B2CF} 2623\makelabel{ref:ImagesSet}{32.4.4}{X8781348F7F5796A0} 2624\makelabel{ref:ImageElm}{32.4.5}{X7CFAB0157BFB1806} 2625\makelabel{ref:Image set of images of the source of a general mapping}{32.4.6}{X87F4D35A826599C6} 2626\makelabel{ref:Image unique image of an element under a mapping}{32.4.6}{X87F4D35A826599C6} 2627\makelabel{ref:Image set of images of a collection under a mapping}{32.4.6}{X87F4D35A826599C6} 2628\makelabel{ref:Images set of images of the source of a general mapping}{32.4.7}{X86114B2E7E77488C} 2629\makelabel{ref:Images set of images of an element under a mapping}{32.4.7}{X86114B2E7E77488C} 2630\makelabel{ref:Images set of images of a collection under a mapping}{32.4.7}{X86114B2E7E77488C} 2631\makelabel{ref:PreImagesRange}{32.5.1}{X78EF1FE77B0973C0} 2632\makelabel{ref:PreImagesElm}{32.5.2}{X7FBB830C8729E995} 2633\makelabel{ref:PreImageElm}{32.5.3}{X7D212F727CAE971A} 2634\makelabel{ref:PreImagesRepresentative}{32.5.4}{X7AE24A1586B7DE79} 2635\makelabel{ref:PreImagesSet}{32.5.5}{X856BAFC87B2D2811} 2636\makelabel{ref:PreImage set of preimages of the range of a general mapping}{32.5.6}{X836FAEAC78B55BF4} 2637\makelabel{ref:PreImage unique preimage of an element under a general mapping}{32.5.6}{X836FAEAC78B55BF4} 2638\makelabel{ref:PreImage set of preimages of a collection under a general mapping}{32.5.6}{X836FAEAC78B55BF4} 2639\makelabel{ref:PreImages set of preimages of the range of a general mapping}{32.5.7}{X85C8590E832002EF} 2640\makelabel{ref:PreImages set of preimages of an elm under a general mapping}{32.5.7}{X85C8590E832002EF} 2641\makelabel{ref:PreImages set of preimages of a collection under a general mapping}{32.5.7}{X85C8590E832002EF} 2642\makelabel{ref:IsMagmaHomomorphism}{32.8.1}{X7DC72CF28539A251} 2643\makelabel{ref:MagmaHomomorphismByFunctionNC}{32.8.2}{X8181676787E760A2} 2644\makelabel{ref:NaturalHomomorphismByGenerators}{32.8.3}{X79D0216E871B7051} 2645\makelabel{ref:RespectsMultiplication}{32.9.1}{X7BEFF95883EAEC78} 2646\makelabel{ref:RespectsOne}{32.9.2}{X7EE4DA097AE9CBC1} 2647\makelabel{ref:RespectsInverses}{32.9.3}{X7F27AE9C84A4DF90} 2648\makelabel{ref:IsGroupGeneralMapping}{32.9.4}{X819DD174829BF3AE} 2649\makelabel{ref:IsGroupHomomorphism}{32.9.4}{X819DD174829BF3AE} 2650\makelabel{ref:KernelOfMultiplicativeGeneralMapping}{32.9.5}{X81A5A5CF846E5FBF} 2651\makelabel{ref:CoKernelOfMultiplicativeGeneralMapping}{32.9.6}{X7F09B6E28080DCB4} 2652\makelabel{ref:RespectsAddition}{32.10.1}{X7A3321E878925C3A} 2653\makelabel{ref:RespectsAdditiveInverses}{32.10.2}{X8130D8907B92F746} 2654\makelabel{ref:RespectsZero}{32.10.3}{X7D342736781EB280} 2655\makelabel{ref:IsAdditiveGroupGeneralMapping}{32.10.4}{X7B99EF287A8A0BD9} 2656\makelabel{ref:IsAdditiveGroupHomomorphism}{32.10.4}{X7B99EF287A8A0BD9} 2657\makelabel{ref:KernelOfAdditiveGeneralMapping}{32.10.5}{X7EC0E9907D6631D6} 2658\makelabel{ref:CoKernelOfAdditiveGeneralMapping}{32.10.6}{X813C6D7980213F41} 2659\makelabel{ref:RespectsScalarMultiplication}{32.11.1}{X87842ED97FA19973} 2660\makelabel{ref:IsLeftModuleGeneralMapping}{32.11.2}{X780BE6307A3271A9} 2661\makelabel{ref:IsLeftModuleHomomorphism}{32.11.2}{X780BE6307A3271A9} 2662\makelabel{ref:IsLinearMapping}{32.11.3}{X7F6841107E59107F} 2663\makelabel{ref:IsRingGeneralMapping}{32.12.1}{X7C8DA031799B79D5} 2664\makelabel{ref:IsRingHomomorphism}{32.12.1}{X7C8DA031799B79D5} 2665\makelabel{ref:IsRingWithOneGeneralMapping}{32.12.2}{X7988102883675606} 2666\makelabel{ref:IsRingWithOneHomomorphism}{32.12.2}{X7988102883675606} 2667\makelabel{ref:IsAlgebraGeneralMapping}{32.12.3}{X86B14F908601DEA9} 2668\makelabel{ref:IsAlgebraHomomorphism}{32.12.3}{X86B14F908601DEA9} 2669\makelabel{ref:IsAlgebraWithOneGeneralMapping}{32.12.4}{X842AD44679C5BDC2} 2670\makelabel{ref:IsAlgebraWithOneHomomorphism}{32.12.4}{X842AD44679C5BDC2} 2671\makelabel{ref:IsFieldHomomorphism}{32.12.5}{X8324DA78879DF4D7} 2672\makelabel{ref:IsGeneralMapping}{32.13.1}{X8656AB8A7D672CAE} 2673\makelabel{ref:IsConstantTimeAccessGeneralMapping}{32.13.2}{X791690817E23D90C} 2674\makelabel{ref:IsEndoGeneralMapping}{32.13.3}{X81CFF5F87BBEA8AD} 2675\makelabel{ref:IsSPGeneralMapping}{32.14.1}{X7D28581F82481163} 2676\makelabel{ref:IsNonSPGeneralMapping}{32.14.1}{X7D28581F82481163} 2677\makelabel{ref:IsGeneralMappingFamily}{32.14.2}{X80D02AD183E01F16} 2678\makelabel{ref:FamilyRange}{32.14.3}{X86CFADBA7F2FE446} 2679\makelabel{ref:FamilySource}{32.14.4}{X7C3736E281A9E505} 2680\makelabel{ref:FamiliesOfGeneralMappingsAndRanges}{32.14.5}{X7AE54FB67E2E6374} 2681\makelabel{ref:GeneralMappingsFamily}{32.14.6}{X7E1E26E37C413F6F} 2682\makelabel{ref:TypeOfDefaultGeneralMapping}{32.14.7}{X7CF92CC37A6BBDA5} 2683\makelabel{ref:binary relation}{33}{X838651287FCCEFD8} 2684\makelabel{ref:IsBinaryRelation same as IsEndoGeneralMapping}{33}{X838651287FCCEFD8} 2685\makelabel{ref:IsEndoGeneralMapping same as IsBinaryRelation}{33}{X838651287FCCEFD8} 2686\makelabel{ref:IsBinaryRelation}{33.1.1}{X788D722F82165551} 2687\makelabel{ref:BinaryRelationByElements}{33.1.2}{X7A1D8EEF8034B0B5} 2688\makelabel{ref:IdentityBinaryRelation for a degree}{33.1.3}{X81878EEF873B34D5} 2689\makelabel{ref:IdentityBinaryRelation for a domain}{33.1.3}{X81878EEF873B34D5} 2690\makelabel{ref:EmptyBinaryRelation for a degree}{33.1.4}{X80DDCDD387BA23F2} 2691\makelabel{ref:EmptyBinaryRelation for a domain}{33.1.4}{X80DDCDD387BA23F2} 2692\makelabel{ref:IsReflexiveBinaryRelation}{33.2.1}{X79D69B667F5FE8FE} 2693\makelabel{ref:reflexive relation}{33.2.1}{X79D69B667F5FE8FE} 2694\makelabel{ref:IsSymmetricBinaryRelation}{33.2.2}{X785916A181555368} 2695\makelabel{ref:symmetric relation}{33.2.2}{X785916A181555368} 2696\makelabel{ref:IsTransitiveBinaryRelation}{33.2.3}{X7823942478124563} 2697\makelabel{ref:transitive relation}{33.2.3}{X7823942478124563} 2698\makelabel{ref:IsAntisymmetricBinaryRelation}{33.2.4}{X870F72C38550A0A4} 2699\makelabel{ref:antisymmetric relation}{33.2.4}{X870F72C38550A0A4} 2700\makelabel{ref:IsPreOrderBinaryRelation}{33.2.5}{X782B7C8A8136532F} 2701\makelabel{ref:preorder}{33.2.5}{X782B7C8A8136532F} 2702\makelabel{ref:IsPartialOrderBinaryRelation}{33.2.6}{X7A1228207AB4FBA3} 2703\makelabel{ref:partial order}{33.2.6}{X7A1228207AB4FBA3} 2704\makelabel{ref:IsHasseDiagram}{33.2.7}{X80D3735C84D1CDC2} 2705\makelabel{ref:IsEquivalenceRelation}{33.2.8}{X82D6CB4B7CCE9E25} 2706\makelabel{ref:equivalence relation}{33.2.8}{X82D6CB4B7CCE9E25} 2707\makelabel{ref:Successors}{33.2.9}{X85E2FD8B82652876} 2708\makelabel{ref:DegreeOfBinaryRelation}{33.2.10}{X7B4D22A17E752A91} 2709\makelabel{ref:PartialOrderOfHasseDiagram}{33.2.11}{X8278E4457C3C3A0D} 2710\makelabel{ref:BinaryRelationOnPoints}{33.3.1}{X79E40E9385274F89} 2711\makelabel{ref:BinaryRelationOnPointsNC}{33.3.1}{X79E40E9385274F89} 2712\makelabel{ref:RandomBinaryRelationOnPoints}{33.3.2}{X7D9323C283867515} 2713\makelabel{ref:AsBinaryRelationOnPoints for a transformation}{33.3.3}{X8315C7A47CEB6BB3} 2714\makelabel{ref:AsBinaryRelationOnPoints for a permutation}{33.3.3}{X8315C7A47CEB6BB3} 2715\makelabel{ref:AsBinaryRelationOnPoints for a binary relation}{33.3.3}{X8315C7A47CEB6BB3} 2716\makelabel{ref:ReflexiveClosureBinaryRelation}{33.4.1}{X8252B17C864A4904} 2717\makelabel{ref:SymmetricClosureBinaryRelation}{33.4.2}{X820811E9785A7274} 2718\makelabel{ref:TransitiveClosureBinaryRelation}{33.4.3}{X853BFAD9858DCDF7} 2719\makelabel{ref:HasseDiagramBinaryRelation}{33.4.4}{X79672B3A7BCB6991} 2720\makelabel{ref:StronglyConnectedComponents}{33.4.5}{X85C22B3D812957C0} 2721\makelabel{ref:PartialOrderByOrderingFunction}{33.4.6}{X86AAE6027A3AEF72} 2722\makelabel{ref:equivalence relation}{33.5}{X7DAA67338458BB64} 2723\makelabel{ref:EquivalenceRelationByPartition}{33.5.1}{X7A44D73D8150266A} 2724\makelabel{ref:EquivalenceRelationByPartitionNC}{33.5.1}{X7A44D73D8150266A} 2725\makelabel{ref:EquivalenceRelationByRelation}{33.5.2}{X82CD1C00810F6042} 2726\makelabel{ref:EquivalenceRelationByPairs}{33.5.3}{X7B70215E7E3F9CA4} 2727\makelabel{ref:EquivalenceRelationByPairsNC}{33.5.3}{X7B70215E7E3F9CA4} 2728\makelabel{ref:EquivalenceRelationByProperty}{33.5.4}{X7C5AA9B97EE42DA5} 2729\makelabel{ref:EquivalenceRelationPartition}{33.6.1}{X877389B683DD8F1A} 2730\makelabel{ref:GeneratorsOfEquivalenceRelationPartition}{33.6.2}{X79DC914C82D7903B} 2731\makelabel{ref:JoinEquivalenceRelations}{33.6.3}{X82BE360381476D92} 2732\makelabel{ref:MeetEquivalenceRelations}{33.6.3}{X82BE360381476D92} 2733\makelabel{ref:IsEquivalenceClass}{33.7.1}{X8424996186DB14EA} 2734\makelabel{ref:equivalence class}{33.7.1}{X8424996186DB14EA} 2735\makelabel{ref:EquivalenceClassRelation}{33.7.2}{X78F967E77EB16386} 2736\makelabel{ref:EquivalenceClasses attribute}{33.7.3}{X879439897EF4D728} 2737\makelabel{ref:EquivalenceClassOfElement}{33.7.4}{X7BB985BA7FD7A82E} 2738\makelabel{ref:EquivalenceClassOfElementNC}{33.7.4}{X7BB985BA7FD7A82E} 2739\makelabel{ref:IsOrdering}{34.1.1}{X7EFDF115780934AF} 2740\makelabel{ref:OrderingsFamily}{34.1.2}{X85E6445C87283BEC} 2741\makelabel{ref:OrderingByLessThanFunctionNC}{34.2.1}{X78B5D91278EFAFC9} 2742\makelabel{ref:OrderingByLessThanOrEqualFunctionNC}{34.2.2}{X813D5BEB80506CE4} 2743\makelabel{ref:IsWellFoundedOrdering}{34.3.1}{X84FA448B7B4DDFDC} 2744\makelabel{ref:IsTotalOrdering}{34.3.2}{X867AC932843AD921} 2745\makelabel{ref:IsIncomparableUnder}{34.3.3}{X814E5E7D85EDCAC7} 2746\makelabel{ref:FamilyForOrdering}{34.3.4}{X872497B9782B97B4} 2747\makelabel{ref:LessThanFunction}{34.3.5}{X7D08ED6882015BFB} 2748\makelabel{ref:LessThanOrEqualFunction}{34.3.6}{X857E800583E9026D} 2749\makelabel{ref:IsLessThanUnder}{34.3.7}{X87F51D737C695D41} 2750\makelabel{ref:IsLessThanOrEqualUnder}{34.3.8}{X8308B7DF7AAF6D9C} 2751\makelabel{ref:IsOrderingOnFamilyOfAssocWords}{34.4.1}{X7C1808AE84B989AE} 2752\makelabel{ref:IsTranslationInvariantOrdering}{34.4.2}{X8175B8887868F29A} 2753\makelabel{ref:IsReductionOrdering}{34.4.3}{X816CD4BD82D41ED0} 2754\makelabel{ref:OrderingOnGenerators}{34.4.4}{X7B6051C282EA88D5} 2755\makelabel{ref:LexicographicOrdering}{34.4.5}{X79B2DEB786680F51} 2756\makelabel{ref:ShortLexOrdering}{34.4.6}{X802EB44B7E7B1F57} 2757\makelabel{ref:IsShortLexOrdering}{34.4.7}{X7B6ED9327E0A2099} 2758\makelabel{ref:WeightLexOrdering}{34.4.8}{X849DD7C6782333D5} 2759\makelabel{ref:IsWeightLexOrdering}{34.4.9}{X7C7D7954784F5C73} 2760\makelabel{ref:WeightOfGenerators}{34.4.10}{X7E7FAEA484148947} 2761\makelabel{ref:BasicWreathProductOrdering}{34.4.11}{X79D1019E7C3E575E} 2762\makelabel{ref:IsBasicWreathProductOrdering}{34.4.12}{X7CB765477FBC3383} 2763\makelabel{ref:WreathProductOrdering}{34.4.13}{X7E6DF1B17F53642E} 2764\makelabel{ref:IsWreathProductOrdering}{34.4.14}{X7F0EE6E987148C96} 2765\makelabel{ref:LevelsOfGenerators}{34.4.15}{X7901AA4479EDBE72} 2766\makelabel{ref:IsMagma}{35.1.1}{X87D3F38B7EAB13FA} 2767\makelabel{ref:IsMagmaWithOne}{35.1.2}{X86071DE7835F1C7C} 2768\makelabel{ref:IsMagmaWithInversesIfNonzero}{35.1.3}{X83E4903D7FBB2E24} 2769\makelabel{ref:IsMagmaWithInverses}{35.1.4}{X82CBFF648574B830} 2770\makelabel{ref:Magma}{35.2.1}{X839147CF813312D6} 2771\makelabel{ref:MagmaWithOne}{35.2.2}{X7854B23286B17321} 2772\makelabel{ref:MagmaWithInverses}{35.2.3}{X7A2B51F67EF4DA28} 2773\makelabel{ref:MagmaByGenerators}{35.2.4}{X7F629A498383A0AD} 2774\makelabel{ref:MagmaWithOneByGenerators}{35.2.5}{X84DABBEB803107EB} 2775\makelabel{ref:MagmaWithInversesByGenerators}{35.2.6}{X82C08CFB854E3F1A} 2776\makelabel{ref:Submagma}{35.2.7}{X8268EAA47E4A3A64} 2777\makelabel{ref:SubmagmaNC}{35.2.7}{X8268EAA47E4A3A64} 2778\makelabel{ref:SubmagmaWithOne}{35.2.8}{X7F295EBC7A9CE87E} 2779\makelabel{ref:SubmagmaWithOneNC}{35.2.8}{X7F295EBC7A9CE87E} 2780\makelabel{ref:SubmagmaWithInverses}{35.2.9}{X79441F1F7A277E28} 2781\makelabel{ref:SubmagmaWithInversesNC}{35.2.9}{X79441F1F7A277E28} 2782\makelabel{ref:AsMagma}{35.2.10}{X84ED076D7E46AB79} 2783\makelabel{ref:AsSubmagma}{35.2.11}{X87EEEC018129F0F4} 2784\makelabel{ref:IsMagmaWithZeroAdjoined}{35.2.12}{X8553F44D8123B2C6} 2785\makelabel{ref:InjectionZeroMagma}{35.2.13}{X8620878D7FD98823} 2786\makelabel{ref:MagmaWithZeroAdjoined}{35.2.13}{X8620878D7FD98823} 2787\makelabel{ref:UnderlyingInjectionZeroMagma}{35.2.14}{X7B353674859BF659} 2788\makelabel{ref:MagmaByMultiplicationTable}{35.3.1}{X85CD1E7678295CA6} 2789\makelabel{ref:MagmaWithOneByMultiplicationTable}{35.3.2}{X865526C881645D65} 2790\makelabel{ref:MagmaWithInversesByMultiplicationTable}{35.3.3}{X7EDAFB987EE8A770} 2791\makelabel{ref:MagmaElement}{35.3.4}{X828BED4580D28FB8} 2792\makelabel{ref:MultiplicationTable for a list of elements}{35.3.5}{X849BDCC27C4C3191} 2793\makelabel{ref:MultiplicationTable for a magma}{35.3.5}{X849BDCC27C4C3191} 2794\makelabel{ref:GeneratorsOfMagma}{35.4.1}{X872E05B478EC20CA} 2795\makelabel{ref:GeneratorsOfMagmaWithOne}{35.4.2}{X87DD93EC8061DD81} 2796\makelabel{ref:GeneratorsOfMagmaWithInverses}{35.4.3}{X83A901B1857C8489} 2797\makelabel{ref:Centralizer for a magma and an element}{35.4.4}{X7DE33AFC823C7873} 2798\makelabel{ref:Centralizer for a magma and a submagma}{35.4.4}{X7DE33AFC823C7873} 2799\makelabel{ref:Centralizer for a class of objects in a magma}{35.4.4}{X7DE33AFC823C7873} 2800\makelabel{ref:centraliser}{35.4.4}{X7DE33AFC823C7873} 2801\makelabel{ref:center}{35.4.4}{X7DE33AFC823C7873} 2802\makelabel{ref:Centre}{35.4.5}{X847ABE6F781C7FE8} 2803\makelabel{ref:Center}{35.4.5}{X847ABE6F781C7FE8} 2804\makelabel{ref:Idempotents}{35.4.6}{X7C651C9C78398FFF} 2805\makelabel{ref:IsAssociative}{35.4.7}{X7C83B5A47FD18FB7} 2806\makelabel{ref:IsCentral}{35.4.8}{X857B0E507D745ADB} 2807\makelabel{ref:IsCommutative}{35.4.9}{X830A4A4C795FBC2D} 2808\makelabel{ref:IsAbelian}{35.4.9}{X830A4A4C795FBC2D} 2809\makelabel{ref:MultiplicativeNeutralElement}{35.4.10}{X7EE2EA5F7EB7FEC2} 2810\makelabel{ref:MultiplicativeZero}{35.4.11}{X7B39F93C8136D642} 2811\makelabel{ref:IsMultiplicativeZero}{35.4.11}{X7B39F93C8136D642} 2812\makelabel{ref:SquareRoots}{35.4.12}{X867DB05A8218FB1E} 2813\makelabel{ref:TrivialSubmagmaWithOne}{35.4.13}{X837DA95883CFB985} 2814\makelabel{ref:IsWord}{36.1.1}{X843F5C3A82239398} 2815\makelabel{ref:IsWordWithOne}{36.1.1}{X843F5C3A82239398} 2816\makelabel{ref:IsWordWithInverse}{36.1.1}{X843F5C3A82239398} 2817\makelabel{ref:abstract word}{36.1.1}{X843F5C3A82239398} 2818\makelabel{ref:IsWordCollection}{36.1.2}{X804B616579F223D8} 2819\makelabel{ref:IsNonassocWord}{36.1.3}{X808FA6F97E16502F} 2820\makelabel{ref:IsNonassocWordWithOne}{36.1.3}{X808FA6F97E16502F} 2821\makelabel{ref:IsNonassocWordCollection}{36.1.4}{X7F81276C80F690DC} 2822\makelabel{ref:IsNonassocWordWithOneCollection}{36.1.4}{X7F81276C80F690DC} 2823\makelabel{ref:equality nonassociative words}{36.2.1}{X7CA51DD7874115DF} 2824\makelabel{ref:smaller nonassociative words}{36.2.2}{X82D4C7BE803166D6} 2825\makelabel{ref:MappedWord}{36.3.1}{X7EC17930781D104A} 2826\makelabel{ref:FreeMagma for given rank}{36.4.1}{X7CFFD9027DDD1555} 2827\makelabel{ref:FreeMagma for various names}{36.4.1}{X7CFFD9027DDD1555} 2828\makelabel{ref:FreeMagma for a list of names}{36.4.1}{X7CFFD9027DDD1555} 2829\makelabel{ref:FreeMagma for infinitely many generators}{36.4.1}{X7CFFD9027DDD1555} 2830\makelabel{ref:FreeMagmaWithOne for given rank}{36.4.2}{X86DB748080B4A9B9} 2831\makelabel{ref:FreeMagmaWithOne for various names}{36.4.2}{X86DB748080B4A9B9} 2832\makelabel{ref:FreeMagmaWithOne for a list of names}{36.4.2}{X86DB748080B4A9B9} 2833\makelabel{ref:FreeMagmaWithOne for infinitely many generators}{36.4.2}{X86DB748080B4A9B9} 2834\makelabel{ref:IsAssocWord}{37.1.1}{X7FA8DA728773BA89} 2835\makelabel{ref:IsAssocWordWithOne}{37.1.1}{X7FA8DA728773BA89} 2836\makelabel{ref:IsAssocWordWithInverse}{37.1.1}{X7FA8DA728773BA89} 2837\makelabel{ref:FreeGroup for given rank}{37.2.1}{X8215999E835290F0} 2838\makelabel{ref:FreeGroup for various names}{37.2.1}{X8215999E835290F0} 2839\makelabel{ref:FreeGroup for a list of names}{37.2.1}{X8215999E835290F0} 2840\makelabel{ref:FreeGroup for infinitely many generators}{37.2.1}{X8215999E835290F0} 2841\makelabel{ref:IsFreeGroup}{37.2.2}{X8601654A7C4AF1E7} 2842\makelabel{ref:AssignGeneratorVariables}{37.2.3}{X814203E281F3272E} 2843\makelabel{ref:equality associative words}{37.3.1}{X8206153078E97B90} 2844\makelabel{ref:smaller associative words}{37.3.2}{X7BB12B9D7F990899} 2845\makelabel{ref:IsShortLexLessThanOrEqual}{37.3.3}{X805C519682B0A7ED} 2846\makelabel{ref:IsBasicWreathLessThanOrEqual}{37.3.4}{X84875E08847B39E1} 2847\makelabel{ref:product of words}{37.4}{X79AF6C757A3547BD} 2848\makelabel{ref:quotient of words}{37.4}{X79AF6C757A3547BD} 2849\makelabel{ref:power of words}{37.4}{X79AF6C757A3547BD} 2850\makelabel{ref:conjugate of a word}{37.4}{X79AF6C757A3547BD} 2851\makelabel{ref:Comm for words}{37.4}{X79AF6C757A3547BD} 2852\makelabel{ref:LeftQuotient for words}{37.4}{X79AF6C757A3547BD} 2853\makelabel{ref:Length for a associative word}{37.4.1}{X8680FCAD83019E70} 2854\makelabel{ref:length of a word}{37.4.1}{X8680FCAD83019E70} 2855\makelabel{ref:ExponentSumWord}{37.4.2}{X7F5ED4357A9C12E6} 2856\makelabel{ref:Subword}{37.4.3}{X82CC92C17AF6FFA0} 2857\makelabel{ref:PositionWord}{37.4.4}{X8509A0A4851981BB} 2858\makelabel{ref:SubstitutedWord replace an interval by a given word}{37.4.5}{X79186218787C224A} 2859\makelabel{ref:SubstitutedWord replace a subword by a given word}{37.4.5}{X79186218787C224A} 2860\makelabel{ref:EliminatedWord}{37.4.6}{X8486BFE1844CFE59} 2861\makelabel{ref:NumberSyllables}{37.5.1}{X842D0B547CE93CF2} 2862\makelabel{ref:ExponentSyllable}{37.5.2}{X7E91575F848F4526} 2863\makelabel{ref:GeneratorSyllable}{37.5.3}{X7F2A8CFD811C73B1} 2864\makelabel{ref:SubSyllables}{37.5.4}{X7B4F7A167E844FA5} 2865\makelabel{ref:IsLetterAssocWordRep}{37.6.1}{X7E3612247B3E241B} 2866\makelabel{ref:IsLetterWordsFamily}{37.6.2}{X7E36F7897D82417F} 2867\makelabel{ref:IsBLetterAssocWordRep}{37.6.3}{X7C84789D7BB161E9} 2868\makelabel{ref:IsWLetterAssocWordRep}{37.6.3}{X7C84789D7BB161E9} 2869\makelabel{ref:IsBLetterWordsFamily}{37.6.4}{X8719E7F27CDA1995} 2870\makelabel{ref:IsWLetterWordsFamily}{37.6.4}{X8719E7F27CDA1995} 2871\makelabel{ref:IsSyllableAssocWordRep}{37.6.5}{X7886F8BD83CD8081} 2872\makelabel{ref:IsSyllableWordsFamily}{37.6.6}{X7869716C84EA9D81} 2873\makelabel{ref:Is16BitsFamily}{37.6.7}{X83F669828481FC32} 2874\makelabel{ref:Is32BitsFamily}{37.6.7}{X83F669828481FC32} 2875\makelabel{ref:IsInfBitsFamily}{37.6.7}{X83F669828481FC32} 2876\makelabel{ref:LetterRepAssocWord}{37.6.8}{X7BD7647C7B088389} 2877\makelabel{ref:AssocWordByLetterRep}{37.6.9}{X7AC8EC757CFB9A51} 2878\makelabel{ref:IsStraightLineProgram}{37.8.1}{X7F69FF3F7C6694CB} 2879\makelabel{ref:StraightLineProgram for a list of lines (and the number of generators)}{37.8.2}{X7AECA57280DA3195} 2880\makelabel{ref:StraightLineProgram for a string and a list of generators names}{37.8.2}{X7AECA57280DA3195} 2881\makelabel{ref:StraightLineProgramNC for a list of lines (and the number of generators)}{37.8.2}{X7AECA57280DA3195} 2882\makelabel{ref:StraightLineProgramNC for a string and a list of generators names}{37.8.2}{X7AECA57280DA3195} 2883\makelabel{ref:LinesOfStraightLineProgram}{37.8.3}{X81A8AFC47F8E4B91} 2884\makelabel{ref:NrInputsOfStraightLineProgram}{37.8.4}{X820A592881D57802} 2885\makelabel{ref:ResultOfStraightLineProgram}{37.8.5}{X7847D32B863E822F} 2886\makelabel{ref:LaTeX for the result of a straight line program}{37.8.5}{X7847D32B863E822F} 2887\makelabel{ref:StringOfResultOfStraightLineProgram}{37.8.6}{X8098EAAF7D344466} 2888\makelabel{ref:CompositionOfStraightLinePrograms}{37.8.7}{X8274C7948248C053} 2889\makelabel{ref:IntegratedStraightLineProgram}{37.8.8}{X7A582FA97C786640} 2890\makelabel{ref:RestrictOutputsOfSLP}{37.8.9}{X7C9CABD17BE4850F} 2891\makelabel{ref:IntermediateResultOfSLP}{37.8.10}{X7EF202F17DCA5D1C} 2892\makelabel{ref:IntermediateResultOfSLPWithoutOverwrite}{37.8.11}{X8085CF79856B2889} 2893\makelabel{ref:IntermediateResultsOfSLPWithoutOverwrite}{37.8.12}{X873244F37FAA717A} 2894\makelabel{ref:ProductOfStraightLinePrograms}{37.8.13}{X837101F982C35035} 2895\makelabel{ref:SlotUsagePattern}{37.8.14}{X84C83CE98194FD03} 2896\makelabel{ref:IsStraightLineProgElm}{37.9.1}{X85A5838482944FA5} 2897\makelabel{ref:StraightLineProgElm}{37.9.2}{X78889E5B7E1B3BFF} 2898\makelabel{ref:StraightLineProgGens}{37.9.3}{X81BC263A7E45E775} 2899\makelabel{ref:EvalStraightLineProgElm}{37.9.4}{X7BEAE8AC809B27DC} 2900\makelabel{ref:StretchImportantSLPElement}{37.9.5}{X7D85D1DF84DC68E3} 2901\makelabel{ref:IsRewritingSystem}{38.1.1}{X842C0ED87986F7AA} 2902\makelabel{ref:Rules}{38.1.2}{X833EAA8C86356F42} 2903\makelabel{ref:OrderOfRewritingSystem}{38.1.3}{X7C38C2EF817F9E0A} 2904\makelabel{ref:OrderingOfRewritingSystem}{38.1.3}{X7C38C2EF817F9E0A} 2905\makelabel{ref:ReducedForm}{38.1.4}{X8340EB2280DE6CCC} 2906\makelabel{ref:IsConfluent for a rewriting system}{38.1.5}{X8006790B86328CE8} 2907\makelabel{ref:IsConfluent for an algebra with canonical rewriting system}{38.1.5}{X8006790B86328CE8} 2908\makelabel{ref:ConfluentRws}{38.1.6}{X870A1E1C7FB45A55} 2909\makelabel{ref:IsReduced}{38.1.7}{X8134689C7B576946} 2910\makelabel{ref:ReduceRules}{38.1.8}{X864C82FD7FBA31A6} 2911\makelabel{ref:AddRule}{38.1.9}{X81E6B5CB789A7C3A} 2912\makelabel{ref:AddRuleReduced}{38.1.10}{X7FA0B54D7C533DDC} 2913\makelabel{ref:MakeConfluent}{38.1.11}{X7BD6299E85561DC3} 2914\makelabel{ref:GeneratorsOfRws}{38.1.12}{X795DC25886007DFE} 2915\makelabel{ref:ReducedProduct}{38.2.1}{X81BB38CC793F7CE2} 2916\makelabel{ref:ReducedSum}{38.2.1}{X81BB38CC793F7CE2} 2917\makelabel{ref:ReducedOne}{38.2.1}{X81BB38CC793F7CE2} 2918\makelabel{ref:ReducedAdditiveInverse}{38.2.1}{X81BB38CC793F7CE2} 2919\makelabel{ref:ReducedComm}{38.2.1}{X81BB38CC793F7CE2} 2920\makelabel{ref:ReducedConjugate}{38.2.1}{X81BB38CC793F7CE2} 2921\makelabel{ref:ReducedDifference}{38.2.1}{X81BB38CC793F7CE2} 2922\makelabel{ref:ReducedInverse}{38.2.1}{X81BB38CC793F7CE2} 2923\makelabel{ref:ReducedLeftQuotient}{38.2.1}{X81BB38CC793F7CE2} 2924\makelabel{ref:ReducedPower}{38.2.1}{X81BB38CC793F7CE2} 2925\makelabel{ref:ReducedQuotient}{38.2.1}{X81BB38CC793F7CE2} 2926\makelabel{ref:ReducedScalarProduct}{38.2.1}{X81BB38CC793F7CE2} 2927\makelabel{ref:ReducedZero}{38.2.1}{X81BB38CC793F7CE2} 2928\makelabel{ref:IsBuiltFromAdditiveMagmaWithInverses}{38.3.1}{X7B647DB77D138A49} 2929\makelabel{ref:IsBuiltFromMagma}{38.3.1}{X7B647DB77D138A49} 2930\makelabel{ref:IsBuiltFromMagmaWithOne}{38.3.1}{X7B647DB77D138A49} 2931\makelabel{ref:IsBuiltFromMagmaWithInverses}{38.3.1}{X7B647DB77D138A49} 2932\makelabel{ref:IsBuiltFromSemigroup}{38.3.1}{X7B647DB77D138A49} 2933\makelabel{ref:IsBuiltFromGroup}{38.3.1}{X7B647DB77D138A49} 2934\makelabel{ref:order of a group}{39.1}{X822370B47DEA37B1} 2935\makelabel{ref:Group for several generators}{39.2.1}{X7D8E473384DE9CD4} 2936\makelabel{ref:Group for a list of generators (and an identity element)}{39.2.1}{X7D8E473384DE9CD4} 2937\makelabel{ref:GroupByGenerators}{39.2.2}{X7F81960287F3E32A} 2938\makelabel{ref:GroupByGenerators with explicitly specified identity element}{39.2.2}{X7F81960287F3E32A} 2939\makelabel{ref:GroupWithGenerators}{39.2.3}{X8589EF9C7B658B94} 2940\makelabel{ref:GeneratorsOfGroup}{39.2.4}{X79C44528864044C5} 2941\makelabel{ref:AsGroup}{39.2.5}{X7A0747F17B50D967} 2942\makelabel{ref:ConjugateGroup}{39.2.6}{X7E4143A08040BB47} 2943\makelabel{ref:IsGroup}{39.2.7}{X7939B3177BBD61E4} 2944\makelabel{ref:InfoGroup}{39.2.8}{X845874BA82E1A11F} 2945\makelabel{ref:Subgroup}{39.3.1}{X7C82AA387A42DCA0} 2946\makelabel{ref:SubgroupNC}{39.3.1}{X7C82AA387A42DCA0} 2947\makelabel{ref:Subgroup for a group}{39.3.1}{X7C82AA387A42DCA0} 2948\makelabel{ref:Index for a group and its subgroup}{39.3.2}{X842AD37E79CE953E} 2949\makelabel{ref:IndexNC for a group and its subgroup}{39.3.2}{X842AD37E79CE953E} 2950\makelabel{ref:IndexInWholeGroup}{39.3.3}{X8014135884DCC53E} 2951\makelabel{ref:AsSubgroup}{39.3.4}{X7904AC9D7E9A3BB7} 2952\makelabel{ref:IsSubgroup}{39.3.5}{X7839D8927E778334} 2953\makelabel{ref:IsNormal}{39.3.6}{X838186F9836F678C} 2954\makelabel{ref:IsCharacteristicSubgroup}{39.3.7}{X8390B5117A10CC52} 2955\makelabel{ref:ConjugateSubgroup}{39.3.8}{X84F5464983655590} 2956\makelabel{ref:ConjugateSubgroups}{39.3.9}{X7D9990EB837075A4} 2957\makelabel{ref:IsSubnormal}{39.3.10}{X82ABF80780CC27AF} 2958\makelabel{ref:SubgroupByProperty}{39.3.11}{X829766158665FB54} 2959\makelabel{ref:SubgroupShell}{39.3.12}{X7E95101F80583E77} 2960\makelabel{ref:ClosureGroup}{39.4.1}{X7D13FC1F8576FFD8} 2961\makelabel{ref:ClosureGroupAddElm}{39.4.2}{X81A20A397C308483} 2962\makelabel{ref:ClosureGroupCompare}{39.4.2}{X81A20A397C308483} 2963\makelabel{ref:ClosureGroupIntest}{39.4.2}{X81A20A397C308483} 2964\makelabel{ref:ClosureGroupDefault}{39.4.3}{X82F59F6680D1B0D5} 2965\makelabel{ref:ClosureSubgroup}{39.4.4}{X7A7AF14A8052F055} 2966\makelabel{ref:ClosureSubgroupNC}{39.4.4}{X7A7AF14A8052F055} 2967\makelabel{ref:factorization}{39.5}{X7E19F92284F6684E} 2968\makelabel{ref:words in generators}{39.5}{X7E19F92284F6684E} 2969\makelabel{ref:EpimorphismFromFreeGroup}{39.5.1}{X7FE8A3B08458A1BF} 2970\makelabel{ref:Factorization}{39.5.2}{X8357294D7B164106} 2971\makelabel{ref:GrowthFunctionOfGroup}{39.5.3}{X871508DD808EB487} 2972\makelabel{ref:GrowthFunctionOfGroup with word length limit}{39.5.3}{X871508DD808EB487} 2973\makelabel{ref:StructureDescription}{39.6.1}{X8199B74B84446971} 2974\makelabel{ref:right cosets}{39.7}{X81002AA87DDBC02F} 2975\makelabel{ref:coset}{39.7}{X81002AA87DDBC02F} 2976\makelabel{ref:RightCoset}{39.7.1}{X8412ABD57986B9FC} 2977\makelabel{ref:RightCosets}{39.7.2}{X835F48248571364F} 2978\makelabel{ref:RightCosetsNC}{39.7.2}{X835F48248571364F} 2979\makelabel{ref:CanonicalRightCosetElement}{39.7.3}{X85884F177B5D98AE} 2980\makelabel{ref:IsRightCoset}{39.7.4}{X7D7625A1861D9DAB} 2981\makelabel{ref:left cosets}{39.7.4}{X7D7625A1861D9DAB} 2982\makelabel{ref:IsBiCoset}{39.7.5}{X78F4F0D8838F5ABF} 2983\makelabel{ref:bicoset}{39.7.5}{X78F4F0D8838F5ABF} 2984\makelabel{ref:CosetDecomposition}{39.7.6}{X82F6ABE378B928D1} 2985\makelabel{ref:RightTransversal}{39.8.1}{X85C65D06822E716F} 2986\makelabel{ref:DoubleCoset}{39.9.1}{X7E51ED757D17254B} 2987\makelabel{ref:RepresentativesContainedRightCosets}{39.9.2}{X7F53DABD79BA4F72} 2988\makelabel{ref:DoubleCosets}{39.9.3}{X7A5EFABB86E6D4D5} 2989\makelabel{ref:DoubleCosetsNC}{39.9.3}{X7A5EFABB86E6D4D5} 2990\makelabel{ref:IsDoubleCoset operation}{39.9.4}{X85ED464F878EF24C} 2991\makelabel{ref:DoubleCosetRepsAndSizes}{39.9.5}{X7A25B1C886CF8C6A} 2992\makelabel{ref:InfoCoset}{39.9.6}{X84AE7EE77E5FB30E} 2993\makelabel{ref:ConjugacyClass}{39.10.1}{X7B2F207F7F85F5B8} 2994\makelabel{ref:ConjugacyClasses attribute}{39.10.2}{X871B570284BBA685} 2995\makelabel{ref:ConjugacyClassesByRandomSearch}{39.10.3}{X7D6ED84C86C2979B} 2996\makelabel{ref:ConjugacyClassesByOrbits}{39.10.4}{X852B3634789D770E} 2997\makelabel{ref:NrConjugacyClasses}{39.10.5}{X8733F87B7E4C9903} 2998\makelabel{ref:RationalClass}{39.10.6}{X7BD2A4427B7FE248} 2999\makelabel{ref:RationalClasses}{39.10.7}{X81E9EF0A811072E8} 3000\makelabel{ref:GaloisGroup of rational class of a group}{39.10.8}{X877691247DE23386} 3001\makelabel{ref:IsConjugate for a group and two elements}{39.10.9}{X83DD148D7DA2ABA9} 3002\makelabel{ref:IsConjugate for a group and two groups}{39.10.9}{X83DD148D7DA2ABA9} 3003\makelabel{ref:NthRootsInGroup}{39.10.10}{X81A92F828400FC8A} 3004\makelabel{ref:normalizer}{39.11}{X804F0F037F06E25E} 3005\makelabel{ref:Normalizer for two groups}{39.11.1}{X87B5370C7DFD401D} 3006\makelabel{ref:Normalizer for a group and a group element}{39.11.1}{X87B5370C7DFD401D} 3007\makelabel{ref:Core}{39.11.2}{X7C4E00297E37AA44} 3008\makelabel{ref:PCore}{39.11.3}{X7CF497C77B1E8938} 3009\makelabel{ref:Op(G) see PCore}{39.11.3}{X7CF497C77B1E8938} 3010\makelabel{ref:NormalClosure}{39.11.4}{X7BDEA0A98720D1BB} 3011\makelabel{ref:NormalIntersection}{39.11.5}{X7D25E7DC7834A703} 3012\makelabel{ref:ComplementClassesRepresentatives}{39.11.6}{X811B8A4683DDE1F9} 3013\makelabel{ref:InfoComplement}{39.11.7}{X8581F4E77B11C610} 3014\makelabel{ref:TrivialSubgroup}{39.12.1}{X829759F67D4247CA} 3015\makelabel{ref:CommutatorSubgroup}{39.12.2}{X7A9A3D5578CE33A0} 3016\makelabel{ref:DerivedSubgroup}{39.12.3}{X7CC17CF179ED7EF2} 3017\makelabel{ref:CommutatorLength}{39.12.4}{X7B10B58F83DDE56E} 3018\makelabel{ref:FittingSubgroup}{39.12.5}{X780552B57C30DD8F} 3019\makelabel{ref:FrattiniSubgroup}{39.12.6}{X788C856C82243274} 3020\makelabel{ref:PrefrattiniSubgroup}{39.12.7}{X81D86CCE84193E4F} 3021\makelabel{ref:PerfectResiduum}{39.12.8}{X83D5C8B8865C85F1} 3022\makelabel{ref:RadicalGroup}{39.12.9}{X787F5F14844FAACE} 3023\makelabel{ref:Socle}{39.12.10}{X81F647FA83D8854F} 3024\makelabel{ref:SupersolvableResiduum}{39.12.11}{X8440C61080CDAA14} 3025\makelabel{ref:PRump}{39.12.12}{X796DA805853FAC90} 3026\makelabel{ref:SylowSubgroup}{39.13.1}{X7AA351308787544C} 3027\makelabel{ref:SylowComplement}{39.13.2}{X8605F3FE7A3B8E12} 3028\makelabel{ref:HallSubgroup}{39.13.3}{X7EDBA19E828CD584} 3029\makelabel{ref:SylowSystem}{39.13.4}{X832E8E6B8347B13F} 3030\makelabel{ref:ComplementSystem}{39.13.5}{X87A245E180D27147} 3031\makelabel{ref:HallSystem}{39.13.6}{X82FE5DFD84F8A3C6} 3032\makelabel{ref:Omega}{39.14.1}{X7F069ACC83DB3374} 3033\makelabel{ref:Agemo}{39.14.2}{X83DB33747F069ACC} 3034\makelabel{ref:IsCyclic}{39.15.1}{X7DA27D338374FD28} 3035\makelabel{ref:IsElementaryAbelian}{39.15.2}{X813C952F80E775D4} 3036\makelabel{ref:IsNilpotentGroup}{39.15.3}{X87D062608719F2CD} 3037\makelabel{ref:NilpotencyClassOfGroup}{39.15.4}{X7E3056237C6A5D43} 3038\makelabel{ref:IsPerfectGroup}{39.15.5}{X8755147280C84DBB} 3039\makelabel{ref:IsSolvableGroup}{39.15.6}{X809C78D5877D31DF} 3040\makelabel{ref:IsPolycyclicGroup}{39.15.7}{X7D7456077D3D1B86} 3041\makelabel{ref:IsSupersolvableGroup}{39.15.8}{X7AADF2E88501B9FF} 3042\makelabel{ref:IsMonomialGroup}{39.15.9}{X83977EB97A8E2290} 3043\makelabel{ref:IsSimpleGroup}{39.15.10}{X7A6685D7819AEC32} 3044\makelabel{ref:IsNonabelianSimpleGroup}{39.15.10}{X7A6685D7819AEC32} 3045\makelabel{ref:IsAlmostSimpleGroup}{39.15.11}{X78CC9764803601E7} 3046\makelabel{ref:IsomorphismTypeInfoFiniteSimpleGroup for a group}{39.15.12}{X7C6AA6897C4409AC} 3047\makelabel{ref:IsomorphismTypeInfoFiniteSimpleGroup for a group order}{39.15.12}{X7C6AA6897C4409AC} 3048\makelabel{ref:SimpleGroup}{39.15.13}{X8492B05B822AC58C} 3049\makelabel{ref:SimpleGroupsIterator}{39.15.14}{X839CDD8C7AE39FD6} 3050\makelabel{ref:SmallSimpleGroup}{39.15.15}{X872E93F586F54FCE} 3051\makelabel{ref:AllSmallNonabelianSimpleGroups}{39.15.16}{X7EB47BF27D8CBF72} 3052\makelabel{ref:IsFinitelyGeneratedGroup}{39.15.17}{X81E22D07871DF37E} 3053\makelabel{ref:IsSubsetLocallyFiniteGroup}{39.15.18}{X8648EDA287829755} 3054\makelabel{ref:IsPGroup}{39.15.19}{X8089F18C810B7E3E} 3055\makelabel{ref:p-group}{39.15.19}{X8089F18C810B7E3E} 3056\makelabel{ref:IsPowerfulPGroup}{39.15.20}{X7F232B3F8261CE25} 3057\makelabel{ref:Powerful p-group}{39.15.20}{X7F232B3F8261CE25} 3058\makelabel{ref:PrimePGroup}{39.15.21}{X87356BAA7E9E2142} 3059\makelabel{ref:PClassPGroup}{39.15.22}{X863434AD7DDE514B} 3060\makelabel{ref:RankPGroup}{39.15.23}{X840A4F937ABF15E1} 3061\makelabel{ref:IsPSolvable}{39.15.24}{X81130F9A7CFCF6BF} 3062\makelabel{ref:IsPNilpotent}{39.15.25}{X87415A8485FCF510} 3063\makelabel{ref:AbelianInvariants}{39.16.1}{X812827937F403300} 3064\makelabel{ref:AbelianInvariants for groups}{39.16.1}{X812827937F403300} 3065\makelabel{ref:Exponent}{39.16.2}{X7D44470C7DA59C1C} 3066\makelabel{ref:EulerianFunction}{39.16.3}{X843E0CCA8351FDF4} 3067\makelabel{ref:ChiefSeries}{39.17.1}{X7BDD116F7833800F} 3068\makelabel{ref:ChiefSeriesThrough}{39.17.2}{X7AC93E977AC9ED58} 3069\makelabel{ref:ChiefSeriesUnderAction}{39.17.3}{X8724E15F81B51173} 3070\makelabel{ref:SubnormalSeries}{39.17.4}{X7A0E7A8B8495B79D} 3071\makelabel{ref:CompositionSeries}{39.17.5}{X81CDCBD67BC98A5A} 3072\makelabel{ref:DisplayCompositionSeries}{39.17.6}{X82C0D0217ACB2042} 3073\makelabel{ref:DerivedSeriesOfGroup}{39.17.7}{X7A879948834BD889} 3074\makelabel{ref:DerivedLength}{39.17.8}{X7A9AA1577CEC891F} 3075\makelabel{ref:ElementaryAbelianSeries for a group}{39.17.9}{X83F057E5791944D6} 3076\makelabel{ref:ElementaryAbelianSeriesLargeSteps}{39.17.9}{X83F057E5791944D6} 3077\makelabel{ref:ElementaryAbelianSeries for a list}{39.17.9}{X83F057E5791944D6} 3078\makelabel{ref:InvariantElementaryAbelianSeries}{39.17.10}{X782BD7A47D6B6503} 3079\makelabel{ref:LowerCentralSeriesOfGroup}{39.17.11}{X879D55A67DB42676} 3080\makelabel{ref:UpperCentralSeriesOfGroup}{39.17.12}{X8428592E8773CD7B} 3081\makelabel{ref:PCentralSeries}{39.17.13}{X7809B7ED792669F3} 3082\makelabel{ref:JenningsSeries}{39.17.14}{X82A34BD681F24A94} 3083\makelabel{ref:DimensionsLoewyFactors}{39.17.15}{X7C08A8B77EC09CFF} 3084\makelabel{ref:AscendingChain}{39.17.16}{X84112774812180DD} 3085\makelabel{ref:IntermediateGroup}{39.17.17}{X7C5029EE86D7FC96} 3086\makelabel{ref:IntermediateSubgroups}{39.17.18}{X781661FB78DC83B5} 3087\makelabel{ref:NaturalHomomorphismByNormalSubgroup}{39.18.1}{X80FC390C7F38A13F} 3088\makelabel{ref:NaturalHomomorphismByNormalSubgroupNC}{39.18.1}{X80FC390C7F38A13F} 3089\makelabel{ref:FactorGroup}{39.18.2}{X7E6EED0185B27C48} 3090\makelabel{ref:FactorGroupNC}{39.18.2}{X7E6EED0185B27C48} 3091\makelabel{ref:CommutatorFactorGroup}{39.18.3}{X7816FA867BF1B8ED} 3092\makelabel{ref:MaximalAbelianQuotient}{39.18.4}{X7BB93B9778C5A0B2} 3093\makelabel{ref:HasAbelianFactorGroup}{39.18.5}{X7FC83E4C783572E7} 3094\makelabel{ref:HasElementaryAbelianFactorGroup}{39.18.6}{X7FAC018680B766B7} 3095\makelabel{ref:CentralizerModulo}{39.18.7}{X822A3AB27919BC1E} 3096\makelabel{ref:ConjugacyClassSubgroups}{39.19.1}{X7DDE67C67E871336} 3097\makelabel{ref:IsConjugacyClassSubgroupsRep}{39.19.2}{X7C5BBF487977B8CD} 3098\makelabel{ref:IsConjugacyClassSubgroupsByStabilizerRep}{39.19.2}{X7C5BBF487977B8CD} 3099\makelabel{ref:ConjugacyClassesSubgroups}{39.19.3}{X7E986BF48393113A} 3100\makelabel{ref:ConjugacyClassesMaximalSubgroups}{39.19.4}{X8486C25380853F9B} 3101\makelabel{ref:MaximalSubgroupClassReps}{39.19.5}{X798BF55C837DB188} 3102\makelabel{ref:LowIndexSubgroups}{39.19.6}{X85DAFB7582A88463} 3103\makelabel{ref:AllSubgroups}{39.19.7}{X80399CD4870FFC4B} 3104\makelabel{ref:MaximalSubgroups}{39.19.8}{X861CD8DA790D81C2} 3105\makelabel{ref:NormalSubgroups}{39.19.9}{X80237A847E24E6CF} 3106\makelabel{ref:MaximalNormalSubgroups}{39.19.10}{X82ECAA427C987318} 3107\makelabel{ref:MinimalNormalSubgroups}{39.19.11}{X86FDD9BA819F5644} 3108\makelabel{ref:CharacteristicSubgroups}{39.19.12}{X7A823C5A810910C3} 3109\makelabel{ref:LatticeSubgroups}{39.20.1}{X7B104E2C86166188} 3110\makelabel{ref:ClassElementLattice}{39.20.2}{X78928A3582882BFD} 3111\makelabel{ref:DotFileLatticeSubgroups}{39.20.3}{X7E5DF287825EE7BA} 3112\makelabel{ref:dot-file}{39.20.3}{X7E5DF287825EE7BA} 3113\makelabel{ref:graphviz}{39.20.3}{X7E5DF287825EE7BA} 3114\makelabel{ref:OmniGraffle}{39.20.3}{X7E5DF287825EE7BA} 3115\makelabel{ref:MaximalSubgroupsLattice}{39.20.4}{X815CDA447C5DB285} 3116\makelabel{ref:MinimalSupergroupsLattice}{39.20.5}{X8138997C871EDF96} 3117\makelabel{ref:LowLayerSubgroups}{39.20.6}{X87BE970D7B18E2C5} 3118\makelabel{ref:ContainedConjugates}{39.20.7}{X87FABD5F87AD2568} 3119\makelabel{ref:ContainingConjugates}{39.20.8}{X79C3619C849F97B8} 3120\makelabel{ref:MinimalFaithfulPermutationDegree}{39.20.9}{X8111F50C798B0D76} 3121\makelabel{ref:RepresentativesPerfectSubgroups}{39.20.10}{X7BA3484E7AE0A0E1} 3122\makelabel{ref:RepresentativesSimpleSubgroups}{39.20.10}{X7BA3484E7AE0A0E1} 3123\makelabel{ref:ConjugacyClassesPerfectSubgroups}{39.20.11}{X7B2233D180DF77A1} 3124\makelabel{ref:Zuppos}{39.20.12}{X7BFE573187B4BEF8} 3125\makelabel{ref:InfoLattice}{39.20.13}{X82C12E2C81963B23} 3126\makelabel{ref:LatticeByCyclicExtension}{39.21.1}{X86462A567DDBA6BC} 3127\makelabel{ref:InvariantSubgroupsElementaryAbelianGroup}{39.21.2}{X78918D83835A0EDF} 3128\makelabel{ref:SubgroupsSolvableGroup}{39.21.3}{X7AD7804A803910AC} 3129\makelabel{ref:SizeConsiderFunction}{39.21.4}{X7F60BBB8874DFE40} 3130\makelabel{ref:ExactSizeConsiderFunction}{39.21.5}{X833C51BD7E7812C4} 3131\makelabel{ref:InfoPcSubgroup}{39.21.6}{X7A2C774B7CFF3E07} 3132\makelabel{ref:GeneratorsSmallest}{39.22.1}{X82FD78AF7F80A0E2} 3133\makelabel{ref:LargestElementGroup}{39.22.2}{X7A258CCF79552198} 3134\makelabel{ref:MinimalGeneratingSet}{39.22.3}{X81D15723804771E2} 3135\makelabel{ref:SmallGeneratingSet}{39.22.4}{X814DBABC878D5232} 3136\makelabel{ref:IndependentGeneratorsOfAbelianGroup}{39.22.5}{X7D1574457B152333} 3137\makelabel{ref:IndependentGeneratorExponents}{39.22.6}{X86F835DA8264A0CE} 3138\makelabel{ref:one cohomology}{39.23}{X7CA0B6A27E0BE6B8} 3139\makelabel{ref:cohomology}{39.23}{X7CA0B6A27E0BE6B8} 3140\makelabel{ref:cocycles}{39.23}{X7CA0B6A27E0BE6B8} 3141\makelabel{ref:OneCocycles for two groups}{39.23.1}{X847BEC137A49BAF4} 3142\makelabel{ref:OneCocycles for a group and a pcgs}{39.23.1}{X847BEC137A49BAF4} 3143\makelabel{ref:OneCocycles for generators and a group}{39.23.1}{X847BEC137A49BAF4} 3144\makelabel{ref:OneCocycles for generators and a pcgs}{39.23.1}{X847BEC137A49BAF4} 3145\makelabel{ref:OneCoboundaries}{39.23.2}{X7E6438D5834ACCDA} 3146\makelabel{ref:OCOneCocycles}{39.23.3}{X80400ABD7F40FAA0} 3147\makelabel{ref:ComplementClassesRepresentativesEA}{39.23.4}{X811E1CF07DABE924} 3148\makelabel{ref:InfoCoh}{39.23.5}{X8199B1D27D487897} 3149\makelabel{ref:Darstellungsgruppe see EpimorphismSchurCover}{39.24}{X80A4B0F282977074} 3150\makelabel{ref:EpimorphismSchurCover}{39.24.1}{X7F619DDA7DD6C43B} 3151\makelabel{ref:SchurCover}{39.24.2}{X7DD1E37987612042} 3152\makelabel{ref:AbelianInvariantsMultiplier}{39.24.3}{X792BC39D7CEB1D27} 3153\makelabel{ref:Multiplier}{39.24.3}{X792BC39D7CEB1D27} 3154\makelabel{ref:Schur multiplier}{39.24.3}{X792BC39D7CEB1D27} 3155\makelabel{ref:Epicentre}{39.24.4}{X819E8AEC835F8CD1} 3156\makelabel{ref:ExteriorCentre}{39.24.4}{X819E8AEC835F8CD1} 3157\makelabel{ref:NonabelianExteriorSquare}{39.24.5}{X8739CD4686301A0E} 3158\makelabel{ref:EpimorphismNonabelianExteriorSquare}{39.24.6}{X7E1C8CD77CDB9F71} 3159\makelabel{ref:IsCentralFactor}{39.24.7}{X7BF8DB3D8300BB3F} 3160\makelabel{ref:BasicSpinRepresentationOfSymmetricGroup}{39.24.9}{X7DDA6BC1824F78FD} 3161\makelabel{ref:SchurCoverOfSymmetricGroup}{39.24.10}{X844CFFDE80F6AD15} 3162\makelabel{ref:DoubleCoverOfAlternatingGroup}{39.24.11}{X7E0F4896795E34FC} 3163\makelabel{ref:TwoCohomologyGeneric}{39.25.1}{X7A1EBC3A7AB0D614} 3164\makelabel{ref:FpGroupCocycle}{39.25.2}{X7A65366879BB3977} 3165\makelabel{ref:CanEasilyTestMembership}{39.26.1}{X798F13EA810FB215} 3166\makelabel{ref:CanEasilyComputeWithIndependentGensAbelianGroup}{39.26.2}{X7C2A89607BDFD920} 3167\makelabel{ref:CanComputeSize}{39.26.3}{X83245C82835D496C} 3168\makelabel{ref:CanComputeSizeAnySubgroup}{39.26.4}{X8268965487364912} 3169\makelabel{ref:CanComputeIndex}{39.26.5}{X82DDE00D82A32083} 3170\makelabel{ref:CanComputeIsSubset}{39.26.6}{X7BE7C36B84C23511} 3171\makelabel{ref:KnowsHowToDecompose}{39.26.7}{X87D62C2C7C375E2D} 3172\makelabel{ref:NormalizerViaRadical}{39.27.1}{X84ABCA997D294B36} 3173\makelabel{ref:GroupHomomorphismByImages}{40.1.1}{X7F348F497C813BE0} 3174\makelabel{ref:GroupHomomorphismByImagesNC}{40.1.2}{X7AB15AF5830F2A6B} 3175\makelabel{ref:GroupGeneralMappingByImages}{40.1.3}{X7A59F2C47BD41DC8} 3176\makelabel{ref:GroupGeneralMappingByImages from group to itself}{40.1.3}{X7A59F2C47BD41DC8} 3177\makelabel{ref:GroupGeneralMappingByImagesNC}{40.1.3}{X7A59F2C47BD41DC8} 3178\makelabel{ref:GroupGeneralMappingByImagesNC from group to itself}{40.1.3}{X7A59F2C47BD41DC8} 3179\makelabel{ref:GroupHomomorphismByFunction by function (and inverse function) between two domains}{40.1.4}{X7BC6C20E7CEDBFC5} 3180\makelabel{ref:GroupHomomorphismByFunction by function and function that computes one preimage}{40.1.4}{X7BC6C20E7CEDBFC5} 3181\makelabel{ref:AsGroupGeneralMappingByImages}{40.1.5}{X785AB6057F736344} 3182\makelabel{ref:kernel group homomorphism}{40.2}{X794043AC7E4FAF9E} 3183\makelabel{ref:Inverse group homomorphism}{40.2}{X794043AC7E4FAF9E} 3184\makelabel{ref:ImagesSmallestGenerators}{40.3.5}{X80B8ABEC7CC20DFB} 3185\makelabel{ref:IsHandledByNiceMonomorphism}{40.5.1}{X78849F81804C44B3} 3186\makelabel{ref:NiceMonomorphism}{40.5.2}{X7965086E82ABCF41} 3187\makelabel{ref:NiceObject}{40.5.3}{X7B47BE0983E93A83} 3188\makelabel{ref:IsCanonicalNiceMonomorphism}{40.5.4}{X8652149F7F291EE3} 3189\makelabel{ref:ConjugatorIsomorphism}{40.6.1}{X7E52E99487562F3A} 3190\makelabel{ref:ConjugatorAutomorphism}{40.6.2}{X79ED68CF8139F08A} 3191\makelabel{ref:ConjugatorAutomorphismNC}{40.6.2}{X79ED68CF8139F08A} 3192\makelabel{ref:InnerAutomorphism}{40.6.3}{X7E937A947856D9DA} 3193\makelabel{ref:InnerAutomorphismNC}{40.6.3}{X7E937A947856D9DA} 3194\makelabel{ref:IsConjugatorIsomorphism}{40.6.4}{X7F31FECC7A3D4A8A} 3195\makelabel{ref:IsConjugatorAutomorphism}{40.6.4}{X7F31FECC7A3D4A8A} 3196\makelabel{ref:IsInnerAutomorphism}{40.6.4}{X7F31FECC7A3D4A8A} 3197\makelabel{ref:ConjugatorOfConjugatorIsomorphism}{40.6.5}{X78FE7E307E86525A} 3198\makelabel{ref:AutomorphismGroup}{40.7.1}{X87677B0787B4461A} 3199\makelabel{ref:IsGroupOfAutomorphisms}{40.7.2}{X7FC631B786C1DC8B} 3200\makelabel{ref:AutomorphismDomain}{40.7.3}{X7B767B9D827EB0FC} 3201\makelabel{ref:IsAutomorphismGroup}{40.7.4}{X7F87D5957D9B991E} 3202\makelabel{ref:InnerAutomorphismsAutomorphismGroup}{40.7.5}{X8476738A7BF9BADA} 3203\makelabel{ref:InducedAutomorphism}{40.7.6}{X7FC9B6EA7CAADC0A} 3204\makelabel{ref:AssignNiceMonomorphismAutomorphismGroup}{40.8.1}{X85691E8386107403} 3205\makelabel{ref:NiceMonomorphismAutomGroup}{40.8.2}{X7C9FB0A57BFF6CC0} 3206\makelabel{ref:homomorphisms find all}{40.9}{X81B79CC27F47D429} 3207\makelabel{ref:IsomorphismGroups}{40.9.1}{X7B536A32827788C6} 3208\makelabel{ref:isomorphisms find all}{40.9.1}{X7B536A32827788C6} 3209\makelabel{ref:AllHomomorphismClasses}{40.9.2}{X7D0C3D5E864CE954} 3210\makelabel{ref:AllHomomorphisms}{40.9.3}{X791D12B7845610CE} 3211\makelabel{ref:AllEndomorphisms}{40.9.3}{X791D12B7845610CE} 3212\makelabel{ref:AllAutomorphisms}{40.9.3}{X791D12B7845610CE} 3213\makelabel{ref:GQuotients}{40.9.4}{X790C261184EEAB94} 3214\makelabel{ref:epimorphisms find all}{40.9.4}{X790C261184EEAB94} 3215\makelabel{ref:projections find all}{40.9.4}{X790C261184EEAB94} 3216\makelabel{ref:IsomorphicSubgroups}{40.9.5}{X83B417BE7C508DC4} 3217\makelabel{ref:embeddings find all}{40.9.5}{X83B417BE7C508DC4} 3218\makelabel{ref:monomorphisms find all}{40.9.5}{X83B417BE7C508DC4} 3219\makelabel{ref:MorClassLoop}{40.9.6}{X7AABA9A27E30BF2B} 3220\makelabel{ref:IsGroupGeneralMappingByImages}{40.10.1}{X82B77A5F7F9EDBC7} 3221\makelabel{ref:MappingGeneratorsImages}{40.10.2}{X863805187A24B5E3} 3222\makelabel{ref:IsGroupGeneralMappingByAsGroupGeneralMappingByImages}{40.10.3}{X7DFBBAB18126B4D9} 3223\makelabel{ref:IsPreimagesByAsGroupGeneralMappingByImages}{40.10.4}{X78707DF57C3927EB} 3224\makelabel{ref:IsPermGroupGeneralMapping}{40.10.5}{X83E10338798F552B} 3225\makelabel{ref:IsPermGroupGeneralMappingByImages}{40.10.5}{X83E10338798F552B} 3226\makelabel{ref:IsPermGroupHomomorphism}{40.10.5}{X83E10338798F552B} 3227\makelabel{ref:IsPermGroupHomomorphismByImages}{40.10.5}{X83E10338798F552B} 3228\makelabel{ref:IsToPermGroupGeneralMappingByImages}{40.10.6}{X83DADD9F7CAD829B} 3229\makelabel{ref:IsToPermGroupHomomorphismByImages}{40.10.6}{X83DADD9F7CAD829B} 3230\makelabel{ref:IsGroupGeneralMappingByPcgs}{40.10.7}{X798E72E77EC85D4A} 3231\makelabel{ref:IsPcGroupGeneralMappingByImages}{40.10.8}{X86FF63B784FB8F85} 3232\makelabel{ref:IsPcGroupHomomorphismByImages}{40.10.8}{X86FF63B784FB8F85} 3233\makelabel{ref:IsToPcGroupGeneralMappingByImages}{40.10.9}{X79A853B579B250C0} 3234\makelabel{ref:IsToPcGroupHomomorphismByImages}{40.10.9}{X79A853B579B250C0} 3235\makelabel{ref:IsFromFpGroupGeneralMappingByImages}{40.10.10}{X7BE2A2EB80DC5CFF} 3236\makelabel{ref:IsFromFpGroupHomomorphismByImages}{40.10.10}{X7BE2A2EB80DC5CFF} 3237\makelabel{ref:IsFromFpGroupStdGensGeneralMappingByImages}{40.10.11}{X81090C207F4F6423} 3238\makelabel{ref:IsFromFpGroupStdGensHomomorphismByImages}{40.10.11}{X81090C207F4F6423} 3239\makelabel{ref:group actions}{41}{X87115591851FB7F4} 3240\makelabel{ref:group actions operations syntax}{41.1}{X83661AFD7B7BD1D9} 3241\makelabel{ref:group actions}{41.2}{X81B8F9CD868CD953} 3242\makelabel{ref:actions}{41.2}{X81B8F9CD868CD953} 3243\makelabel{ref:group operations}{41.2}{X81B8F9CD868CD953} 3244\makelabel{ref:OnPoints}{41.2.1}{X7FE417DD837987B4} 3245\makelabel{ref:conjugation}{41.2.1}{X7FE417DD837987B4} 3246\makelabel{ref:action by conjugation}{41.2.1}{X7FE417DD837987B4} 3247\makelabel{ref:OnRight}{41.2.2}{X7960924D84B5B18F} 3248\makelabel{ref:OnLeftInverse}{41.2.3}{X832DF5327ECA0E44} 3249\makelabel{ref:OnSets}{41.2.4}{X85AA04347CD117F9} 3250\makelabel{ref:action on sets}{41.2.4}{X85AA04347CD117F9} 3251\makelabel{ref:action on blocks}{41.2.4}{X85AA04347CD117F9} 3252\makelabel{ref:OnTuples}{41.2.5}{X832CC5F87EEA4A7E} 3253\makelabel{ref:OnPairs}{41.2.6}{X80DAA1D2855B1456} 3254\makelabel{ref:OnSetsSets}{41.2.7}{X7C10492081D72376} 3255\makelabel{ref:OnSetsDisjointSets}{41.2.8}{X7E23686E7A9D3A20} 3256\makelabel{ref:OnSetsTuples}{41.2.9}{X7ADE244E819035FF} 3257\makelabel{ref:OnTuplesSets}{41.2.10}{X7FF556CD7E6739A9} 3258\makelabel{ref:OnTuplesTuples}{41.2.11}{X844E902382EB4151} 3259\makelabel{ref:OnLines}{41.2.12}{X86DC2DD5829CAD9A} 3260\makelabel{ref:OnIndeterminates as a permutation action}{41.2.13}{X7FA394D27E721E2B} 3261\makelabel{ref:Permuted as a permutation action}{41.2.14}{X7BA8D76586F1F06E} 3262\makelabel{ref:OnSubspacesByCanonicalBasis}{41.2.15}{X85124D197F0F9C4D} 3263\makelabel{ref:OnSubspacesByCanonicalBasisConcatenations}{41.2.15}{X85124D197F0F9C4D} 3264\makelabel{ref:Orbit}{41.4.1}{X80E0234E7BD79409} 3265\makelabel{ref:Orbits operation}{41.4.2}{X86BCAE17869BBEAA} 3266\makelabel{ref:Orbits for a permutation group}{41.4.2}{X86BCAE17869BBEAA} 3267\makelabel{ref:Orbits attribute}{41.4.2}{X86BCAE17869BBEAA} 3268\makelabel{ref:OrbitsDomain for a group and an action domain}{41.4.3}{X86BC8B958123F953} 3269\makelabel{ref:OrbitsDomain for a permutation group}{41.4.3}{X86BC8B958123F953} 3270\makelabel{ref:OrbitsDomain of an external set}{41.4.3}{X86BC8B958123F953} 3271\makelabel{ref:OrbitLength}{41.4.4}{X799910CF832EDC45} 3272\makelabel{ref:OrbitLengths for a group, a set of seeds, etc.}{41.4.5}{X8032F73078DF2DDB} 3273\makelabel{ref:OrbitLengths for a permutation group}{41.4.5}{X8032F73078DF2DDB} 3274\makelabel{ref:OrbitLengths for an external set}{41.4.5}{X8032F73078DF2DDB} 3275\makelabel{ref:OrbitLengthsDomain for a group and a set of seeds}{41.4.6}{X8520E2487F7E98AF} 3276\makelabel{ref:OrbitLengthsDomain for a permutation group}{41.4.6}{X8520E2487F7E98AF} 3277\makelabel{ref:OrbitLengthsDomain of an external set}{41.4.6}{X8520E2487F7E98AF} 3278\makelabel{ref:point stabilizer}{41.5}{X797BD60E7ACEF1B1} 3279\makelabel{ref:set stabilizer}{41.5}{X797BD60E7ACEF1B1} 3280\makelabel{ref:tuple stabilizer}{41.5}{X797BD60E7ACEF1B1} 3281\makelabel{ref:OrbitStabilizer}{41.5.1}{X7C34EC437EF598BF} 3282\makelabel{ref:Stabilizer}{41.5.2}{X86FB962786397E02} 3283\makelabel{ref:OrbitStabilizerAlgorithm}{41.5.3}{X78C3A8568414BC44} 3284\makelabel{ref:transporter}{41.6}{X7A9389097BAF670D} 3285\makelabel{ref:RepresentativeAction}{41.6.1}{X857DC7B085EB0539} 3286\makelabel{ref:ActionHomomorphism for a group, an action domain, etc.}{41.7.1}{X78E6A002835288A4} 3287\makelabel{ref:ActionHomomorphism for an external set}{41.7.1}{X78E6A002835288A4} 3288\makelabel{ref:ActionHomomorphism for an action image}{41.7.1}{X78E6A002835288A4} 3289\makelabel{ref:Action for a group, an action domain, etc.}{41.7.2}{X85A8E93D786C3C9C} 3290\makelabel{ref:Action for an external set}{41.7.2}{X85A8E93D786C3C9C} 3291\makelabel{ref:regular action}{41.7.2}{X85A8E93D786C3C9C} 3292\makelabel{ref:SparseActionHomomorphism}{41.7.3}{X86FF54A383B73967} 3293\makelabel{ref:SortedSparseActionHomomorphism}{41.7.3}{X86FF54A383B73967} 3294\makelabel{ref:FactorCosetAction}{41.8.1}{X78C37C4C7B2BDC44} 3295\makelabel{ref:RegularActionHomomorphism}{41.8.2}{X8561DEBA79E01ABD} 3296\makelabel{ref:AbelianSubfactorAction}{41.8.3}{X835317A7847477D4} 3297\makelabel{ref:Permutation for a group, an action domain, etc.}{41.9.1}{X7807A33381DCAB26} 3298\makelabel{ref:Permutation for an external set}{41.9.1}{X7807A33381DCAB26} 3299\makelabel{ref:PermutationCycle}{41.9.2}{X81D4EA42810974A0} 3300\makelabel{ref:Cycle}{41.9.3}{X80AF6E0683CA7F14} 3301\makelabel{ref:CycleLength}{41.9.4}{X7F559E897B333758} 3302\makelabel{ref:Cycles}{41.9.5}{X7F3B387A7FD8AE5E} 3303\makelabel{ref:CycleLengths}{41.9.6}{X83040A6080C2C6C6} 3304\makelabel{ref:CycleIndex for a permutation and an action domain}{41.9.7}{X87FDA6838065CDCB} 3305\makelabel{ref:CycleIndex for a permutation group and an action domain}{41.9.7}{X87FDA6838065CDCB} 3306\makelabel{ref:IsTransitive for a group, an action domain, etc.}{41.10.1}{X79B15750851828CB} 3307\makelabel{ref:IsTransitive for a permutation group}{41.10.1}{X79B15750851828CB} 3308\makelabel{ref:IsTransitive for an external set}{41.10.1}{X79B15750851828CB} 3309\makelabel{ref:transitive}{41.10.1}{X79B15750851828CB} 3310\makelabel{ref:Transitivity for a group and an action domain}{41.10.2}{X8295D733796B7A37} 3311\makelabel{ref:Transitivity for a permutation group}{41.10.2}{X8295D733796B7A37} 3312\makelabel{ref:Transitivity for an external set}{41.10.2}{X8295D733796B7A37} 3313\makelabel{ref:RankAction for a group, an action domain, etc.}{41.10.3}{X8166A6A17C8D6E73} 3314\makelabel{ref:RankAction for an external set}{41.10.3}{X8166A6A17C8D6E73} 3315\makelabel{ref:IsSemiRegular for a group, an action domain, etc.}{41.10.4}{X7B77040F8543CD6E} 3316\makelabel{ref:IsSemiRegular for a permutation group}{41.10.4}{X7B77040F8543CD6E} 3317\makelabel{ref:IsSemiRegular for an external set}{41.10.4}{X7B77040F8543CD6E} 3318\makelabel{ref:semiregular}{41.10.4}{X7B77040F8543CD6E} 3319\makelabel{ref:IsRegular for a group, an action domain, etc.}{41.10.5}{X7CF02C4785F0EAB5} 3320\makelabel{ref:IsRegular for a permutation group}{41.10.5}{X7CF02C4785F0EAB5} 3321\makelabel{ref:IsRegular for an external set}{41.10.5}{X7CF02C4785F0EAB5} 3322\makelabel{ref:regular}{41.10.5}{X7CF02C4785F0EAB5} 3323\makelabel{ref:Earns for a group, an action domain, etc.}{41.10.6}{X7CB1D74280F92AFC} 3324\makelabel{ref:Earns for an external set}{41.10.6}{X7CB1D74280F92AFC} 3325\makelabel{ref:IsPrimitive for a group, an action domain, etc.}{41.10.7}{X84C19AD68247B760} 3326\makelabel{ref:IsPrimitive for a permutation group}{41.10.7}{X84C19AD68247B760} 3327\makelabel{ref:IsPrimitive for an external set}{41.10.7}{X84C19AD68247B760} 3328\makelabel{ref:primitive}{41.10.7}{X84C19AD68247B760} 3329\makelabel{ref:Blocks for a group, an action domain, etc.}{41.11.1}{X84FE699F85371643} 3330\makelabel{ref:Blocks for an external set}{41.11.1}{X84FE699F85371643} 3331\makelabel{ref:MaximalBlocks for a group, an action domain, etc.}{41.11.2}{X79936EB97AAD1144} 3332\makelabel{ref:MaximalBlocks for an external set}{41.11.2}{X79936EB97AAD1144} 3333\makelabel{ref:RepresentativesMinimalBlocks for a group, an action domain, etc.}{41.11.3}{X7941DB6380B74510} 3334\makelabel{ref:RepresentativesMinimalBlocks for an external set}{41.11.3}{X7941DB6380B74510} 3335\makelabel{ref:AllBlocks}{41.11.4}{X835658B07B28EF3B} 3336\makelabel{ref:G-sets}{41.12}{X7FD3D2D2788709B7} 3337\makelabel{ref:IsExternalSet}{41.12.1}{X8264C3C479FF0A8B} 3338\makelabel{ref:ExternalSet}{41.12.2}{X7C90F648793E47DD} 3339\makelabel{ref:ActingDomain}{41.12.3}{X7B9DB15D80CE28B4} 3340\makelabel{ref:FunctionAction}{41.12.4}{X86153CB087394DC1} 3341\makelabel{ref:HomeEnumerator}{41.12.5}{X86A0CC1479A5932A} 3342\makelabel{ref:IsExternalSubset}{41.12.6}{X879DE63C7858453C} 3343\makelabel{ref:ExternalSubset}{41.12.7}{X87D1EA1486D86233} 3344\makelabel{ref:IsExternalOrbit}{41.12.8}{X7E081F568407317F} 3345\makelabel{ref:ExternalOrbit}{41.12.9}{X7FB656AE7A066C35} 3346\makelabel{ref:StabilizerOfExternalSet}{41.12.10}{X7BAFF02B7D6DF9F2} 3347\makelabel{ref:ExternalOrbits for a group, an action domain, etc.}{41.12.11}{X867262FA82FDD592} 3348\makelabel{ref:ExternalOrbits for an external set}{41.12.11}{X867262FA82FDD592} 3349\makelabel{ref:ExternalOrbitsStabilizers for a group, an action domain, etc.}{41.12.12}{X7A64EF807CE8893E} 3350\makelabel{ref:ExternalOrbitsStabilizers for an external set}{41.12.12}{X7A64EF807CE8893E} 3351\makelabel{ref:CanonicalRepresentativeOfExternalSet}{41.12.13}{X8048AE727A7F1A2F} 3352\makelabel{ref:CanonicalRepresentativeDeterminatorOfExternalSet}{41.12.14}{X8071A8D784DC8325} 3353\makelabel{ref:ActorOfExternalSet}{41.12.15}{X85E9A6A77B8D00B8} 3354\makelabel{ref:UnderlyingExternalSet}{41.12.16}{X8190A8247F29A5C7} 3355\makelabel{ref:SurjectiveActionHomomorphismAttr}{41.12.17}{X7A3D87DE809FBFD4} 3356\makelabel{ref:IsPerm}{42.1.1}{X7AA69C6686FC49EA} 3357\makelabel{ref:IsPermCollection}{42.1.2}{X82069E437D2DF9AA} 3358\makelabel{ref:IsPermCollColl}{42.1.2}{X82069E437D2DF9AA} 3359\makelabel{ref:PermutationsFamily}{42.1.3}{X819628B083B3939B} 3360\makelabel{ref:PERMINVERSETHRESHOLD}{42.1.4}{X83C711557DEB4B36} 3361\makelabel{ref:equality test for permutations}{42.2.1}{X7CEC03A9808E2E7C} 3362\makelabel{ref:precedence test for permutations}{42.2.1}{X7CEC03A9808E2E7C} 3363\makelabel{ref:DistancePerms}{42.2.2}{X7BC944F57A04AFF2} 3364\makelabel{ref:SmallestGeneratorPerm}{42.2.3}{X83A917F67D45C7EA} 3365\makelabel{ref:SmallestMovedPoint for a permutation}{42.3.1}{X84EF0A697F7A87DC} 3366\makelabel{ref:SmallestMovedPoint for a list or collection of permutations}{42.3.1}{X84EF0A697F7A87DC} 3367\makelabel{ref:LargestMovedPoint for a permutation}{42.3.2}{X84AA603987C94AC0} 3368\makelabel{ref:LargestMovedPoint for a list or collection of permutations}{42.3.2}{X84AA603987C94AC0} 3369\makelabel{ref:MovedPoints for a permutation}{42.3.3}{X85E61B9C7A6B0CCA} 3370\makelabel{ref:MovedPoints for a list or collection of permutations}{42.3.3}{X85E61B9C7A6B0CCA} 3371\makelabel{ref:NrMovedPoints for a permutation}{42.3.4}{X85E7B1E28430F49E} 3372\makelabel{ref:NrMovedPoints for a list or collection of permutations}{42.3.4}{X85E7B1E28430F49E} 3373\makelabel{ref:SignPerm}{42.4.1}{X7BE5011B7C0DB704} 3374\makelabel{ref:CycleStructurePerm}{42.4.2}{X7944D1447804A69A} 3375\makelabel{ref:ListPerm}{42.5.1}{X7A9DCFD986958C1E} 3376\makelabel{ref:PermList}{42.5.2}{X78D611D17EA6E3BC} 3377\makelabel{ref:MappingPermListList}{42.5.3}{X8087DCC780B9656A} 3378\makelabel{ref:RestrictedPerm}{42.5.4}{X7EF8388E7DA8E600} 3379\makelabel{ref:RestrictedPermNC}{42.5.4}{X7EF8388E7DA8E600} 3380\makelabel{ref:CycleFromList}{42.5.5}{X80665A5D800CAFE1} 3381\makelabel{ref:AsPermutation}{42.5.6}{X8353AB8987E35DF3} 3382\makelabel{ref:IsPermGroup}{43.1.1}{X7879877482F59676} 3383\makelabel{ref:OrbitPerms}{43.2.1}{X84CFA16D858B00B8} 3384\makelabel{ref:OrbitsPerms}{43.2.2}{X81F98222818DA35B} 3385\makelabel{ref:IsomorphismPermGroup}{43.3.1}{X80B7B1C783AA1567} 3386\makelabel{ref:SmallerDegreePermutationRepresentation}{43.3.2}{X8086628878AFD3EA} 3387\makelabel{ref:IsNaturalSymmetricGroup}{43.4.1}{X8129BE59781478E1} 3388\makelabel{ref:IsNaturalAlternatingGroup}{43.4.1}{X8129BE59781478E1} 3389\makelabel{ref:IsSymmetricGroup}{43.4.2}{X85CA6AD17BE90C95} 3390\makelabel{ref:IsAlternatingGroup}{43.4.3}{X8514BE9E79C608E0} 3391\makelabel{ref:SymmetricParentGroup}{43.4.4}{X7ED60F7E81F1B614} 3392\makelabel{ref:ONanScottType}{43.5.1}{X7E50211A7B92455F} 3393\makelabel{ref:SocleTypePrimitiveGroup}{43.5.2}{X7E89A46A86A3F4A2} 3394\makelabel{ref:Schreier-Sims random}{43.7}{X7C2406B97E057196} 3395\makelabel{ref:StabChain for a group (and a record)}{43.8.1}{X80B5CF78829495C2} 3396\makelabel{ref:StabChain for a group and a base}{43.8.1}{X80B5CF78829495C2} 3397\makelabel{ref:StabChainOp}{43.8.1}{X80B5CF78829495C2} 3398\makelabel{ref:StabChainMutable for a group}{43.8.1}{X80B5CF78829495C2} 3399\makelabel{ref:StabChainMutable for a homomorphism}{43.8.1}{X80B5CF78829495C2} 3400\makelabel{ref:StabChainImmutable}{43.8.1}{X80B5CF78829495C2} 3401\makelabel{ref:StabChainOptions}{43.8.2}{X790C27B8783EDE68} 3402\makelabel{ref:DefaultStabChainOptions}{43.8.3}{X87E1292E85A5D31C} 3403\makelabel{ref:StabChainBaseStrongGenerators}{43.8.4}{X86D64D2B81D58431} 3404\makelabel{ref:MinimalStabChain}{43.8.5}{X7BEC5F5A7851CAAB} 3405\makelabel{ref:BaseStabChain}{43.10.1}{X7FBE6EB57EBE8B7D} 3406\makelabel{ref:BaseOfGroup}{43.10.2}{X7D2A190D8308ED39} 3407\makelabel{ref:SizeStabChain}{43.10.3}{X7EF36DC78465026A} 3408\makelabel{ref:StrongGeneratorsStabChain}{43.10.4}{X8384170881B9B531} 3409\makelabel{ref:GroupStabChain}{43.10.5}{X87F473777EFDE867} 3410\makelabel{ref:OrbitStabChain}{43.10.6}{X87FB6DED80692D3F} 3411\makelabel{ref:IndicesStabChain}{43.10.7}{X7AC8F165875906DE} 3412\makelabel{ref:ListStabChain}{43.10.8}{X7CF607BC82C2C202} 3413\makelabel{ref:ElementsStabChain}{43.10.9}{X7F40E52D7B0438BF} 3414\makelabel{ref:IteratorStabChain}{43.10.10}{X780875477CD2A57D} 3415\makelabel{ref:InverseRepresentative}{43.10.11}{X861062AE87ACF340} 3416\makelabel{ref:SiftedPermutation}{43.10.12}{X79D2248C8787EAF2} 3417\makelabel{ref:MinimalElementCosetStabChain}{43.10.13}{X7B870C217D0B9997} 3418\makelabel{ref:LargestElementStabChain}{43.10.14}{X87435B7884D9B353} 3419\makelabel{ref:ApproximateSuborbitsStabilizerPermGroup}{43.10.15}{X809B2C3B7C5F77AB} 3420\makelabel{ref:CopyStabChain}{43.11.1}{X86B31E6A81AE5FCB} 3421\makelabel{ref:CopyOptionsDefaults}{43.11.2}{X7E167E557B567C6A} 3422\makelabel{ref:ChangeStabChain}{43.11.3}{X87FF64AB87BFC779} 3423\makelabel{ref:ExtendStabChain}{43.11.4}{X8778B4657D3FD97B} 3424\makelabel{ref:ReduceStabChain}{43.11.5}{X7E5E9F727D0B19D9} 3425\makelabel{ref:RemoveStabChain}{43.11.6}{X85BF290D848C4091} 3426\makelabel{ref:EmptyStabChain}{43.11.7}{X84E4906B86E5C089} 3427\makelabel{ref:InsertTrivialStabilizer}{43.11.8}{X80C7D2E87E6EE357} 3428\makelabel{ref:IsFixedStabilizer}{43.11.9}{X7B47B379824F6150} 3429\makelabel{ref:AddGeneratorsExtendSchreierTree}{43.11.10}{X8373007880EBF736} 3430\makelabel{ref:SubgroupProperty}{43.12.1}{X7BE3F03C80BF8B08} 3431\makelabel{ref:ElementProperty}{43.12.2}{X7EE7DDCC87C4BC31} 3432\makelabel{ref:TwoClosure}{43.12.3}{X7A2D046B83DD5F5F} 3433\makelabel{ref:InfoBckt}{43.12.4}{X861461AB7964DC64} 3434\makelabel{ref:IsMatrixGroup}{44.1.1}{X7E6093FF85F1C3A1} 3435\makelabel{ref:DimensionOfMatrixGroup}{44.2.1}{X7E55258C783C50CA} 3436\makelabel{ref:DefaultFieldOfMatrixGroup}{44.2.2}{X7D540083793CD496} 3437\makelabel{ref:FieldOfMatrixGroup}{44.2.3}{X78A9F0E580DA613A} 3438\makelabel{ref:TransposedMatrixGroup}{44.2.4}{X832D18C77ED608DE} 3439\makelabel{ref:IsFFEMatrixGroup}{44.2.5}{X84B36A827E5EFC35} 3440\makelabel{ref:ProjectiveActionOnFullSpace}{44.3.1}{X7BD4F38E8624735D} 3441\makelabel{ref:ProjectiveActionHomomorphismMatrixGroup}{44.3.2}{X7F8EA8D583C1E9B2} 3442\makelabel{ref:BlowUpIsomorphism}{44.3.3}{X849C451A80B4A210} 3443\makelabel{ref:IsGeneralLinearGroup}{44.4.1}{X781387AF7999EA99} 3444\makelabel{ref:IsGL}{44.4.1}{X781387AF7999EA99} 3445\makelabel{ref:IsNaturalGL}{44.4.2}{X86F9A27D7AFAEB5A} 3446\makelabel{ref:IsSpecialLinearGroup}{44.4.3}{X816677CD821261FA} 3447\makelabel{ref:IsSL}{44.4.3}{X816677CD821261FA} 3448\makelabel{ref:IsNaturalSL}{44.4.4}{X84134F08781EB943} 3449\makelabel{ref:IsSubgroupSL}{44.4.5}{X7ED43D4F7E993A31} 3450\makelabel{ref:InvariantBilinearForm}{44.5.1}{X7C08385A81AB05E1} 3451\makelabel{ref:IsFullSubgroupGLorSLRespectingBilinearForm}{44.5.2}{X8652FBF781940AC3} 3452\makelabel{ref:InvariantSesquilinearForm}{44.5.3}{X82F22079852130C9} 3453\makelabel{ref:IsFullSubgroupGLorSLRespectingSesquilinearForm}{44.5.4}{X7B35A8AF7D8F0313} 3454\makelabel{ref:InvariantQuadraticForm}{44.5.5}{X7BCACC007EB9B613} 3455\makelabel{ref:IsFullSubgroupGLorSLRespectingQuadraticForm}{44.5.6}{X84AB04A67DFC0274} 3456\makelabel{ref:IsCyclotomicMatrixGroup}{44.6.1}{X850821F78558C829} 3457\makelabel{ref:IsRationalMatrixGroup}{44.6.2}{X7FEDB2E17EE02674} 3458\makelabel{ref:IsIntegerMatrixGroup}{44.6.3}{X7F737FC4795F3E48} 3459\makelabel{ref:IsNaturalGLnZ}{44.6.4}{X86F9CC1E7DB97CB6} 3460\makelabel{ref:IsNaturalSLnZ}{44.6.5}{X7B0E70127F5D2EAF} 3461\makelabel{ref:InvariantLattice}{44.6.6}{X7DE412A37A6975B3} 3462\makelabel{ref:NormalizerInGLnZ}{44.6.7}{X7CC4D6DC81739698} 3463\makelabel{ref:CentralizerInGLnZ}{44.6.8}{X7DAFB71F86525DE7} 3464\makelabel{ref:ZClassRepsQClass}{44.6.9}{X8217762A863F1382} 3465\makelabel{ref:IsBravaisGroup}{44.6.10}{X84FD9FC97FB90795} 3466\makelabel{ref:BravaisGroup}{44.6.11}{X7AAE301C83116451} 3467\makelabel{ref:BravaisSubgroups}{44.6.12}{X788C7D9C7C2301C5} 3468\makelabel{ref:BravaisSupergroups}{44.6.13}{X7F5FF1A481E08AD5} 3469\makelabel{ref:NormalizerInGLnZBravaisGroup}{44.6.14}{X79B7CD797A420720} 3470\makelabel{ref:CrystGroupDefaultAction}{44.7.1}{X7D1318A6780CD88B} 3471\makelabel{ref:SetCrystGroupDefaultAction}{44.7.2}{X792D237385977BE6} 3472\makelabel{ref:Pcgs}{45.2.1}{X84C3750C7A4EEC34} 3473\makelabel{ref:IsPcgs}{45.2.2}{X8635E61A7DB73BA6} 3474\makelabel{ref:CanEasilyComputePcgs}{45.2.3}{X7B561B1685CEC2AB} 3475\makelabel{ref:PcgsByPcSequence}{45.3.1}{X7E139C3D80847D76} 3476\makelabel{ref:PcgsByPcSequenceNC}{45.3.1}{X7E139C3D80847D76} 3477\makelabel{ref:RelativeOrders}{45.4.1}{X7DD0DF677AC1CF10} 3478\makelabel{ref:RelativeOrders of a pcgs}{45.4.1}{X7DD0DF677AC1CF10} 3479\makelabel{ref:IsFiniteOrdersPcgs}{45.4.2}{X80D526848427A5C6} 3480\makelabel{ref:IsPrimeOrdersPcgs}{45.4.3}{X866C3A5382FF231A} 3481\makelabel{ref:PcSeries}{45.4.4}{X827A7B097A959579} 3482\makelabel{ref:GroupOfPcgs}{45.4.5}{X7903702E8194EF29} 3483\makelabel{ref:OneOfPcgs}{45.4.6}{X878FB11887524E2C} 3484\makelabel{ref:RelativeOrderOfPcElement}{45.5.1}{X7B941D4A7CAFCD73} 3485\makelabel{ref:ExponentOfPcElement}{45.5.2}{X78134914842E2F5F} 3486\makelabel{ref:ExponentsOfPcElement}{45.5.3}{X848DAEBF7DC448A5} 3487\makelabel{ref:DepthOfPcElement}{45.5.4}{X829BCB267CDBC5C0} 3488\makelabel{ref:LeadingExponentOfPcElement}{45.5.5}{X7D47966479EA2890} 3489\makelabel{ref:PcElementByExponents}{45.5.6}{X87AF746B8328F5D0} 3490\makelabel{ref:PcElementByExponentsNC}{45.5.6}{X87AF746B8328F5D0} 3491\makelabel{ref:LinearCombinationPcgs}{45.5.7}{X7F8BD7A87DB3933A} 3492\makelabel{ref:SiftedPcElement}{45.5.8}{X8066B66D8069BAB4} 3493\makelabel{ref:CanonicalPcElement}{45.5.9}{X7B52ADE7878A749A} 3494\makelabel{ref:ReducedPcElement}{45.5.10}{X7A94AA357DB2F86C} 3495\makelabel{ref:CleanedTailPcElement}{45.5.11}{X8702D76D8284CF3E} 3496\makelabel{ref:HeadPcElementByNumber}{45.5.12}{X830A0D037DBEAA97} 3497\makelabel{ref:ExponentsConjugateLayer}{45.6.1}{X868D6DB07D349460} 3498\makelabel{ref:ExponentsOfRelativePower}{45.6.2}{X874F70697FE7B6DF} 3499\makelabel{ref:ExponentsOfConjugate}{45.6.3}{X78CAF32F864EF656} 3500\makelabel{ref:ExponentsOfCommutator}{45.6.4}{X875689897DD0CAFC} 3501\makelabel{ref:IsInducedPcgs}{45.7.1}{X81FA878C854D63F8} 3502\makelabel{ref:InducedPcgsByPcSequence}{45.7.2}{X83F6759184937F1B} 3503\makelabel{ref:InducedPcgsByPcSequenceNC}{45.7.2}{X83F6759184937F1B} 3504\makelabel{ref:ParentPcgs}{45.7.3}{X86308E80843BF9E5} 3505\makelabel{ref:InducedPcgs}{45.7.4}{X7F0EB20080590B23} 3506\makelabel{ref:InducedPcgsByGenerators}{45.7.5}{X8332F1197DF6FEDE} 3507\makelabel{ref:InducedPcgsByGeneratorsNC}{45.7.5}{X8332F1197DF6FEDE} 3508\makelabel{ref:InducedPcgsByPcSequenceAndGenerators}{45.7.6}{X7AF82BD079D811E5} 3509\makelabel{ref:LeadCoeffsIGS}{45.7.7}{X845FF8CA783D6CB3} 3510\makelabel{ref:ExtendedPcgs}{45.7.8}{X800287C680C5DEC3} 3511\makelabel{ref:SubgroupByPcgs}{45.7.9}{X817E16D67B31389B} 3512\makelabel{ref:IsCanonicalPcgs}{45.8.1}{X80D122B986B42F80} 3513\makelabel{ref:CanonicalPcgs}{45.8.2}{X816F6B4187032A10} 3514\makelabel{ref:ModuloPcgs}{45.9.1}{X7FE689A37E559F66} 3515\makelabel{ref:IsModuloPcgs}{45.9.2}{X868207D77D09D915} 3516\makelabel{ref:NumeratorOfModuloPcgs}{45.9.3}{X8027CC9878031D74} 3517\makelabel{ref:DenominatorOfModuloPcgs}{45.9.4}{X87DBE2797D51B2F1} 3518\makelabel{ref:CorrespondingGeneratorsByModuloPcgs}{45.9.6}{X876A41F97FBA7754} 3519\makelabel{ref:CanonicalPcgsByGeneratorsWithImages}{45.9.7}{X8480852A7D49BC3F} 3520\makelabel{ref:ProjectedPcElement}{45.10.1}{X806C2D827E04ACF3} 3521\makelabel{ref:ProjectedInducedPcgs}{45.10.2}{X82F39CCE7C928D3A} 3522\makelabel{ref:LiftedPcElement}{45.10.3}{X816813A078B93A6B} 3523\makelabel{ref:LiftedInducedPcgs}{45.10.4}{X83C60F1587577D65} 3524\makelabel{ref:IsPcgsElementaryAbelianSeries}{45.11.1}{X7E7E89C278DDE20D} 3525\makelabel{ref:PcgsElementaryAbelianSeries for a group}{45.11.2}{X863A20B57EA37BAC} 3526\makelabel{ref:PcgsElementaryAbelianSeries for a list of normal subgroups}{45.11.2}{X863A20B57EA37BAC} 3527\makelabel{ref:IndicesEANormalSteps}{45.11.3}{X7BCC1E2A80544CC7} 3528\makelabel{ref:IndicesEANormalStepsBounded}{45.11.3}{X7BCC1E2A80544CC7} 3529\makelabel{ref:EANormalSeriesByPcgs}{45.11.4}{X7FCE308887F621FC} 3530\makelabel{ref:IsPcgsCentralSeries}{45.11.5}{X79675266796D7254} 3531\makelabel{ref:PcgsCentralSeries}{45.11.6}{X8187FCF483659E69} 3532\makelabel{ref:IndicesCentralNormalSteps}{45.11.7}{X7FB73FEB7BED5BFA} 3533\makelabel{ref:CentralNormalSeriesByPcgs}{45.11.8}{X82266ADA86B2A689} 3534\makelabel{ref:IsPcgsPCentralSeriesPGroup}{45.11.9}{X786E60AF7B61BF9E} 3535\makelabel{ref:PcgsPCentralSeriesPGroup}{45.11.10}{X86F19DBD7D346E7F} 3536\makelabel{ref:IndicesPCentralNormalStepsPGroup}{45.11.11}{X863968F08509E7D4} 3537\makelabel{ref:PCentralNormalSeriesByPcgsPGroup}{45.11.12}{X7A92C9EA7BAF60CA} 3538\makelabel{ref:IsPcgsChiefSeries}{45.11.13}{X7EA5BC3B7FE9D98D} 3539\makelabel{ref:PcgsChiefSeries}{45.11.14}{X7E7326947EAE4BC9} 3540\makelabel{ref:IndicesChiefNormalSteps}{45.11.15}{X7C05E84A78CA405E} 3541\makelabel{ref:ChiefNormalSeriesByPcgs}{45.11.16}{X83C5ABC587074B14} 3542\makelabel{ref:IndicesNormalSteps}{45.11.17}{X7A954E3887189842} 3543\makelabel{ref:NormalSeriesByPcgs}{45.11.18}{X7947B0FB87F44042} 3544\makelabel{ref:SumFactorizationFunctionPcgs}{45.12.1}{X7833DAAA7C07CFD7} 3545\makelabel{ref:IsSpecialPcgs}{45.13.1}{X7C8A82FA786AC021} 3546\makelabel{ref:SpecialPcgs for a pcgs}{45.13.2}{X827EB7767BACD023} 3547\makelabel{ref:SpecialPcgs for a group}{45.13.2}{X827EB7767BACD023} 3548\makelabel{ref:LGWeights}{45.13.3}{X82DC7CE682140588} 3549\makelabel{ref:LGLayers}{45.13.4}{X824645C97E347EEE} 3550\makelabel{ref:LGFirst}{45.13.5}{X7A655F4C7D9AE130} 3551\makelabel{ref:LGLength}{45.13.6}{X7C3912F77B12C8B6} 3552\makelabel{ref:IsInducedPcgsWrtSpecialPcgs}{45.13.7}{X814C35BF7C9A8DEF} 3553\makelabel{ref:InducedPcgsWrtSpecialPcgs}{45.13.8}{X7C14AE5C82FB0771} 3554\makelabel{ref:VectorSpaceByPcgsOfElementaryAbelianGroup}{45.14.1}{X7A9BB9D0817CA949} 3555\makelabel{ref:LinearAction}{45.14.2}{X81FC09DD7FC06C6E} 3556\makelabel{ref:LinearOperation}{45.14.2}{X81FC09DD7FC06C6E} 3557\makelabel{ref:LinearActionLayer}{45.14.3}{X7C2135B98732BBC3} 3558\makelabel{ref:LinearOperationLayer}{45.14.3}{X7C2135B98732BBC3} 3559\makelabel{ref:AffineAction}{45.14.4}{X79C2D6BF7DD69ED6} 3560\makelabel{ref:AffineActionLayer}{45.14.5}{X7E4CB1358524497B} 3561\makelabel{ref:StabilizerPcgs}{45.15.1}{X7CFCCF607A30B5EE} 3562\makelabel{ref:PcgsOrbitStabilizer}{45.15.2}{X7A87E72F86813132} 3563\makelabel{ref:IsNilpotent for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3564\makelabel{ref:IsSupersolvable for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3565\makelabel{ref:Size for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3566\makelabel{ref:CompositionSeries for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3567\makelabel{ref:ConjugacyClasses for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3568\makelabel{ref:Centralizer for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3569\makelabel{ref:FrattiniSubgroup for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3570\makelabel{ref:PrefrattiniSubgroup for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3571\makelabel{ref:MaximalSubgroups for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3572\makelabel{ref:HallSystem for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3573\makelabel{ref:MinimalGeneratingSet for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3574\makelabel{ref:Centre for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3575\makelabel{ref:Intersection for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3576\makelabel{ref:AutomorphismGroup for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3577\makelabel{ref:IrreducibleModules for groups with pcgs}{45.16}{X7A19DF1E7E841074} 3578\makelabel{ref:ClassesSolvableGroup}{45.17.1}{X79593F667A68A21D} 3579\makelabel{ref:CentralizerSizeLimitConsiderFunction}{45.17.2}{X7B358D3B7E236973} 3580\makelabel{ref:FamilyPcgs}{46.1.1}{X79EDB35E82C99304} 3581\makelabel{ref:IsFamilyPcgs}{46.1.2}{X80893D2A7FFC791B} 3582\makelabel{ref:InducedPcgsWrtFamilyPcgs}{46.1.3}{X85C1596A867BE93D} 3583\makelabel{ref:IsParentPcgsFamilyPcgs}{46.1.4}{X8333ACCB7F530406} 3584\makelabel{ref:equality for pcwords}{46.2.1}{X869DCE7D86E32337} 3585\makelabel{ref:smaller for pcwords}{46.2.1}{X869DCE7D86E32337} 3586\makelabel{ref:Inverse for a pcword}{46.2.2}{X7D1B700882FC6C78} 3587\makelabel{ref:IsPcGroup}{46.3.1}{X7D1F506D7830B1D9} 3588\makelabel{ref:IsomorphismFpGroupByPcgs}{46.3.2}{X7D2735A18111FE39} 3589\makelabel{ref:PcGroupFpGroup}{46.4.1}{X84C10D1F7CB5274F} 3590\makelabel{ref:SingleCollector}{46.4.2}{X7E958DB281E070FD} 3591\makelabel{ref:CombinatorialCollector}{46.4.2}{X7E958DB281E070FD} 3592\makelabel{ref:SetConjugate}{46.4.3}{X86A08D887E049347} 3593\makelabel{ref:SetCommutator}{46.4.4}{X7B25997C7DF92B6D} 3594\makelabel{ref:SetPower}{46.4.5}{X7BC319BA8698420C} 3595\makelabel{ref:GroupByRws}{46.4.6}{X84F0521486672C3C} 3596\makelabel{ref:GroupByRwsNC}{46.4.6}{X84F0521486672C3C} 3597\makelabel{ref:IsConfluent for pc groups}{46.4.7}{X7DF4835F79667099} 3598\makelabel{ref:IsomorphismRefinedPcGroup}{46.4.8}{X7E6226597DFE5F8F} 3599\makelabel{ref:isomorphic pc group}{46.4.8}{X7E6226597DFE5F8F} 3600\makelabel{ref:RefinedPcGroup}{46.4.9}{X821560A387762DD1} 3601\makelabel{ref:PcGroupWithPcgs}{46.5.1}{X81C55D4F825C36D4} 3602\makelabel{ref:IsomorphismPcGroup}{46.5.2}{X873CEB137BA1CD6E} 3603\makelabel{ref:isomorphic pc group}{46.5.2}{X873CEB137BA1CD6E} 3604\makelabel{ref:IsomorphismSpecialPcGroup}{46.5.3}{X82BE14A986FA6882} 3605\makelabel{ref:GapInputPcGroup}{46.6.1}{X8593253380D84508} 3606\makelabel{ref:TwoCoboundaries}{46.8.1}{X78E6E11E8285E288} 3607\makelabel{ref:TwoCocycles}{46.8.2}{X784FCA207B8694A6} 3608\makelabel{ref:TwoCohomology}{46.8.3}{X838065F97F60468F} 3609\makelabel{ref:Extensions}{46.8.4}{X8236AD927A5A0E5A} 3610\makelabel{ref:Extension}{46.8.5}{X7B3BE908867CE4F9} 3611\makelabel{ref:ExtensionNC}{46.8.5}{X7B3BE908867CE4F9} 3612\makelabel{ref:SplitExtension}{46.8.6}{X83DCB5AB7B6EE785} 3613\makelabel{ref:ModuleOfExtension}{46.8.7}{X7EAC6B8B7ABEEB86} 3614\makelabel{ref:CompatiblePairs}{46.8.8}{X824F2B2E7C11ABAF} 3615\makelabel{ref:ExtensionRepresentatives}{46.8.9}{X854FFEF187C4AAB9} 3616\makelabel{ref:SplitExtension with specified homomorphism}{46.8.10}{X84E2DA897FAAF6D8} 3617\makelabel{ref:CodePcgs}{46.9.1}{X79948F1D7D4FF8D9} 3618\makelabel{ref:CodePcGroup}{46.9.2}{X8041C2D88721EEA9} 3619\makelabel{ref:PcGroupCode}{46.9.3}{X826BFDA07A707C54} 3620\makelabel{ref:RandomIsomorphismTest}{46.10.1}{X84F6F9787CB2CF16} 3621\makelabel{ref:IsSubgroupFpGroup}{47.1.1}{X7AF7E2B48199452C} 3622\makelabel{ref:IsFpGroup}{47.1.2}{X850B9DF17D90C3A2} 3623\makelabel{ref:InfoFpGroup}{47.1.3}{X8370BF3B78D0B14D} 3624\makelabel{ref:quotient for finitely presented groups}{47.2.1}{X7EF4179E78BC7313} 3625\makelabel{ref:FactorGroupFpGroupByRels}{47.2.2}{X7CE0FA5F8695241E} 3626\makelabel{ref:ParseRelators}{47.2.3}{X7B3D290B87B6EFE4} 3627\makelabel{ref:StringFactorizationWord}{47.2.4}{X85EAA789848B528E} 3628\makelabel{ref:equality elements of finitely presented groups}{47.3.1}{X797D29628203CBD6} 3629\makelabel{ref:smaller elements of finitely presented groups}{47.3.2}{X7B350C718573B8DF} 3630\makelabel{ref:FpElmComparisonMethod}{47.3.3}{X87512CF485CC4128} 3631\makelabel{ref:SetReducedMultiplication}{47.3.4}{X82CB9EC982CDAEAC} 3632\makelabel{ref:FreeGroupOfFpGroup}{47.4.1}{X85CF3931849FB441} 3633\makelabel{ref:FreeGeneratorsOfFpGroup}{47.4.2}{X79C77C5184CA02B6} 3634\makelabel{ref:FreeGeneratorsOfWholeGroup}{47.4.2}{X79C77C5184CA02B6} 3635\makelabel{ref:RelatorsOfFpGroup}{47.4.3}{X87BA180287CD1F71} 3636\makelabel{ref:UnderlyingElement fp group elements}{47.4.4}{X8447A2397A1E524B} 3637\makelabel{ref:ElementOfFpGroup}{47.4.5}{X7F34C8017DC03FDB} 3638\makelabel{ref:PseudoRandom for finitely presented groups}{47.5.1}{X7AB7187779EDC9BA} 3639\makelabel{ref:CosetTable}{47.6.1}{X7F7F31E47D7F6EF8} 3640\makelabel{ref:TracedCosetFpGroup}{47.6.2}{X87D175757C581E62} 3641\makelabel{ref:FactorCosetAction for fp groups}{47.6.3}{X7EC1B0EE876E478A} 3642\makelabel{ref:CosetTableBySubgroup}{47.6.4}{X82926A7F8365A341} 3643\makelabel{ref:CosetTableFromGensAndRels}{47.6.5}{X7DE601F179E6FD09} 3644\makelabel{ref:TCENUM}{47.6.5}{X7DE601F179E6FD09} 3645\makelabel{ref:GAPTCENUM}{47.6.5}{X7DE601F179E6FD09} 3646\makelabel{ref:CosetTableDefaultMaxLimit}{47.6.6}{X822B188F87E9E642} 3647\makelabel{ref:CosetTableDefaultLimit}{47.6.7}{X7A80A00E7E088E44} 3648\makelabel{ref:MostFrequentGeneratorFpGroup}{47.6.8}{X829D31A981CB2AF4} 3649\makelabel{ref:IndicesInvolutaryGenerators}{47.6.9}{X7912E6577B577A5C} 3650\makelabel{ref:CosetTableStandard}{47.7.1}{X85FD1D637EF1EBE7} 3651\makelabel{ref:StandardizeTable}{47.7.2}{X85FCD8DF81BA94D5} 3652\makelabel{ref:CosetTableInWholeGroup}{47.8.1}{X846EC8AB7803114D} 3653\makelabel{ref:TryCosetTableInWholeGroup}{47.8.1}{X846EC8AB7803114D} 3654\makelabel{ref:SubgroupOfWholeGroupByCosetTable}{47.8.2}{X857F239583AFE0B7} 3655\makelabel{ref:AugmentedCosetTableInWholeGroup}{47.9.1}{X80F8BF1D867DA7C1} 3656\makelabel{ref:AugmentedCosetTableMtc}{47.9.2}{X7AF67CFD846C1159} 3657\makelabel{ref:AugmentedCosetTableRrs}{47.9.3}{X7F3F09C778552811} 3658\makelabel{ref:RewriteWord}{47.9.4}{X86B65EA186140244} 3659\makelabel{ref:LowIndexSubgroupsFpGroupIterator}{47.10.1}{X85C5151380E19122} 3660\makelabel{ref:LowIndexSubgroupsFpGroup}{47.10.1}{X85C5151380E19122} 3661\makelabel{ref:iterator for low index subgroups}{47.10.1}{X85C5151380E19122} 3662\makelabel{ref:IsomorphismFpGroup}{47.11.1}{X7F28268F850F454E} 3663\makelabel{ref:IsomorphismFpGroupByGenerators}{47.11.2}{X81B2B3B6812FD62D} 3664\makelabel{ref:IsomorphismFpGroupByGeneratorsNC}{47.11.2}{X81B2B3B6812FD62D} 3665\makelabel{ref:IsomorphismFpGroup for subgroups of fp groups}{47.12}{X826604AA7F18BFA3} 3666\makelabel{ref:IsomorphismSimplifiedFpGroup}{47.12.1}{X78D87FA68233C401} 3667\makelabel{ref:SubgroupOfWholeGroupByQuotientSubgroup}{47.13.1}{X7ABC3C917D41A74B} 3668\makelabel{ref:IsSubgroupOfWholeGroupByQuotientRep}{47.13.2}{X8047D7A37B27FEEA} 3669\makelabel{ref:AsSubgroupOfWholeGroupByQuotient}{47.13.3}{X84E6CEA28611C112} 3670\makelabel{ref:DefiningQuotientHomomorphism}{47.13.4}{X7DA1151D84289FC9} 3671\makelabel{ref:PQuotient}{47.14.1}{X7B5DDADC80F5796B} 3672\makelabel{ref:EpimorphismQuotientSystem}{47.14.2}{X86EB30A7867EEF16} 3673\makelabel{ref:EpimorphismPGroup}{47.14.3}{X7CA738DB80B20D67} 3674\makelabel{ref:EpimorphismNilpotentQuotient}{47.14.4}{X7CA20E2582DC45FD} 3675\makelabel{ref:SolvableQuotient for a f.p. group and a size}{47.14.5}{X869F70CC818C946D} 3676\makelabel{ref:SolvableQuotient for a f.p. group and a list of primes}{47.14.5}{X869F70CC818C946D} 3677\makelabel{ref:SolvableQuotient for a f.p. group and a list of tuples}{47.14.5}{X869F70CC818C946D} 3678\makelabel{ref:SQ synonym of solvablequotient}{47.14.5}{X869F70CC818C946D} 3679\makelabel{ref:EpimorphismSolvableQuotient}{47.14.6}{X79A4D3B68110F48A} 3680\makelabel{ref:LargerQuotientBySubgroupAbelianization}{47.14.7}{X81167847832DD3B1} 3681\makelabel{ref:AbelianInvariantsSubgroupFpGroup}{47.15.1}{X83B63ED8826F4268} 3682\makelabel{ref:AbelianInvariantsSubgroupFpGroupMtc}{47.15.2}{X804F664180BA2134} 3683\makelabel{ref:AbelianInvariantsSubgroupFpGroupRrs for two groups}{47.15.3}{X8586137B7AAA6C10} 3684\makelabel{ref:AbelianInvariantsSubgroupFpGroupRrs for a group and a coset table}{47.15.3}{X8586137B7AAA6C10} 3685\makelabel{ref:AbelianInvariantsNormalClosureFpGroup}{47.15.4}{X850E4CD784F6EAA8} 3686\makelabel{ref:AbelianInvariantsNormalClosureFpGroupRrs}{47.15.5}{X801635B28079E56A} 3687\makelabel{ref:IsInfiniteAbelianizationGroup}{47.16.1}{X82F444F67BE0E4FE} 3688\makelabel{ref:IsInfiniteAbelianizationGroup for groups}{47.16.1}{X82F444F67BE0E4FE} 3689\makelabel{ref:NewmanInfinityCriterion}{47.16.2}{X85C9FD548394C1E2} 3690\makelabel{ref:PresentationFpGroup}{48.1.1}{X797867B287AD92F8} 3691\makelabel{ref:TzSort}{48.1.2}{X8637837A79422445} 3692\makelabel{ref:GeneratorsOfPresentation}{48.1.3}{X849429BC7D435F77} 3693\makelabel{ref:FpGroupPresentation}{48.1.4}{X7D6F40A87F24D3D6} 3694\makelabel{ref:PresentationViaCosetTable}{48.1.5}{X84E056C57AFEDEA8} 3695\makelabel{ref:SimplifiedFpGroup}{48.1.6}{X7E1F2658827FC228} 3696\makelabel{ref:Schreier}{48.2}{X8118FECE7AD1879B} 3697\makelabel{ref:PresentationSubgroup}{48.2.1}{X7DB32FA97DAC5AC8} 3698\makelabel{ref:PresentationSubgroupRrs for two groups (and a string)}{48.2.2}{X857365CD87ADC29E} 3699\makelabel{ref:PresentationSubgroupRrs for a group and a coset table (and a string)}{48.2.2}{X857365CD87ADC29E} 3700\makelabel{ref:PrimaryGeneratorWords}{48.2.3}{X7FCE7ED581CF7897} 3701\makelabel{ref:PresentationSubgroupMtc}{48.2.4}{X80BA10F780EAE68E} 3702\makelabel{ref:PresentationNormalClosureRrs}{48.2.5}{X7D6A52837BEE5C3D} 3703\makelabel{ref:PresentationNormalClosure}{48.2.6}{X7A7E5D0084DB0B4F} 3704\makelabel{ref:TietzeWordAbstractWord}{48.3.1}{X8365BAFA785FCD8D} 3705\makelabel{ref:AbstractWordTietzeWord}{48.3.2}{X8573E91C838B1D13} 3706\makelabel{ref:TzPrintGenerators}{48.4.1}{X847EA6737C21171C} 3707\makelabel{ref:TzPrintRelators}{48.4.2}{X821B63DD82894443} 3708\makelabel{ref:TzPrintLengths}{48.4.3}{X852C52C37FAAB7DD} 3709\makelabel{ref:TzPrintStatus}{48.4.4}{X7D7B3F46865443E4} 3710\makelabel{ref:TzPrintPresentation}{48.4.5}{X85F8DAE27F06C32B} 3711\makelabel{ref:TzPrint}{48.4.6}{X7CA8BA51802655FC} 3712\makelabel{ref:TzPrintPairs}{48.4.7}{X82F6B0EE7C7C7901} 3713\makelabel{ref:AddGenerator}{48.5.1}{X7F632A6D8685855D} 3714\makelabel{ref:TzNewGenerator}{48.5.2}{X83A5667086FD538A} 3715\makelabel{ref:AddRelator}{48.5.3}{X78D1BCE67FA852D8} 3716\makelabel{ref:RemoveRelator}{48.5.4}{X7B11E89E78A22EBF} 3717\makelabel{ref:TzGo}{48.6.1}{X7C4A30328224C466} 3718\makelabel{ref:SimplifyPresentation}{48.6.2}{X78C3D23387DAC35A} 3719\makelabel{ref:TzGoGo}{48.6.3}{X801D3D8984E1CA55} 3720\makelabel{ref:TzEliminate for a presentation (and a generator)}{48.7.1}{X85989AF886EC2BF6} 3721\makelabel{ref:TzEliminate for a presentation (and an integer)}{48.7.1}{X85989AF886EC2BF6} 3722\makelabel{ref:TzSearch}{48.7.2}{X7DF4BBDF839643DD} 3723\makelabel{ref:TzSearchEqual}{48.7.3}{X87F7A87A7ACF2445} 3724\makelabel{ref:TzFindCyclicJoins}{48.7.4}{X80D31A0F7C2A51BD} 3725\makelabel{ref:TzSubstitute for a presentation and a word}{48.8.1}{X846DB23E8236FF8A} 3726\makelabel{ref:TzSubstituteCyclicJoins}{48.8.2}{X7ADE3B437C19B94D} 3727\makelabel{ref:TzInitGeneratorImages}{48.9.1}{X7D855FA08242898A} 3728\makelabel{ref:OldGeneratorsOfPresentation}{48.9.2}{X7AB9A06F80FB3659} 3729\makelabel{ref:TzImagesOldGens}{48.9.3}{X798B38F87C082C45} 3730\makelabel{ref:TzPreImagesNewGens}{48.9.4}{X7AC41B117DBB87D6} 3731\makelabel{ref:TzPrintGeneratorImages}{48.9.5}{X7F086D0E7AD6173B} 3732\makelabel{ref:DecodeTree}{48.10.1}{X7ACBFE2F78D72A31} 3733\makelabel{ref:secondary subgroup generators}{48.10.1}{X7ACBFE2F78D72A31} 3734\makelabel{ref:primary subgroup generators}{48.10.1}{X7ACBFE2F78D72A31} 3735\makelabel{ref:subgroup generators tree}{48.10.1}{X7ACBFE2F78D72A31} 3736\makelabel{ref:TzOptions}{48.11.1}{X8178683283214D88} 3737\makelabel{ref:TzPrintOptions}{48.11.2}{X7BC90B6882DE6D10} 3738\makelabel{ref:DirectProduct}{49.1.1}{X861BA02C7902A4F4} 3739\makelabel{ref:DirectProductOp}{49.1.1}{X861BA02C7902A4F4} 3740\makelabel{ref:Embedding example for direct products}{49.1.1}{X861BA02C7902A4F4} 3741\makelabel{ref:Projection example for direct products}{49.1.1}{X861BA02C7902A4F4} 3742\makelabel{ref:SemidirectProduct for acting group, action, and a group}{49.2.1}{X7D905A5778D7ACDE} 3743\makelabel{ref:SemidirectProduct for a group of automorphisms and a group}{49.2.1}{X7D905A5778D7ACDE} 3744\makelabel{ref:Embedding example for semidirect products}{49.2.1}{X7D905A5778D7ACDE} 3745\makelabel{ref:Projection example for semidirect products}{49.2.1}{X7D905A5778D7ACDE} 3746\makelabel{ref:SubdirectProduct}{49.3.1}{X82112D768085AD98} 3747\makelabel{ref:Projection example for subdirect products}{49.3.1}{X82112D768085AD98} 3748\makelabel{ref:SubdirectProducts}{49.3.2}{X814204E97812894C} 3749\makelabel{ref:WreathProduct}{49.4.1}{X8786EFBC78D7D6ED} 3750\makelabel{ref:StandardWreathProduct}{49.4.1}{X8786EFBC78D7D6ED} 3751\makelabel{ref:Embedding example for wreath products}{49.4.1}{X8786EFBC78D7D6ED} 3752\makelabel{ref:Projection example for wreath products}{49.4.1}{X8786EFBC78D7D6ED} 3753\makelabel{ref:WreathProductImprimitiveAction}{49.4.2}{X8589DCFA7C2E5FAA} 3754\makelabel{ref:WreathProductProductAction}{49.4.3}{X82B8DD1C868A3726} 3755\makelabel{ref:KuKGenerators}{49.4.4}{X80634C3180E0C593} 3756\makelabel{ref:Krasner-Kaloujnine theorem}{49.4.4}{X80634C3180E0C593} 3757\makelabel{ref:Wreath product embedding}{49.4.4}{X80634C3180E0C593} 3758\makelabel{ref:FreeProduct for several groups}{49.5.1}{X837AC5A081EECF50} 3759\makelabel{ref:FreeProduct for a list}{49.5.1}{X837AC5A081EECF50} 3760\makelabel{ref:Embedding for group products}{49.6.1}{X784149B8847B20FF} 3761\makelabel{ref:Projection for group products}{49.6.2}{X86F275AC7C625626} 3762\makelabel{ref:TrivialGroup}{50.1.1}{X8489BECB78664847} 3763\makelabel{ref:CyclicGroup}{50.1.2}{X7A7C473D87B31F3B} 3764\makelabel{ref:AbelianGroup}{50.1.3}{X81CCC3BF8005A2D7} 3765\makelabel{ref:ElementaryAbelianGroup}{50.1.4}{X8778256286E50743} 3766\makelabel{ref:FreeAbelianGroup}{50.1.5}{X7F43050D8587E767} 3767\makelabel{ref:DihedralGroup}{50.1.6}{X838DE1AB7B3D70FF} 3768\makelabel{ref:IsDihedralGroup}{50.1.7}{X8233A853818CAF33} 3769\makelabel{ref:DihedralGenerators}{50.1.7}{X8233A853818CAF33} 3770\makelabel{ref:DicyclicGroup}{50.1.8}{X7E9844EF7C47EEB0} 3771\makelabel{ref:QuaternionGroup}{50.1.8}{X7E9844EF7C47EEB0} 3772\makelabel{ref:IsGeneralisedQuaternionGroup}{50.1.9}{X7FE58CB9799F54D5} 3773\makelabel{ref:IsQuaternionGroup}{50.1.9}{X7FE58CB9799F54D5} 3774\makelabel{ref:GeneralisedQuaternionGenerators}{50.1.9}{X7FE58CB9799F54D5} 3775\makelabel{ref:QuaternionGenerators}{50.1.9}{X7FE58CB9799F54D5} 3776\makelabel{ref:ExtraspecialGroup}{50.1.10}{X86E76B3A796BEFA8} 3777\makelabel{ref:AlternatingGroup for a degree}{50.1.11}{X7E54D3E778E6A53E} 3778\makelabel{ref:AlternatingGroup for a domain}{50.1.11}{X7E54D3E778E6A53E} 3779\makelabel{ref:SymmetricGroup for a degree}{50.1.12}{X858666F97BD85ABB} 3780\makelabel{ref:SymmetricGroup for a domain}{50.1.12}{X858666F97BD85ABB} 3781\makelabel{ref:MathieuGroup}{50.1.13}{X788FA7DE84E0FE6A} 3782\makelabel{ref:SuzukiGroup}{50.1.14}{X8469DBBF82F8E5C3} 3783\makelabel{ref:Sz}{50.1.14}{X8469DBBF82F8E5C3} 3784\makelabel{ref:ReeGroup}{50.1.15}{X87E5B0F679CA7FE4} 3785\makelabel{ref:Ree}{50.1.15}{X87E5B0F679CA7FE4} 3786\makelabel{ref:GeneralLinearGroup for dimension and a ring}{50.2.1}{X85D607DD82AF3E27} 3787\makelabel{ref:GL for dimension and a ring}{50.2.1}{X85D607DD82AF3E27} 3788\makelabel{ref:GeneralLinearGroup for dimension and field size}{50.2.1}{X85D607DD82AF3E27} 3789\makelabel{ref:GL for dimension and field size}{50.2.1}{X85D607DD82AF3E27} 3790\makelabel{ref:OnLines example}{50.2.1}{X85D607DD82AF3E27} 3791\makelabel{ref:SpecialLinearGroup for dimension and a ring}{50.2.2}{X7CA3F7BF83992C6B} 3792\makelabel{ref:SL for dimension and a ring}{50.2.2}{X7CA3F7BF83992C6B} 3793\makelabel{ref:SpecialLinearGroup for dimension and a field size}{50.2.2}{X7CA3F7BF83992C6B} 3794\makelabel{ref:SL for dimension and a field size}{50.2.2}{X7CA3F7BF83992C6B} 3795\makelabel{ref:GeneralUnitaryGroup}{50.2.3}{X866D4E2B816BDFA5} 3796\makelabel{ref:GU}{50.2.3}{X866D4E2B816BDFA5} 3797\makelabel{ref:SpecialUnitaryGroup}{50.2.4}{X82A2AADE805DCDE9} 3798\makelabel{ref:SU}{50.2.4}{X82A2AADE805DCDE9} 3799\makelabel{ref:SymplecticGroup for dimension and field size}{50.2.5}{X8142A8B07811CA90} 3800\makelabel{ref:SymplecticGroup for dimension and a ring}{50.2.5}{X8142A8B07811CA90} 3801\makelabel{ref:Sp for dimension and field size}{50.2.5}{X8142A8B07811CA90} 3802\makelabel{ref:Sp for dimension and a ring}{50.2.5}{X8142A8B07811CA90} 3803\makelabel{ref:SP for dimension and field size}{50.2.5}{X8142A8B07811CA90} 3804\makelabel{ref:SP for dimension and a ring}{50.2.5}{X8142A8B07811CA90} 3805\makelabel{ref:GeneralOrthogonalGroup}{50.2.6}{X7C2051CB7B94CEB1} 3806\makelabel{ref:GO}{50.2.6}{X7C2051CB7B94CEB1} 3807\makelabel{ref:SpecialOrthogonalGroup}{50.2.7}{X78D4EEF27AA2DCFD} 3808\makelabel{ref:SO}{50.2.7}{X78D4EEF27AA2DCFD} 3809\makelabel{ref:Omega construct an orthogonal group}{50.2.8}{X8365E0AB8338DA3F} 3810\makelabel{ref:GeneralSemilinearGroup}{50.2.9}{X79C3C61A7D83A6D0} 3811\makelabel{ref:GammaL}{50.2.9}{X79C3C61A7D83A6D0} 3812\makelabel{ref:SpecialSemilinearGroup}{50.2.10}{X7D3779237CB5B49C} 3813\makelabel{ref:SigmaL}{50.2.10}{X7D3779237CB5B49C} 3814\makelabel{ref:ProjectiveGeneralLinearGroup}{50.2.11}{X7F0DBEB880D2D574} 3815\makelabel{ref:PGL}{50.2.11}{X7F0DBEB880D2D574} 3816\makelabel{ref:ProjectiveSpecialLinearGroup}{50.2.12}{X86784EDA80224B74} 3817\makelabel{ref:PSL}{50.2.12}{X86784EDA80224B74} 3818\makelabel{ref:ProjectiveGeneralUnitaryGroup}{50.2.13}{X7E471ADE7E095604} 3819\makelabel{ref:PGU}{50.2.13}{X7E471ADE7E095604} 3820\makelabel{ref:ProjectiveSpecialUnitaryGroup}{50.2.14}{X7A88FE2B7EF9C804} 3821\makelabel{ref:PSU}{50.2.14}{X7A88FE2B7EF9C804} 3822\makelabel{ref:ProjectiveSymplecticGroup}{50.2.15}{X7DEDE2537B8FFFF5} 3823\makelabel{ref:PSP}{50.2.15}{X7DEDE2537B8FFFF5} 3824\makelabel{ref:PSp}{50.2.15}{X7DEDE2537B8FFFF5} 3825\makelabel{ref:ProjectiveOmega}{50.2.16}{X7F546F907A37DF15} 3826\makelabel{ref:POmega}{50.2.16}{X7F546F907A37DF15} 3827\makelabel{ref:ConjugacyClasses for linear groups}{50.3}{X85B9F2D379616C35} 3828\makelabel{ref:NrConjugacyClassesGL}{50.3.1}{X831789117E93171E} 3829\makelabel{ref:NrConjugacyClassesGU}{50.3.1}{X831789117E93171E} 3830\makelabel{ref:NrConjugacyClassesSL}{50.3.1}{X831789117E93171E} 3831\makelabel{ref:NrConjugacyClassesSU}{50.3.1}{X831789117E93171E} 3832\makelabel{ref:NrConjugacyClassesPGL}{50.3.1}{X831789117E93171E} 3833\makelabel{ref:NrConjugacyClassesPGU}{50.3.1}{X831789117E93171E} 3834\makelabel{ref:NrConjugacyClassesPSL}{50.3.1}{X831789117E93171E} 3835\makelabel{ref:NrConjugacyClassesPSU}{50.3.1}{X831789117E93171E} 3836\makelabel{ref:NrConjugacyClassesSLIsogeneous}{50.3.1}{X831789117E93171E} 3837\makelabel{ref:NrConjugacyClassesSUIsogeneous}{50.3.1}{X831789117E93171E} 3838\makelabel{ref:AllPrimitiveGroups}{50.5}{X82676ED5826E9E2E} 3839\makelabel{ref:AllTransitiveGroups}{50.5}{X82676ED5826E9E2E} 3840\makelabel{ref:AllLibraryGroups}{50.5}{X82676ED5826E9E2E} 3841\makelabel{ref:OnePrimitiveGroup}{50.5}{X82676ED5826E9E2E} 3842\makelabel{ref:OneTransitiveGroup}{50.5}{X82676ED5826E9E2E} 3843\makelabel{ref:OneLibraryGroup}{50.5}{X82676ED5826E9E2E} 3844\makelabel{ref:perfect groups}{50.6}{X7A884ECF813C2026} 3845\makelabel{ref:SizesPerfectGroups}{50.6.1}{X866A25F882A4E97B} 3846\makelabel{ref:PerfectGroup for group order (and index)}{50.6.2}{X7906BBA7818E9415} 3847\makelabel{ref:PerfectGroup for a pair [ order, index ]}{50.6.2}{X7906BBA7818E9415} 3848\makelabel{ref:PerfectIdentification}{50.6.3}{X7E1CB2D18085FF9D} 3849\makelabel{ref:NumberPerfectGroups}{50.6.4}{X7D68BE547FE5C0F5} 3850\makelabel{ref:NumberPerfectLibraryGroups}{50.6.5}{X7FE695DA86A066E1} 3851\makelabel{ref:SizeNumbersPerfectGroups}{50.6.6}{X866356A684F6B15E} 3852\makelabel{ref:DisplayInformationPerfectGroups for group order (and index)}{50.6.7}{X845419F07BB92867} 3853\makelabel{ref:DisplayInformationPerfectGroups for a pair [ order, index ]}{50.6.7}{X845419F07BB92867} 3854\makelabel{ref:ImfNumberQQClasses}{50.7.1}{X8693FD647EF3C53B} 3855\makelabel{ref:ImfNumberQClasses}{50.7.1}{X8693FD647EF3C53B} 3856\makelabel{ref:ImfNumberZClasses}{50.7.1}{X8693FD647EF3C53B} 3857\makelabel{ref:DisplayImfInvariants}{50.7.2}{X8705F64B7E19DDC7} 3858\makelabel{ref:ImfInvariants}{50.7.3}{X8604A2167B2E8434} 3859\makelabel{ref:ImfMatrixGroup}{50.7.4}{X78935B307B909101} 3860\makelabel{ref:IsomorphismPermGroup for imf matrix groups}{50.7.5}{X84BF34B27CD5E85C} 3861\makelabel{ref:IsomorphismPermGroupImfGroup}{50.7.6}{X7CEDB6CE7BAC4518} 3862\makelabel{ref:IsSemigroup}{51.1.1}{X7B412E5B8543E9B7} 3863\makelabel{ref:semigroup}{51.1.1}{X7B412E5B8543E9B7} 3864\makelabel{ref:Semigroup for various generators}{51.1.2}{X7F55D28F819B2817} 3865\makelabel{ref:Semigroup for a list}{51.1.2}{X7F55D28F819B2817} 3866\makelabel{ref:Subsemigroup}{51.1.3}{X8678D40878CC09A1} 3867\makelabel{ref:SubsemigroupNC}{51.1.3}{X8678D40878CC09A1} 3868\makelabel{ref:IsSubsemigroup}{51.1.4}{X782B7BDD8252581C} 3869\makelabel{ref:SemigroupByGenerators}{51.1.5}{X79FBBEC9841544F3} 3870\makelabel{ref:AsSemigroup}{51.1.6}{X80ED104F85AE5134} 3871\makelabel{ref:AsSubsemigroup}{51.1.7}{X7B1EEA3E82BFE09F} 3872\makelabel{ref:GeneratorsOfSemigroup}{51.1.8}{X78147A247963F23B} 3873\makelabel{ref:IsGeneratorsOfSemigroup}{51.1.9}{X79776D7C8399F2CF} 3874\makelabel{ref:FreeSemigroup for given rank}{51.1.10}{X7C72E4747BF642BB} 3875\makelabel{ref:FreeSemigroup for various names}{51.1.10}{X7C72E4747BF642BB} 3876\makelabel{ref:FreeSemigroup for a list of names}{51.1.10}{X7C72E4747BF642BB} 3877\makelabel{ref:FreeSemigroup for infinitely many generators}{51.1.10}{X7C72E4747BF642BB} 3878\makelabel{ref:SemigroupByMultiplicationTable}{51.1.11}{X7E67E13F7A01F8D3} 3879\makelabel{ref:IsMonoid}{51.2.1}{X861C523483C6248C} 3880\makelabel{ref:Monoid for various generators}{51.2.2}{X7F95328B7C7E49EA} 3881\makelabel{ref:Monoid for a list}{51.2.2}{X7F95328B7C7E49EA} 3882\makelabel{ref:Submonoid}{51.2.3}{X8322D01E84912FD7} 3883\makelabel{ref:SubmonoidNC}{51.2.3}{X8322D01E84912FD7} 3884\makelabel{ref:MonoidByGenerators}{51.2.4}{X85129EE387CC4D28} 3885\makelabel{ref:AsMonoid}{51.2.5}{X7B22038F832B9C0F} 3886\makelabel{ref:AsSubmonoid}{51.2.6}{X7C9A12DE8287B2D3} 3887\makelabel{ref:GeneratorsOfMonoid}{51.2.7}{X83CA2E7279C44718} 3888\makelabel{ref:TrivialSubmonoid}{51.2.8}{X7EC77C0184587181} 3889\makelabel{ref:FreeMonoid for given rank}{51.2.9}{X79FA3FA978CA2E43} 3890\makelabel{ref:FreeMonoid for various names}{51.2.9}{X79FA3FA978CA2E43} 3891\makelabel{ref:FreeMonoid for a list of names}{51.2.9}{X79FA3FA978CA2E43} 3892\makelabel{ref:FreeMonoid for infinitely many generators}{51.2.9}{X79FA3FA978CA2E43} 3893\makelabel{ref:MonoidByMultiplicationTable}{51.2.10}{X7BFE938E857CA27D} 3894\makelabel{ref:InverseSemigroup}{51.3.1}{X78B13FED7AFB4326} 3895\makelabel{ref:InverseMonoid}{51.3.2}{X80D9B9A98736051B} 3896\makelabel{ref:GeneratorsOfInverseSemigroup}{51.3.3}{X87C373597F787250} 3897\makelabel{ref:GeneratorsOfInverseMonoid}{51.3.4}{X7A3B262C85B6D475} 3898\makelabel{ref:IsInverseSubsemigroup}{51.3.5}{X7C4C6EE681E7A57E} 3899\makelabel{ref:IsRegularSemigroup}{51.4.1}{X7C4663827C5ACEF1} 3900\makelabel{ref:IsRegularSemigroupElement}{51.4.2}{X87532A76854347E0} 3901\makelabel{ref:InversesOfSemigroupElement}{51.4.3}{X7AFDE0F17AE516C5} 3902\makelabel{ref:IsSimpleSemigroup}{51.4.4}{X836F4692839F4874} 3903\makelabel{ref:IsZeroSimpleSemigroup}{51.4.5}{X8193A60F839C064E} 3904\makelabel{ref:IsZeroGroup}{51.4.6}{X85F7E5CD86F0643B} 3905\makelabel{ref:IsReesCongruenceSemigroup}{51.4.7}{X7FFEC81F7F2C4EAA} 3906\makelabel{ref:IsInverseSemigroup}{51.4.8}{X83F1529479D56665} 3907\makelabel{ref:IsInverseMonoid}{51.4.8}{X83F1529479D56665} 3908\makelabel{ref:SemigroupIdealByGenerators}{51.5.1}{X7D5CEE4D7D4318ED} 3909\makelabel{ref:ReesCongruenceOfSemigroupIdeal}{51.5.2}{X7F01FFB18125DED5} 3910\makelabel{ref:IsLeftSemigroupIdeal}{51.5.3}{X7A3FF85984345540} 3911\makelabel{ref:IsRightSemigroupIdeal}{51.5.3}{X7A3FF85984345540} 3912\makelabel{ref:IsSemigroupIdeal}{51.5.3}{X7A3FF85984345540} 3913\makelabel{ref:IsSemigroupCongruence}{51.6.1}{X78E34B737F0E009F} 3914\makelabel{ref:IsReesCongruence}{51.6.2}{X822DB78579BCB7B5} 3915\makelabel{ref:IsQuotientSemigroup}{51.7.1}{X80EF3E6F842BE64E} 3916\makelabel{ref:HomomorphismQuotientSemigroup}{51.7.2}{X7CAD3D1687956F7F} 3917\makelabel{ref:QuotientSemigroupPreimage}{51.7.3}{X87120C46808F7289} 3918\makelabel{ref:QuotientSemigroupCongruence}{51.7.3}{X87120C46808F7289} 3919\makelabel{ref:QuotientSemigroupHomomorphism}{51.7.3}{X87120C46808F7289} 3920\makelabel{ref:GreensRRelation}{51.8.1}{X786CEDD4814A9079} 3921\makelabel{ref:GreensLRelation}{51.8.1}{X786CEDD4814A9079} 3922\makelabel{ref:GreensJRelation}{51.8.1}{X786CEDD4814A9079} 3923\makelabel{ref:GreensDRelation}{51.8.1}{X786CEDD4814A9079} 3924\makelabel{ref:GreensHRelation}{51.8.1}{X786CEDD4814A9079} 3925\makelabel{ref:IsGreensRelation}{51.8.2}{X8364D69987D49DE1} 3926\makelabel{ref:IsGreensRRelation}{51.8.2}{X8364D69987D49DE1} 3927\makelabel{ref:IsGreensLRelation}{51.8.2}{X8364D69987D49DE1} 3928\makelabel{ref:IsGreensJRelation}{51.8.2}{X8364D69987D49DE1} 3929\makelabel{ref:IsGreensHRelation}{51.8.2}{X8364D69987D49DE1} 3930\makelabel{ref:IsGreensDRelation}{51.8.2}{X8364D69987D49DE1} 3931\makelabel{ref:IsGreensClass}{51.8.3}{X82A11A087AFB3EB0} 3932\makelabel{ref:IsGreensRClass}{51.8.3}{X82A11A087AFB3EB0} 3933\makelabel{ref:IsGreensLClass}{51.8.3}{X82A11A087AFB3EB0} 3934\makelabel{ref:IsGreensJClass}{51.8.3}{X82A11A087AFB3EB0} 3935\makelabel{ref:IsGreensHClass}{51.8.3}{X82A11A087AFB3EB0} 3936\makelabel{ref:IsGreensDClass}{51.8.3}{X82A11A087AFB3EB0} 3937\makelabel{ref:IsGreensLessThanOrEqual}{51.8.4}{X7AA204C8850F9070} 3938\makelabel{ref:RClassOfHClass}{51.8.5}{X86FE5F5585EBCF13} 3939\makelabel{ref:LClassOfHClass}{51.8.5}{X86FE5F5585EBCF13} 3940\makelabel{ref:EggBoxOfDClass}{51.8.6}{X78C56F4A78E0088A} 3941\makelabel{ref:DisplayEggBoxOfDClass}{51.8.7}{X803237F17ACD44E3} 3942\makelabel{ref:GreensRClassOfElement}{51.8.8}{X87C75A9D86122D93} 3943\makelabel{ref:GreensLClassOfElement}{51.8.8}{X87C75A9D86122D93} 3944\makelabel{ref:GreensDClassOfElement}{51.8.8}{X87C75A9D86122D93} 3945\makelabel{ref:GreensJClassOfElement}{51.8.8}{X87C75A9D86122D93} 3946\makelabel{ref:GreensHClassOfElement}{51.8.8}{X87C75A9D86122D93} 3947\makelabel{ref:GreensRClasses}{51.8.9}{X844D20467A644811} 3948\makelabel{ref:GreensLClasses}{51.8.9}{X844D20467A644811} 3949\makelabel{ref:GreensHClasses}{51.8.9}{X844D20467A644811} 3950\makelabel{ref:GreensJClasses}{51.8.9}{X844D20467A644811} 3951\makelabel{ref:GreensDClasses}{51.8.9}{X844D20467A644811} 3952\makelabel{ref:GroupHClassOfGreensDClass}{51.8.10}{X7CB4A18685B850E2} 3953\makelabel{ref:IsGroupHClass}{51.8.11}{X79D740EF7F0E53BD} 3954\makelabel{ref:IsRegularDClass}{51.8.12}{X7F5860927CAD920F} 3955\makelabel{ref:DisplaySemigroup}{51.8.13}{X81AF2EAB7CEF8C19} 3956\makelabel{ref:ReesMatrixSemigroup}{51.9.1}{X8526AA557CDF6C49} 3957\makelabel{ref:ReesZeroMatrixSemigroup}{51.9.1}{X8526AA557CDF6C49} 3958\makelabel{ref:ReesMatrixSubsemigroup}{51.9.2}{X78D2A48C87FC8E38} 3959\makelabel{ref:ReesZeroMatrixSubsemigroup}{51.9.2}{X78D2A48C87FC8E38} 3960\makelabel{ref:IsomorphismReesMatrixSemigroup}{51.9.3}{X7964B5C97FB9C07D} 3961\makelabel{ref:IsomorphismReesZeroMatrixSemigroup}{51.9.3}{X7964B5C97FB9C07D} 3962\makelabel{ref:IsReesMatrixSemigroupElement}{51.9.4}{X7F6B852B81488C86} 3963\makelabel{ref:IsReesZeroMatrixSemigroupElement}{51.9.4}{X7F6B852B81488C86} 3964\makelabel{ref:ReesMatrixSemigroupElement}{51.9.5}{X7A0DE1F28470295E} 3965\makelabel{ref:ReesZeroMatrixSemigroupElement}{51.9.5}{X7A0DE1F28470295E} 3966\makelabel{ref:IsReesMatrixSubsemigroup}{51.9.6}{X7F03BE707AC7F8A0} 3967\makelabel{ref:IsReesZeroMatrixSubsemigroup}{51.9.6}{X7F03BE707AC7F8A0} 3968\makelabel{ref:IsReesMatrixSemigroup}{51.9.7}{X780BB78A79275244} 3969\makelabel{ref:IsReesZeroMatrixSemigroup}{51.9.7}{X780BB78A79275244} 3970\makelabel{ref:Matrix}{51.9.8}{X879384D479EB1D82} 3971\makelabel{ref:Rows}{51.9.9}{X82FC5D6980C66AC4} 3972\makelabel{ref:Columns}{51.9.9}{X82FC5D6980C66AC4} 3973\makelabel{ref:UnderlyingSemigroup for a rees matrix semigroup}{51.9.10}{X7D9719F887AFCF8F} 3974\makelabel{ref:UnderlyingSemigroup for a rees 0-matrix semigroup}{51.9.10}{X7D9719F887AFCF8F} 3975\makelabel{ref:AssociatedReesMatrixSemigroupOfDClass}{51.9.11}{X7D1D9A0382064B8F} 3976\makelabel{ref:IsSubsemigroupFpSemigroup}{52.1.1}{X8496E23C80453C33} 3977\makelabel{ref:IsSubmonoidFpMonoid}{52.1.1}{X8496E23C80453C33} 3978\makelabel{ref:IsFpSemigroup}{52.1.2}{X8239EF2B853411E9} 3979\makelabel{ref:IsFpMonoid}{52.1.2}{X8239EF2B853411E9} 3980\makelabel{ref:IsElementOfFpSemigroup}{52.1.3}{X81ABBE997A4C19B7} 3981\makelabel{ref:IsElementOfFpMonoid}{52.1.3}{X81ABBE997A4C19B7} 3982\makelabel{ref:FpGrpMonSmgOfFpGrpMonSmgElement}{52.1.4}{X7DC8A5D380AFE5DB} 3983\makelabel{ref:quotient of free semigroup}{52.2.1}{X84745EC6789FEB4C} 3984\makelabel{ref:quotient of free monoid}{52.2.1}{X84745EC6789FEB4C} 3985\makelabel{ref:FactorFreeSemigroupByRelations}{52.2.2}{X822F04B2833BE254} 3986\makelabel{ref:FactorFreeMonoidByRelations}{52.2.2}{X822F04B2833BE254} 3987\makelabel{ref:IsomorphismFpSemigroup}{52.2.3}{X869F966B8196F28C} 3988\makelabel{ref:IsomorphismFpMonoid}{52.2.3}{X869F966B8196F28C} 3989\makelabel{ref:comparison fp semigroup elements}{52.3.1}{X7DD9D81F863EBE31} 3990\makelabel{ref:UnderlyingElement of an element in a fp semigroup or monoid}{52.4.1}{X784B3DB686E7080C} 3991\makelabel{ref:ElementOfFpSemigroup}{52.4.2}{X847012347856C55E} 3992\makelabel{ref:ElementOfFpMonoid}{52.4.2}{X847012347856C55E} 3993\makelabel{ref:FreeSemigroupOfFpSemigroup}{52.4.3}{X8726523779601873} 3994\makelabel{ref:FreeMonoidOfFpMonoid}{52.4.3}{X8726523779601873} 3995\makelabel{ref:FreeGeneratorsOfFpSemigroup}{52.4.4}{X79A39402806B5EB7} 3996\makelabel{ref:FreeGeneratorsOfFpMonoid}{52.4.4}{X79A39402806B5EB7} 3997\makelabel{ref:RelationsOfFpSemigroup}{52.4.5}{X862BE9FA7C987CAB} 3998\makelabel{ref:RelationsOfFpMonoid}{52.4.5}{X862BE9FA7C987CAB} 3999\makelabel{ref:ReducedConfluentRewritingSystem}{52.5.1}{X7D8F804E814D894D} 4000\makelabel{ref:KBREW}{52.5.2}{X7A3F8AE285C41D80} 4001\makelabel{ref:GAPKBREW}{52.5.2}{X7A3F8AE285C41D80} 4002\makelabel{ref:KnuthBendixRewritingSystem for a semigroup and a reduction ordering}{52.5.3}{X87A3823483E4FF86} 4003\makelabel{ref:KnuthBendixRewritingSystem for a monoid and a reduction ordering}{52.5.3}{X87A3823483E4FF86} 4004\makelabel{ref:SemigroupOfRewritingSystem}{52.5.4}{X7966343587A04AFF} 4005\makelabel{ref:MonoidOfRewritingSystem}{52.5.4}{X7966343587A04AFF} 4006\makelabel{ref:FreeSemigroupOfRewritingSystem}{52.5.5}{X80B8115C8147F605} 4007\makelabel{ref:FreeMonoidOfRewritingSystem}{52.5.5}{X80B8115C8147F605} 4008\makelabel{ref:CosetTableOfFpSemigroup}{52.6.1}{X7C24508A7F677520} 4009\makelabel{ref:IsTransformation}{53.1.1}{X7B6259467974FB70} 4010\makelabel{ref:IsTransformationCollection}{53.1.2}{X7A6747CE85F2E6EA} 4011\makelabel{ref:TransformationFamily}{53.1.3}{X7E58AFA1832FF064} 4012\makelabel{ref:Transformation for an image list}{53.2.1}{X86ADBDE57A20E323} 4013\makelabel{ref:Transformation for a list and function}{53.2.1}{X86ADBDE57A20E323} 4014\makelabel{ref:TransformationList for an image list}{53.2.1}{X86ADBDE57A20E323} 4015\makelabel{ref:Transformation for a source and destination}{53.2.2}{X8040642687531E7F} 4016\makelabel{ref:TransformationListList for a source and destination}{53.2.2}{X8040642687531E7F} 4017\makelabel{ref:TransformationByImageAndKernel for an image and kernel}{53.2.3}{X7E82EBD68455EE4A} 4018\makelabel{ref:Idempotent}{53.2.4}{X85D1071484CE004C} 4019\makelabel{ref:TransformationOp}{53.2.5}{X7C2A3FC9782F2099} 4020\makelabel{ref:TransformationOpNC}{53.2.5}{X7C2A3FC9782F2099} 4021\makelabel{ref:TransformationNumber}{53.2.6}{X7D6FCC417DE86CD1} 4022\makelabel{ref:NumberTransformation}{53.2.6}{X7D6FCC417DE86CD1} 4023\makelabel{ref:RandomTransformation}{53.2.7}{X8475448F87E8CB8A} 4024\makelabel{ref:IdentityTransformation}{53.2.8}{X8268A58685BEFD6F} 4025\makelabel{ref:ConstantTransformation}{53.2.9}{X7F1E4B5184210D2B} 4026\makelabel{ref:AsTransformation}{53.3.1}{X7C5360B2799943F3} 4027\makelabel{ref:RestrictedTransformation}{53.3.2}{X846A6F6B7B715188} 4028\makelabel{ref:PermutationOfImage}{53.3.3}{X8708AE247F5B129B} 4029\makelabel{ref:LQUO for a permutation and transformation}{53.4}{X812CEC008609A8A2} 4030\makelabel{ref:smaller for transformations}{53.4}{X812CEC008609A8A2} 4031\makelabel{ref:equality for transformations}{53.4}{X812CEC008609A8A2} 4032\makelabel{ref:PermLeftQuoTransformation}{53.4.1}{X83DBA2A18719EFA8} 4033\makelabel{ref:PermLeftQuoTransformationNC}{53.4.1}{X83DBA2A18719EFA8} 4034\makelabel{ref:IsInjectiveListTrans}{53.4.2}{X8275DFAA8270BB59} 4035\makelabel{ref:ComponentTransformationInt}{53.4.3}{X834A313B7DAF06D5} 4036\makelabel{ref:PreImagesOfTransformation}{53.4.4}{X82F5DEEC837B60A3} 4037\makelabel{ref:DegreeOfTransformation}{53.5.1}{X78A209C87CF0E32B} 4038\makelabel{ref:DegreeOfTransformationCollection}{53.5.1}{X78A209C87CF0E32B} 4039\makelabel{ref:ImageListOfTransformation}{53.5.2}{X7AEC9E6687B3505A} 4040\makelabel{ref:ListTransformation}{53.5.2}{X7AEC9E6687B3505A} 4041\makelabel{ref:ImageSetOfTransformation}{53.5.3}{X839A6D6082A21D1F} 4042\makelabel{ref:RankOfTransformation for a transformation and a positive integer}{53.5.4}{X818EBB167C7EA37B} 4043\makelabel{ref:RankOfTransformation for a transformation and a list}{53.5.4}{X818EBB167C7EA37B} 4044\makelabel{ref:MovedPoints for a transformation}{53.5.5}{X844F00F982D5BD3C} 4045\makelabel{ref:MovedPoints for a transformation coll}{53.5.5}{X844F00F982D5BD3C} 4046\makelabel{ref:NrMovedPoints for a transformation}{53.5.6}{X7FA6A4B57FDA003D} 4047\makelabel{ref:NrMovedPoints for a transformation coll}{53.5.6}{X7FA6A4B57FDA003D} 4048\makelabel{ref:SmallestMovedPoint for a transformation}{53.5.7}{X86C0DDDC7881273A} 4049\makelabel{ref:SmallestMovedPoint for a transformation coll}{53.5.7}{X86C0DDDC7881273A} 4050\makelabel{ref:LargestMovedPoint for a transformation}{53.5.8}{X8383A7727AC97724} 4051\makelabel{ref:LargestMovedPoint for a transformation coll}{53.5.8}{X8383A7727AC97724} 4052\makelabel{ref:SmallestImageOfMovedPoint for a transformation}{53.5.9}{X7CCFE27E83676572} 4053\makelabel{ref:SmallestImageOfMovedPoint for a transformation coll}{53.5.9}{X7CCFE27E83676572} 4054\makelabel{ref:LargestImageOfMovedPoint for a transformation}{53.5.10}{X7E7172567C3A3E63} 4055\makelabel{ref:LargestImageOfMovedPoint for a transformation coll}{53.5.10}{X7E7172567C3A3E63} 4056\makelabel{ref:FlatKernelOfTransformation}{53.5.11}{X8083794579274E87} 4057\makelabel{ref:KernelOfTransformation}{53.5.12}{X80FCB5048789CF75} 4058\makelabel{ref:InverseOfTransformation}{53.5.13}{X860306EB7FAAD2D4} 4059\makelabel{ref:Inverse for a transformation}{53.5.14}{X7BB9DB6E8558356D} 4060\makelabel{ref:IndexPeriodOfTransformation}{53.5.15}{X863216CB7AF88BED} 4061\makelabel{ref:SmallestIdempotentPower for a transformation}{53.5.16}{X85FE9F20810BCC70} 4062\makelabel{ref:ComponentsOfTransformation}{53.5.17}{X858E944481F6B591} 4063\makelabel{ref:NrComponentsOfTransformation}{53.5.18}{X8640AE1C79201470} 4064\makelabel{ref:ComponentRepsOfTransformation}{53.5.19}{X784650B583CEAF7D} 4065\makelabel{ref:CyclesOfTransformation}{53.5.20}{X7EAA15557D55D93B} 4066\makelabel{ref:CycleTransformationInt}{53.5.21}{X786EB02A829260DB} 4067\makelabel{ref:LeftOne for a transformation}{53.5.22}{X845869E0815A6AA6} 4068\makelabel{ref:RightOne for a transformation}{53.5.22}{X845869E0815A6AA6} 4069\makelabel{ref:TrimTransformation}{53.5.23}{X7F19C9C77F9F8981} 4070\makelabel{ref:IsTransformationSemigroup}{53.7.1}{X7EAF835D7FE4026F} 4071\makelabel{ref:IsTransformationMonoid}{53.7.1}{X7EAF835D7FE4026F} 4072\makelabel{ref:DegreeOfTransformationSemigroup}{53.7.2}{X7EA699C687952544} 4073\makelabel{ref:FullTransformationSemigroup}{53.7.3}{X7D2B0685815B4053} 4074\makelabel{ref:FullTransformationMonoid}{53.7.3}{X7D2B0685815B4053} 4075\makelabel{ref:IsFullTransformationSemigroup}{53.7.4}{X85C58E1E818C838C} 4076\makelabel{ref:IsFullTransformationMonoid}{53.7.4}{X85C58E1E818C838C} 4077\makelabel{ref:IsomorphismTransformationSemigroup}{53.7.5}{X78F29C817CF6827F} 4078\makelabel{ref:IsomorphismTransformationMonoid}{53.7.5}{X78F29C817CF6827F} 4079\makelabel{ref:AntiIsomorphismTransformationSemigroup}{53.7.6}{X820ECE00846E480F} 4080\makelabel{ref:IsPartialPerm}{54.1.1}{X7EECE133792B30FC} 4081\makelabel{ref:IsPartialPermCollection}{54.1.2}{X8262A827790DD1CC} 4082\makelabel{ref:PartialPermFamily}{54.1.3}{X7E63D17780F64FBA} 4083\makelabel{ref:PartialPerm for a domain and image}{54.2.1}{X8538BAE77F2FB2F8} 4084\makelabel{ref:PartialPerm for a dense image}{54.2.1}{X8538BAE77F2FB2F8} 4085\makelabel{ref:PartialPermOp}{54.2.2}{X81188D9F83F64222} 4086\makelabel{ref:PartialPermOpNC}{54.2.2}{X81188D9F83F64222} 4087\makelabel{ref:RestrictedPartialPerm}{54.2.3}{X80ABBF4883C79060} 4088\makelabel{ref:JoinOfPartialPerms}{54.2.4}{X849668DD7B0B9E3B} 4089\makelabel{ref:JoinOfIdempotentPartialPermsNC}{54.2.4}{X849668DD7B0B9E3B} 4090\makelabel{ref:MeetOfPartialPerms}{54.2.5}{X81E2B6977E28CD00} 4091\makelabel{ref:EmptyPartialPerm}{54.2.6}{X80EFB142817A0A9F} 4092\makelabel{ref:RandomPartialPerm for a positive integer}{54.2.7}{X7E6ADC8583C31530} 4093\makelabel{ref:RandomPartialPerm for a set of positive 4094 integers}{54.2.7}{X7E6ADC8583C31530} 4095\makelabel{ref:RandomPartialPerm for domain and image}{54.2.7}{X7E6ADC8583C31530} 4096\makelabel{ref:DegreeOfPartialPerm}{54.3.1}{X8612A4DC864E7959} 4097\makelabel{ref:DegreeOfPartialPermCollection}{54.3.1}{X8612A4DC864E7959} 4098\makelabel{ref:CodegreeOfPartialPerm}{54.3.2}{X8413D0EF7DEE1FFF} 4099\makelabel{ref:CodegreeOfPartialPermCollection}{54.3.2}{X8413D0EF7DEE1FFF} 4100\makelabel{ref:RankOfPartialPerm}{54.3.3}{X7C1ABD8A80E95B39} 4101\makelabel{ref:RankOfPartialPermCollection}{54.3.3}{X7C1ABD8A80E95B39} 4102\makelabel{ref:DomainOfPartialPerm}{54.3.4}{X784A14F787E041D7} 4103\makelabel{ref:DomainOfPartialPermCollection}{54.3.4}{X784A14F787E041D7} 4104\makelabel{ref:ImageOfPartialPermCollection}{54.3.5}{X7CD84B107831E0FC} 4105\makelabel{ref:ImageListOfPartialPerm}{54.3.6}{X8333293F87F654FA} 4106\makelabel{ref:ImageSetOfPartialPerm}{54.3.7}{X7F0724A07A14DCF7} 4107\makelabel{ref:FixedPointsOfPartialPerm for a partial perm}{54.3.8}{X82AAFF938623422E} 4108\makelabel{ref:FixedPointsOfPartialPerm for a partial perm coll}{54.3.8}{X82AAFF938623422E} 4109\makelabel{ref:MovedPoints for a partial perm}{54.3.9}{X82FE981A87FAA2DC} 4110\makelabel{ref:MovedPoints for a partial perm coll}{54.3.9}{X82FE981A87FAA2DC} 4111\makelabel{ref:NrFixedPoints for a partial perm}{54.3.10}{X7FAF969C84CDC742} 4112\makelabel{ref:NrFixedPoints for a partial perm coll}{54.3.10}{X7FAF969C84CDC742} 4113\makelabel{ref:NrMovedPoints for a partial perm}{54.3.11}{X81F5C64E7DAD27A7} 4114\makelabel{ref:NrMovedPoints for a partial perm coll}{54.3.11}{X81F5C64E7DAD27A7} 4115\makelabel{ref:SmallestMovedPoint for a partial perm}{54.3.12}{X84A49C977E1E29AA} 4116\makelabel{ref:SmallestMovedPoint for a partial perm coll}{54.3.12}{X84A49C977E1E29AA} 4117\makelabel{ref:LargestMovedPoint for a partial perm}{54.3.13}{X7D4290A785ABC86D} 4118\makelabel{ref:LargestMovedPoint for a partial perm coll}{54.3.13}{X7D4290A785ABC86D} 4119\makelabel{ref:SmallestImageOfMovedPoint for a partial permutation}{54.3.14}{X85280F1A7B1014BA} 4120\makelabel{ref:SmallestImageOfMovedPoint for a partial permutation coll}{54.3.14}{X85280F1A7B1014BA} 4121\makelabel{ref:LargestImageOfMovedPoint for a partial permutation}{54.3.15}{X7A95CD437BC1CB1A} 4122\makelabel{ref:LargestImageOfMovedPoint for a partial permutation coll}{54.3.15}{X7A95CD437BC1CB1A} 4123\makelabel{ref:IndexPeriodOfPartialPerm}{54.3.16}{X873A9F717DA75CBC} 4124\makelabel{ref:SmallestIdempotentPower for a partial perm}{54.3.17}{X7C04AA377F080722} 4125\makelabel{ref:ComponentsOfPartialPerm}{54.3.18}{X8185065E788BDD0D} 4126\makelabel{ref:NrComponentsOfPartialPerm}{54.3.19}{X7CB51EB67FFA95E9} 4127\makelabel{ref:ComponentRepsOfPartialPerm}{54.3.20}{X7AAAAE4082B30E18} 4128\makelabel{ref:LeftOne for a partial perm}{54.3.21}{X7A8FB86C78C49F85} 4129\makelabel{ref:RightOne for a partial perm}{54.3.21}{X7A8FB86C78C49F85} 4130\makelabel{ref:One for a partial perm}{54.3.22}{X857FC10C81507E8B} 4131\makelabel{ref:MultiplicativeZero for a partial perm}{54.3.23}{X7D90CF497D58D759} 4132\makelabel{ref:AsPartialPerm for a permutation and a set of 4133 positive integers}{54.4.1}{X81B32CB182489ACA} 4134\makelabel{ref:AsPartialPerm for a permutation}{54.4.1}{X81B32CB182489ACA} 4135\makelabel{ref:AsPartialPerm for a permutation and a positive integer}{54.4.1}{X81B32CB182489ACA} 4136\makelabel{ref:AsPartialPerm for a transformation and a set of positive integer}{54.4.2}{X87EC67747B260E98} 4137\makelabel{ref:AsPartialPerm for a transformation and a positive integer}{54.4.2}{X87EC67747B260E98} 4138\makelabel{ref:LQUO for a permutation or partial permutation 4139 and partial permutation}{54.5}{X848CD855802C6CE1} 4140\makelabel{ref:PermLeftQuoPartialPerm}{54.5.1}{X8382A0F8875CEB08} 4141\makelabel{ref:PermLeftQuoPartialPermNC}{54.5.1}{X8382A0F8875CEB08} 4142\makelabel{ref:PreImagePartialPerm}{54.5.2}{X7C7F5EAB7E9A381D} 4143\makelabel{ref:ComponentPartialPermInt}{54.5.3}{X797A6CC084068219} 4144\makelabel{ref:NaturalLeqPartialPerm}{54.5.4}{X87B1ED93785257C1} 4145\makelabel{ref:ShortLexLeqPartialPerm}{54.5.5}{X81BD69307D294A1C} 4146\makelabel{ref:TrimPartialPerm}{54.5.6}{X83560BE678ACF855} 4147\makelabel{ref:IsPartialPermSemigroup}{54.7.1}{X7D161674800B50E0} 4148\makelabel{ref:IsPartialPermMonoid}{54.7.1}{X7D161674800B50E0} 4149\makelabel{ref:DegreeOfPartialPermSemigroup}{54.7.2}{X7D7F0BAB82F0D820} 4150\makelabel{ref:CodegreeOfPartialPermSemigroup}{54.7.2}{X7D7F0BAB82F0D820} 4151\makelabel{ref:RankOfPartialPermSemigroup}{54.7.2}{X7D7F0BAB82F0D820} 4152\makelabel{ref:SymmetricInverseSemigroup}{54.7.3}{X81D271B380995F8A} 4153\makelabel{ref:SymmetricInverseMonoid}{54.7.3}{X81D271B380995F8A} 4154\makelabel{ref:IsSymmetricInverseSemigroup}{54.7.4}{X7C8AEA50834060DD} 4155\makelabel{ref:IsSymmetricInverseMonoid}{54.7.4}{X7C8AEA50834060DD} 4156\makelabel{ref:NaturalPartialOrder}{54.7.5}{X7EA51F087CF7621F} 4157\makelabel{ref:ReverseNaturalPartialOrder}{54.7.5}{X7EA51F087CF7621F} 4158\makelabel{ref:IsomorphismPartialPermSemigroup}{54.7.6}{X7FE18EBE79B9C17C} 4159\makelabel{ref:IsomorphismPartialPermMonoid}{54.7.6}{X7FE18EBE79B9C17C} 4160\makelabel{ref:IsNearAdditiveMagma}{55.1.1}{X8129E95D83227658} 4161\makelabel{ref:IsNearAdditiveMagmaWithZero}{55.1.2}{X7DADE4577D0A7208} 4162\makelabel{ref:IsNearAdditiveGroup}{55.1.3}{X7FC3A9C178185942} 4163\makelabel{ref:IsNearAdditiveMagmaWithInverses}{55.1.3}{X7FC3A9C178185942} 4164\makelabel{ref:IsAdditiveMagma}{55.1.4}{X8565FD0C847BAA3A} 4165\makelabel{ref:IsAdditiveMagmaWithZero}{55.1.5}{X785B41A67D791783} 4166\makelabel{ref:IsAdditiveGroup}{55.1.6}{X7B8FBD9082CE271B} 4167\makelabel{ref:IsAdditiveMagmaWithInverses}{55.1.6}{X7B8FBD9082CE271B} 4168\makelabel{ref:NearAdditiveMagma}{55.2.1}{X79C947CF8060335A} 4169\makelabel{ref:NearAdditiveMagmaWithZero}{55.2.2}{X80F57FB47E1DB380} 4170\makelabel{ref:NearAdditiveGroup}{55.2.3}{X872307537ECC5755} 4171\makelabel{ref:NearAdditiveMagmaByGenerators}{55.2.4}{X85122CFD7BDAD668} 4172\makelabel{ref:NearAdditiveMagmaWithZeroByGenerators}{55.2.5}{X81880460851DEFBC} 4173\makelabel{ref:NearAdditiveGroupByGenerators}{55.2.6}{X85F120B68576B267} 4174\makelabel{ref:SubnearAdditiveMagma}{55.2.7}{X7AA6092683FC0F9C} 4175\makelabel{ref:SubadditiveMagma}{55.2.7}{X7AA6092683FC0F9C} 4176\makelabel{ref:SubnearAdditiveMagmaNC}{55.2.7}{X7AA6092683FC0F9C} 4177\makelabel{ref:SubadditiveMagmaNC}{55.2.7}{X7AA6092683FC0F9C} 4178\makelabel{ref:SubnearAdditiveMagmaWithZero}{55.2.8}{X784859197D89A548} 4179\makelabel{ref:SubadditiveMagmaWithZero}{55.2.8}{X784859197D89A548} 4180\makelabel{ref:SubnearAdditiveMagmaWithZeroNC}{55.2.8}{X784859197D89A548} 4181\makelabel{ref:SubadditiveMagmaWithZeroNC}{55.2.8}{X784859197D89A548} 4182\makelabel{ref:SubnearAdditiveGroup}{55.2.9}{X844C49BA807AB99F} 4183\makelabel{ref:SubadditiveGroup}{55.2.9}{X844C49BA807AB99F} 4184\makelabel{ref:SubnearAdditiveGroupNC}{55.2.9}{X844C49BA807AB99F} 4185\makelabel{ref:SubadditiveGroupNC}{55.2.9}{X844C49BA807AB99F} 4186\makelabel{ref:IsAdditivelyCommutative}{55.3.1}{X82D471327A9CA960} 4187\makelabel{ref:GeneratorsOfNearAdditiveMagma}{55.3.2}{X804B178884002A40} 4188\makelabel{ref:GeneratorsOfAdditiveMagma}{55.3.2}{X804B178884002A40} 4189\makelabel{ref:GeneratorsOfNearAdditiveMagmaWithZero}{55.3.3}{X7EB9ABF880DCAE01} 4190\makelabel{ref:GeneratorsOfAdditiveMagmaWithZero}{55.3.3}{X7EB9ABF880DCAE01} 4191\makelabel{ref:GeneratorsOfNearAdditiveGroup}{55.3.4}{X7EA15714795D71CF} 4192\makelabel{ref:GeneratorsOfAdditiveGroup}{55.3.4}{X7EA15714795D71CF} 4193\makelabel{ref:AdditiveNeutralElement}{55.3.5}{X851EA2E67F0C9A75} 4194\makelabel{ref:TrivialSubnearAdditiveMagmaWithZero}{55.3.6}{X78FB0A5C86DC86F9} 4195\makelabel{ref:ClosureNearAdditiveGroup for a near-additive group and an element}{55.4.1}{X845E915B87D2AC16} 4196\makelabel{ref:ClosureNearAdditiveGroup for two near-additive groups}{55.4.1}{X845E915B87D2AC16} 4197\makelabel{ref:ShowAdditionTable}{55.4.2}{X8142D994794B700A} 4198\makelabel{ref:ShowMultiplicationTable}{55.4.2}{X8142D994794B700A} 4199\makelabel{ref:IsRing}{56.1.1}{X80FD843C8221DAC9} 4200\makelabel{ref:Ring for ring elements}{56.1.2}{X820B172A860A5B1A} 4201\makelabel{ref:Ring for a collection}{56.1.2}{X820B172A860A5B1A} 4202\makelabel{ref:DefaultRing for ring elements}{56.1.3}{X83AFFCC77DE6ABDA} 4203\makelabel{ref:DefaultRing for a collection}{56.1.3}{X83AFFCC77DE6ABDA} 4204\makelabel{ref:RingByGenerators}{56.1.4}{X7D736E027DFD8961} 4205\makelabel{ref:DefaultRingByGenerators}{56.1.5}{X839E609480495E27} 4206\makelabel{ref:GeneratorsOfRing}{56.1.6}{X7D0428D87E63288C} 4207\makelabel{ref:Subring}{56.1.7}{X860E4AC78520D27E} 4208\makelabel{ref:SubringNC}{56.1.7}{X860E4AC78520D27E} 4209\makelabel{ref:ClosureRing for a ring and a ring element}{56.1.8}{X819B0AFE79C78C34} 4210\makelabel{ref:ClosureRing for two rings}{56.1.8}{X819B0AFE79C78C34} 4211\makelabel{ref:Quotient}{56.1.9}{X8350500B8576F833} 4212\makelabel{ref:TwoSidedIdeal}{56.2.1}{X7C486A7C821D79F0} 4213\makelabel{ref:Ideal}{56.2.1}{X7C486A7C821D79F0} 4214\makelabel{ref:LeftIdeal}{56.2.1}{X7C486A7C821D79F0} 4215\makelabel{ref:RightIdeal}{56.2.1}{X7C486A7C821D79F0} 4216\makelabel{ref:TwoSidedIdealNC}{56.2.2}{X7C8E196478C7431A} 4217\makelabel{ref:IdealNC}{56.2.2}{X7C8E196478C7431A} 4218\makelabel{ref:LeftIdealNC}{56.2.2}{X7C8E196478C7431A} 4219\makelabel{ref:RightIdealNC}{56.2.2}{X7C8E196478C7431A} 4220\makelabel{ref:IsTwoSidedIdeal}{56.2.3}{X7DF623847B338850} 4221\makelabel{ref:IsLeftIdeal}{56.2.3}{X7DF623847B338850} 4222\makelabel{ref:IsRightIdeal}{56.2.3}{X7DF623847B338850} 4223\makelabel{ref:IsTwoSidedIdealInParent}{56.2.3}{X7DF623847B338850} 4224\makelabel{ref:IsLeftIdealInParent}{56.2.3}{X7DF623847B338850} 4225\makelabel{ref:IsRightIdealInParent}{56.2.3}{X7DF623847B338850} 4226\makelabel{ref:TwoSidedIdealByGenerators}{56.2.4}{X86C998178690DAE0} 4227\makelabel{ref:IdealByGenerators}{56.2.4}{X86C998178690DAE0} 4228\makelabel{ref:LeftIdealByGenerators}{56.2.5}{X82D8B07281EB0AC7} 4229\makelabel{ref:RightIdealByGenerators}{56.2.6}{X858EAEAF87751428} 4230\makelabel{ref:GeneratorsOfTwoSidedIdeal}{56.2.7}{X86AAF5F9800E97EE} 4231\makelabel{ref:GeneratorsOfIdeal}{56.2.7}{X86AAF5F9800E97EE} 4232\makelabel{ref:GeneratorsOfLeftIdeal}{56.2.8}{X7B20BD2B7FAFBD64} 4233\makelabel{ref:GeneratorsOfRightIdeal}{56.2.9}{X80F2239F8653FF74} 4234\makelabel{ref:LeftActingRingOfIdeal}{56.2.10}{X81D81D027C2F8D06} 4235\makelabel{ref:RightActingRingOfIdeal}{56.2.10}{X81D81D027C2F8D06} 4236\makelabel{ref:AsLeftIdeal}{56.2.11}{X83D9D7408706B69A} 4237\makelabel{ref:AsRightIdeal}{56.2.11}{X83D9D7408706B69A} 4238\makelabel{ref:AsTwoSidedIdeal}{56.2.11}{X83D9D7408706B69A} 4239\makelabel{ref:IsRingWithOne}{56.3.1}{X7E601FBD8020A0F3} 4240\makelabel{ref:RingWithOne for ring elements}{56.3.2}{X80942A318417366E} 4241\makelabel{ref:RingWithOne for a collection}{56.3.2}{X80942A318417366E} 4242\makelabel{ref:RingWithOneByGenerators}{56.3.3}{X851115EC79B8C393} 4243\makelabel{ref:GeneratorsOfRingWithOne}{56.3.4}{X7F9F122C831BCDD1} 4244\makelabel{ref:SubringWithOne}{56.3.5}{X7D0BADF178D4DDF8} 4245\makelabel{ref:SubringWithOneNC}{56.3.5}{X7D0BADF178D4DDF8} 4246\makelabel{ref:IsIntegralRing}{56.4.1}{X87A7D5B584713B52} 4247\makelabel{ref:IsUniqueFactorizationRing}{56.4.2}{X789A917085DB7527} 4248\makelabel{ref:IsLDistributive}{56.4.3}{X7D4BB44187C55BF2} 4249\makelabel{ref:IsRDistributive}{56.4.4}{X79A5AEE786AED315} 4250\makelabel{ref:IsDistributive}{56.4.5}{X86716D4F7B968604} 4251\makelabel{ref:IsAnticommutative}{56.4.6}{X82DECD237D49D937} 4252\makelabel{ref:IsZeroSquaredRing}{56.4.7}{X7EC0FEC88535E8CC} 4253\makelabel{ref:IsJacobianRing}{56.4.8}{X799BEF8581971A13} 4254\makelabel{ref:IsUnit}{56.5.1}{X85CBFBAE78DE72E8} 4255\makelabel{ref:Units}{56.5.2}{X853C045B7BA6A580} 4256\makelabel{ref:IsAssociated}{56.5.3}{X7B307F217DDC7E20} 4257\makelabel{ref:Associates}{56.5.4}{X7A69C9097E17D161} 4258\makelabel{ref:StandardAssociate}{56.5.5}{X7B1A9A4C7C59FB36} 4259\makelabel{ref:StandardAssociateUnit}{56.5.6}{X7EB6803C789E027D} 4260\makelabel{ref:IsIrreducibleRingElement}{56.5.7}{X7CD7C64A7D961A18} 4261\makelabel{ref:IsPrime}{56.5.8}{X7AA107AE7F79C6D8} 4262\makelabel{ref:Factors}{56.5.9}{X82D6EDC685D12AE2} 4263\makelabel{ref:PadicValuation}{56.5.10}{X8559CC7B80C479F1} 4264\makelabel{ref:IsEuclideanRing}{56.6.1}{X808B8E8E80D48E4A} 4265\makelabel{ref:EuclideanDegree}{56.6.2}{X784234088350D4E4} 4266\makelabel{ref:EuclideanQuotient}{56.6.3}{X7A93FA788318B147} 4267\makelabel{ref:EuclideanRemainder}{56.6.4}{X7B5E9639865E91BA} 4268\makelabel{ref:QuotientRemainder}{56.6.5}{X876B7532801A1B35} 4269\makelabel{ref:Gcd for (a ring and) several elements}{56.7.1}{X7DE207718456F98F} 4270\makelabel{ref:Gcd for (a ring and) a list of elements}{56.7.1}{X7DE207718456F98F} 4271\makelabel{ref:GcdOp}{56.7.2}{X7836D50F8341D6E1} 4272\makelabel{ref:GcdRepresentation for (a ring and) several elements}{56.7.3}{X7ABB91EF838075EF} 4273\makelabel{ref:GcdRepresentation for (a ring and) a list of elements}{56.7.3}{X7ABB91EF838075EF} 4274\makelabel{ref:GcdRepresentationOp}{56.7.4}{X81392E7F84956341} 4275\makelabel{ref:ShowGcd}{56.7.5}{X836DB8B47A0219FB} 4276\makelabel{ref:Lcm for (a ring and) several elements}{56.7.6}{X7ABA92057DD6C7AF} 4277\makelabel{ref:Lcm for (a ring and) a list of elements}{56.7.6}{X7ABA92057DD6C7AF} 4278\makelabel{ref:LcmOp}{56.7.7}{X7FB6C5A67AC1E8C1} 4279\makelabel{ref:QuotientMod}{56.7.8}{X8555913A83D716A4} 4280\makelabel{ref:PowerMod}{56.7.9}{X805A35D684B7A952} 4281\makelabel{ref:InterpolatedPolynomial}{56.7.10}{X87711E6F8024A358} 4282\makelabel{ref:RingGeneralMappingByImages}{56.8.1}{X7DE9CC5B877C91DA} 4283\makelabel{ref:RingHomomorphismByImages}{56.8.2}{X78C1016284F08026} 4284\makelabel{ref:RingHomomorphismByImagesNC}{56.8.3}{X7D01646A7CCBEDBB} 4285\makelabel{ref:NaturalHomomorphismByIdeal}{56.8.4}{X83D53D98809EC461} 4286\makelabel{ref:SmallRing}{56.9.1}{X7E86DCB7812DF04C} 4287\makelabel{ref:NumberSmallRings}{56.9.2}{X7F2EE9AF83DCE641} 4288\makelabel{ref:Subrings}{56.9.3}{X8070D20B86148929} 4289\makelabel{ref:Ideals}{56.9.4}{X83629803819C4A6F} 4290\makelabel{ref:DirectSum}{56.9.5}{X82AD6F187B550060} 4291\makelabel{ref:DirectSumOp}{56.9.5}{X82AD6F187B550060} 4292\makelabel{ref:RingByStructureConstants}{56.9.6}{X7E7B1B727EA434CF} 4293\makelabel{ref:IsLeftOperatorAdditiveGroup}{57.1.1}{X7C62FE5282E9C505} 4294\makelabel{ref:IsLeftModule}{57.1.2}{X7ED323027B291BDF} 4295\makelabel{ref:GeneratorsOfLeftOperatorAdditiveGroup}{57.1.3}{X7F76B1FD84775025} 4296\makelabel{ref:GeneratorsOfLeftModule}{57.1.4}{X7C7684EF867323C2} 4297\makelabel{ref:AsLeftModule}{57.1.5}{X7EB3E46D7BC4A35C} 4298\makelabel{ref:IsRightOperatorAdditiveGroup}{57.1.6}{X7F19AD3D799D0469} 4299\makelabel{ref:IsRightModule}{57.1.7}{X8479A5AA7DF25F50} 4300\makelabel{ref:GeneratorsOfRightOperatorAdditiveGroup}{57.1.8}{X7DBC4BCB876EEE1C} 4301\makelabel{ref:GeneratorsOfRightModule}{57.1.9}{X8586A83B85F176F6} 4302\makelabel{ref:LeftModuleByGenerators}{57.1.10}{X79ED1D7D7F0AE59A} 4303\makelabel{ref:LeftActingDomain}{57.1.11}{X86F070E0807DC34E} 4304\makelabel{ref:Submodule}{57.2.1}{X8465103F874BC07B} 4305\makelabel{ref:SubmoduleNC}{57.2.2}{X83CF3AD18050C982} 4306\makelabel{ref:ClosureLeftModule}{57.2.3}{X7C68C4E287481EC0} 4307\makelabel{ref:TrivialSubmodule}{57.2.4}{X7980BC20856B2B7D} 4308\makelabel{ref:IsFreeLeftModule}{57.3.1}{X7C4832187F3D9228} 4309\makelabel{ref:FreeLeftModule}{57.3.2}{X7C043E307E344AEE} 4310\makelabel{ref:Dimension}{57.3.3}{X7E6926C6850E7C4E} 4311\makelabel{ref:IsFiniteDimensional}{57.3.4}{X802DB9FB824B0167} 4312\makelabel{ref:UseBasis}{57.3.5}{X7909E8E785420F0E} 4313\makelabel{ref:IsRowModule}{57.3.6}{X7C8F844783F4FA09} 4314\makelabel{ref:IsMatrixModule}{57.3.7}{X81FCC1D780435CF1} 4315\makelabel{ref:IsFullRowModule}{57.3.8}{X853E085C868196EF} 4316\makelabel{ref:FullRowModule}{57.3.9}{X848041A47BC4B038} 4317\makelabel{ref:IsFullMatrixModule}{57.3.10}{X814CEA62842CF5BB} 4318\makelabel{ref:FullMatrixModule}{57.3.11}{X7A0C871B7C446F1F} 4319\makelabel{ref:fields}{58}{X80A8E676814A19FD} 4320\makelabel{ref:division rings}{58}{X80A8E676814A19FD} 4321\makelabel{ref:IsDivisionRing}{58.1.1}{X7F2CAA9E7A16913D} 4322\makelabel{ref:IsField}{58.1.2}{X7A5AE30E7C0F457C} 4323\makelabel{ref:Field for several generators}{58.1.3}{X871AA7D58263E9AC} 4324\makelabel{ref:Field for (a field and) a list of generators}{58.1.3}{X871AA7D58263E9AC} 4325\makelabel{ref:DefaultField for several generators}{58.1.4}{X7D9F7FD4786691EE} 4326\makelabel{ref:DefaultField for a list of generators}{58.1.4}{X7D9F7FD4786691EE} 4327\makelabel{ref:DefaultFieldByGenerators}{58.1.5}{X7C298A40852C2AFF} 4328\makelabel{ref:GeneratorsOfDivisionRing}{58.1.6}{X7EF624958648D0FA} 4329\makelabel{ref:GeneratorsOfField}{58.1.7}{X7AA715317A81261B} 4330\makelabel{ref:DivisionRingByGenerators}{58.1.8}{X8641861A8550F8BE} 4331\makelabel{ref:FieldByGenerators}{58.1.8}{X8641861A8550F8BE} 4332\makelabel{ref:AsDivisionRing}{58.1.9}{X7C193B7D7AFB29BE} 4333\makelabel{ref:AsField}{58.1.9}{X7C193B7D7AFB29BE} 4334\makelabel{ref:Subfield}{58.2.1}{X7FE1FA217A08DCE5} 4335\makelabel{ref:SubfieldNC}{58.2.1}{X7FE1FA217A08DCE5} 4336\makelabel{ref:FieldOverItselfByGenerators}{58.2.2}{X82A0E79A7B9799E0} 4337\makelabel{ref:PrimitiveElement}{58.2.3}{X86DB31B57FB4F570} 4338\makelabel{ref:PrimeField}{58.2.4}{X7DD27F927BD57FDE} 4339\makelabel{ref:IsPrimeField}{58.2.5}{X84B6F1E67AD0E33D} 4340\makelabel{ref:DegreeOverPrimeField}{58.2.6}{X7845CECE86A83219} 4341\makelabel{ref:DefiningPolynomial}{58.2.7}{X7ADDCBF47E2ED3D4} 4342\makelabel{ref:RootOfDefiningPolynomial}{58.2.8}{X8173DA4982DB1E8A} 4343\makelabel{ref:FieldExtension}{58.2.9}{X82718B3B818DC699} 4344\makelabel{ref:Subfields}{58.2.10}{X83490C65819D85FE} 4345\makelabel{ref:IsFieldControlledByGaloisGroup}{58.3}{X7D9A02B07D08FA40} 4346\makelabel{ref:GaloisGroup of field}{58.3.1}{X80CAA5BA82F09ED2} 4347\makelabel{ref:MinimalPolynomial over a field}{58.3.2}{X8738C6687D784BB5} 4348\makelabel{ref:TracePolynomial}{58.3.3}{X80FE7E017C2D255C} 4349\makelabel{ref:characteristic polynomial for field elements}{58.3.3}{X80FE7E017C2D255C} 4350\makelabel{ref:Norm}{58.3.4}{X838515278587FF01} 4351\makelabel{ref:Trace for a field element}{58.3.5}{X7DD17EB581200AD6} 4352\makelabel{ref:Trace for a matrix}{58.3.5}{X7DD17EB581200AD6} 4353\makelabel{ref:Conjugates}{58.3.6}{X837A4A5781F8EE92} 4354\makelabel{ref:NormalBase}{58.3.7}{X8236A8B47E6AAD93} 4355\makelabel{ref:IsFFE}{59.1.1}{X7D3DF32C84FEBD25} 4356\makelabel{ref:IsFFECollection}{59.1.1}{X7D3DF32C84FEBD25} 4357\makelabel{ref:IsFFECollColl}{59.1.1}{X7D3DF32C84FEBD25} 4358\makelabel{ref:IsFFECollCollColl}{59.1.1}{X7D3DF32C84FEBD25} 4359\makelabel{ref:Z for field size}{59.1.2}{X7AA52FAF7EDEDD56} 4360\makelabel{ref:Z for prime and degree}{59.1.2}{X7AA52FAF7EDEDD56} 4361\makelabel{ref:IsLexOrderedFFE}{59.1.3}{X8612BCEA816CF1B9} 4362\makelabel{ref:IsLogOrderedFFE}{59.1.3}{X8612BCEA816CF1B9} 4363\makelabel{ref:DegreeFFE for a ffe}{59.2.1}{X828E846E7C1EA3DD} 4364\makelabel{ref:DegreeFFE for a vector of ffes}{59.2.1}{X828E846E7C1EA3DD} 4365\makelabel{ref:DegreeFFE for a matrix of ffes}{59.2.1}{X828E846E7C1EA3DD} 4366\makelabel{ref:LogFFE}{59.2.2}{X7B049A3478B369E4} 4367\makelabel{ref:IntFFE}{59.2.3}{X79F48E337FC2746A} 4368\makelabel{ref:Int for a ffe}{59.2.3}{X79F48E337FC2746A} 4369\makelabel{ref:IntFFESymm for a ffe}{59.2.4}{X7DABD827848BCC2A} 4370\makelabel{ref:IntFFESymm for a vector of ffes}{59.2.4}{X7DABD827848BCC2A} 4371\makelabel{ref:IntVecFFE}{59.2.5}{X8009968782F18888} 4372\makelabel{ref:AsInternalFFE}{59.2.6}{X807959EE82CED148} 4373\makelabel{ref:DefaultField for finite field elements}{59.3.1}{X7979F51D7C43AB05} 4374\makelabel{ref:DefaultRing for finite field elements}{59.3.1}{X7979F51D7C43AB05} 4375\makelabel{ref:GaloisField for field size}{59.3.2}{X8592DBB086A8A9BE} 4376\makelabel{ref:GF for field size}{59.3.2}{X8592DBB086A8A9BE} 4377\makelabel{ref:GaloisField for characteristic and degree}{59.3.2}{X8592DBB086A8A9BE} 4378\makelabel{ref:GF for characteristic and degree}{59.3.2}{X8592DBB086A8A9BE} 4379\makelabel{ref:GaloisField for subfield and degree}{59.3.2}{X8592DBB086A8A9BE} 4380\makelabel{ref:GF for subfield and degree}{59.3.2}{X8592DBB086A8A9BE} 4381\makelabel{ref:GaloisField for characteristic and polynomial}{59.3.2}{X8592DBB086A8A9BE} 4382\makelabel{ref:GF for characteristic and polynomial}{59.3.2}{X8592DBB086A8A9BE} 4383\makelabel{ref:GaloisField for subfield and polynomial}{59.3.2}{X8592DBB086A8A9BE} 4384\makelabel{ref:GF for subfield and polynomial}{59.3.2}{X8592DBB086A8A9BE} 4385\makelabel{ref:PrimitiveRoot}{59.3.3}{X788B1ECD83C70516} 4386\makelabel{ref:FrobeniusAutomorphism}{59.4.1}{X8758E4AB7D0A1955} 4387\makelabel{ref:homomorphisms Frobenius, field}{59.4.1}{X8758E4AB7D0A1955} 4388\makelabel{ref:field homomorphisms Frobenius}{59.4.1}{X8758E4AB7D0A1955} 4389\makelabel{ref:CompositionMapping for Frobenius automorphisms}{59.4.1}{X8758E4AB7D0A1955} 4390\makelabel{ref:Frobenius automorphism}{59.4.1}{X8758E4AB7D0A1955} 4391\makelabel{ref:Image for Frobenius automorphisms}{59.4.1}{X8758E4AB7D0A1955} 4392\makelabel{ref:ConwayPolynomial}{59.5.1}{X7C2425A786F09054} 4393\makelabel{ref:InfoText (for Conway polynomials)}{59.5.1}{X7C2425A786F09054} 4394\makelabel{ref:IsCheapConwayPolynomial}{59.5.2}{X78A7C1247E129AD9} 4395\makelabel{ref:RandomPrimitivePolynomial}{59.5.3}{X7ECC593583E68A6C} 4396\makelabel{ref:ViewObj for a ffe}{59.6.1}{X80DAAA5E7C79C94C} 4397\makelabel{ref:PrintObj for a ffe}{59.6.1}{X80DAAA5E7C79C94C} 4398\makelabel{ref:Display for a ffe}{59.6.1}{X80DAAA5E7C79C94C} 4399\makelabel{ref:CyclotomicField for (subfield and) conductor}{60.1.1}{X80D21D80850EFA4B} 4400\makelabel{ref:CyclotomicField for (subfield and) generators}{60.1.1}{X80D21D80850EFA4B} 4401\makelabel{ref:CF for (subfield and) conductor}{60.1.1}{X80D21D80850EFA4B} 4402\makelabel{ref:CF for (subfield and) generators}{60.1.1}{X80D21D80850EFA4B} 4403\makelabel{ref:AbelianNumberField}{60.1.2}{X80E5AD028143E11E} 4404\makelabel{ref:NF}{60.1.2}{X80E5AD028143E11E} 4405\makelabel{ref:GaussianRationals}{60.1.3}{X82F53C65802FF551} 4406\makelabel{ref:IsGaussianRationals}{60.1.3}{X82F53C65802FF551} 4407\makelabel{ref:Factors for polynomials over abelian number fields}{60.2.1}{X7B0AB0FB7A4136C4} 4408\makelabel{ref:IsNumberField}{60.2.2}{X87D78F5E875F2E8A} 4409\makelabel{ref:number field}{60.2.2}{X87D78F5E875F2E8A} 4410\makelabel{ref:IsAbelianNumberField}{60.2.3}{X7D202D707D5708FA} 4411\makelabel{ref:abelian number field}{60.2.3}{X7D202D707D5708FA} 4412\makelabel{ref:IsCyclotomicField}{60.2.4}{X84CAE4627F0CD639} 4413\makelabel{ref:GaloisStabilizer}{60.2.5}{X87E7313D8070B9CC} 4414\makelabel{ref:cyclotomic fields CanonicalBasis}{60.3}{X7D2421AC8491D2BE} 4415\makelabel{ref:abelian number fields CanonicalBasis}{60.3}{X7D2421AC8491D2BE} 4416\makelabel{ref:ZumbroichBase}{60.3.1}{X7F52BEA0862E06F2} 4417\makelabel{ref:LenstraBase}{60.3.2}{X87DB9C2C858B722A} 4418\makelabel{ref:abelian number fields Galois group}{60.4}{X7E4AB4B17C7BA10C} 4419\makelabel{ref:number fields Galois group}{60.4}{X7E4AB4B17C7BA10C} 4420\makelabel{ref:automorphism group of number fields}{60.4}{X7E4AB4B17C7BA10C} 4421\makelabel{ref:GaloisGroup for abelian number fields}{60.4.1}{X7B55A90582E818F3} 4422\makelabel{ref:ANFAutomorphism}{60.4.2}{X8643D4B47A827D9D} 4423\makelabel{ref:GaussianIntegers}{60.5.1}{X80BD5EAB879F096E} 4424\makelabel{ref:IsGaussianIntegers}{60.5.2}{X7BFD33D27BFB7C5A} 4425\makelabel{ref:IsLeftVectorSpace}{61.1.1}{X80290A908241706B} 4426\makelabel{ref:IsVectorSpace}{61.1.1}{X80290A908241706B} 4427\makelabel{ref:VectorSpace}{61.2.1}{X805413157CE9BECF} 4428\makelabel{ref:Subspace}{61.2.2}{X78C9826780BC9AE6} 4429\makelabel{ref:SubspaceNC}{61.2.2}{X78C9826780BC9AE6} 4430\makelabel{ref:AsVectorSpace}{61.2.3}{X7B001BAF7D5FD5D0} 4431\makelabel{ref:AsSubspace}{61.2.4}{X7D4F84C27EDAC89B} 4432\makelabel{ref:GeneratorsOfLeftVectorSpace}{61.3.1}{X849651C6830C94A1} 4433\makelabel{ref:GeneratorsOfVectorSpace}{61.3.1}{X849651C6830C94A1} 4434\makelabel{ref:TrivialSubspace}{61.3.2}{X86DC71A9835430FD} 4435\makelabel{ref:Subspaces}{61.4.1}{X7975E41A7B29C3FD} 4436\makelabel{ref:IsSubspacesVectorSpace}{61.4.2}{X7A8F5C367FAE3D1B} 4437\makelabel{ref:IsBasis}{61.5.1}{X8739510881F5D862} 4438\makelabel{ref:Basis}{61.5.2}{X837BE54C80DE368E} 4439\makelabel{ref:BasisNC}{61.5.2}{X837BE54C80DE368E} 4440\makelabel{ref:CanonicalBasis}{61.5.3}{X7C8EBFF5805F8C51} 4441\makelabel{ref:RelativeBasis}{61.5.4}{X8786D40B84120F38} 4442\makelabel{ref:RelativeBasisNC}{61.5.4}{X8786D40B84120F38} 4443\makelabel{ref:BasisVectors}{61.6.1}{X7B1F17AE8027A590} 4444\makelabel{ref:UnderlyingLeftModule}{61.6.2}{X81E8AE88843B70FF} 4445\makelabel{ref:Coefficients}{61.6.3}{X80B32F667BF6AFD8} 4446\makelabel{ref:LinearCombination}{61.6.4}{X7D305AB3834889BF} 4447\makelabel{ref:EnumeratorByBasis}{61.6.5}{X7EB0D16A7EC2DEE3} 4448\makelabel{ref:IteratorByBasis}{61.6.6}{X855625D47979005D} 4449\makelabel{ref:IsCanonicalBasis}{61.7.1}{X7CC2B3DD81628CE9} 4450\makelabel{ref:IsIntegralBasis}{61.7.2}{X86DE147F8606B739} 4451\makelabel{ref:IsNormalBasis}{61.7.3}{X7FC051C579D61223} 4452\makelabel{ref:IsMutableBasis}{61.8.1}{X7F466FB47F7E9F00} 4453\makelabel{ref:MutableBasis}{61.8.2}{X8115C061819E5172} 4454\makelabel{ref:NrBasisVectors}{61.8.3}{X7EC90F4F7BCAF8D4} 4455\makelabel{ref:ImmutableBasis}{61.8.4}{X7BA87512823A8CFD} 4456\makelabel{ref:IsContainedInSpan}{61.8.5}{X85B50AC77A22108B} 4457\makelabel{ref:CloseMutableBasis}{61.8.6}{X7B52C99B84316F61} 4458\makelabel{ref:row spaces}{61.9}{X7D937EBC7DE2819B} 4459\makelabel{ref:matrix spaces}{61.9}{X7D937EBC7DE2819B} 4460\makelabel{ref:IsRowSpace}{61.9.1}{X79B305CE87511C4B} 4461\makelabel{ref:IsMatrixSpace}{61.9.2}{X7A2BBBA07B2BE8F8} 4462\makelabel{ref:IsGaussianSpace}{61.9.3}{X83724C157F4FDFB4} 4463\makelabel{ref:FullRowSpace}{61.9.4}{X80209A8785126AAB} 4464\makelabel{ref:FullMatrixSpace}{61.9.5}{X876B66C37A7B749F} 4465\makelabel{ref:DimensionOfVectors}{61.9.6}{X8534A750878478D0} 4466\makelabel{ref:IsSemiEchelonized}{61.9.7}{X865A540F85FAE2DF} 4467\makelabel{ref:SemiEchelonBasis}{61.9.8}{X87DCA09579589106} 4468\makelabel{ref:SemiEchelonBasisNC}{61.9.8}{X87DCA09579589106} 4469\makelabel{ref:IsCanonicalBasisFullRowModule}{61.9.9}{X7C3CC5F97FA048A4} 4470\makelabel{ref:canonical basis for row spaces}{61.9.9}{X7C3CC5F97FA048A4} 4471\makelabel{ref:IsCanonicalBasisFullMatrixModule}{61.9.10}{X83D282697C1A3148} 4472\makelabel{ref:canonical basis for matrix spaces}{61.9.10}{X83D282697C1A3148} 4473\makelabel{ref:NormedRowVectors}{61.9.11}{X7D6537F87E940344} 4474\makelabel{ref:SiftedVector}{61.9.12}{X815C69A57C042C34} 4475\makelabel{ref:LeftModuleGeneralMappingByImages}{61.10.1}{X82013D328645E370} 4476\makelabel{ref:LeftModuleHomomorphismByImages}{61.10.2}{X85F5293983E47B5A} 4477\makelabel{ref:LeftModuleHomomorphismByImagesNC}{61.10.2}{X85F5293983E47B5A} 4478\makelabel{ref:LeftModuleHomomorphismByMatrix}{61.10.3}{X8477E6C3872A6DBB} 4479\makelabel{ref:NaturalHomomorphismBySubspace}{61.10.4}{X8494AA5D7C3B88AD} 4480\makelabel{ref:Hom}{61.10.5}{X80015C78876B4F1E} 4481\makelabel{ref:End}{61.10.6}{X8680ADD381ECF879} 4482\makelabel{ref:IsFullHomModule}{61.10.7}{X7A9A08EA79259659} 4483\makelabel{ref:IsPseudoCanonicalBasisFullHomModule}{61.10.8}{X7C4737687E76A24A} 4484\makelabel{ref:IsLinearMappingsModule}{61.10.9}{X84F87C327A1856F2} 4485\makelabel{ref:NiceFreeLeftModule}{61.11.1}{X826FD4BC7BA0559D} 4486\makelabel{ref:NiceVector}{61.11.2}{X807B8032780C59A4} 4487\makelabel{ref:UglyVector}{61.11.2}{X807B8032780C59A4} 4488\makelabel{ref:NiceFreeLeftModuleInfo}{61.11.3}{X79350786800C2DD8} 4489\makelabel{ref:NiceBasis}{61.11.4}{X8388E0248690C214} 4490\makelabel{ref:IsBasisByNiceBasis}{61.11.5}{X82BC30A487967F5B} 4491\makelabel{ref:IsHandledByNiceBasis}{61.11.6}{X79D1DEA679AEDA40} 4492\makelabel{ref:DeclareHandlingByNiceBasis}{61.12.1}{X7DE34C3E837FCBC3} 4493\makelabel{ref:InstallHandlingByNiceBasis}{61.12.1}{X7DE34C3E837FCBC3} 4494\makelabel{ref:NiceBasisFiltersInfo}{61.12.2}{X7E6077F0830A28DA} 4495\makelabel{ref:CheckForHandlingByNiceBasis}{61.12.3}{X7A374553786DF5E7} 4496\makelabel{ref:InfoAlgebra}{62.1.1}{X8665F459841AAD53} 4497\makelabel{ref:Algebra}{62.2.1}{X7B213851791A594B} 4498\makelabel{ref:AlgebraWithOne}{62.2.2}{X80FE16EA84EE56CD} 4499\makelabel{ref:FreeAlgebra for ring, rank (and name)}{62.3.1}{X83484C917D8F7A1A} 4500\makelabel{ref:FreeAlgebra for ring and several names}{62.3.1}{X83484C917D8F7A1A} 4501\makelabel{ref:FreeAlgebraWithOne for ring, rank (and name)}{62.3.2}{X7FBD04B07B85623D} 4502\makelabel{ref:FreeAlgebraWithOne for ring and several names}{62.3.2}{X7FBD04B07B85623D} 4503\makelabel{ref:FreeAssociativeAlgebra for ring, rank (and name)}{62.3.3}{X87835FFE79D2E068} 4504\makelabel{ref:FreeAssociativeAlgebra for ring and several names}{62.3.3}{X87835FFE79D2E068} 4505\makelabel{ref:FreeAssociativeAlgebraWithOne for ring, rank (and name)}{62.3.4}{X845A777584A7D711} 4506\makelabel{ref:FreeAssociativeAlgebraWithOne for ring and several names}{62.3.4}{X845A777584A7D711} 4507\makelabel{ref:AlgebraByStructureConstants}{62.4.1}{X7CC58DFD816E6B65} 4508\makelabel{ref:StructureConstantsTable}{62.4.2}{X804ADF0280F67CDC} 4509\makelabel{ref:EmptySCTable}{62.4.3}{X7F1203A1793411DF} 4510\makelabel{ref:SetEntrySCTable}{62.4.4}{X817BD086876EC1C4} 4511\makelabel{ref:GapInputSCTable}{62.4.5}{X7F333822780B6731} 4512\makelabel{ref:TestJacobi}{62.4.6}{X7C23ED85814C0371} 4513\makelabel{ref:IdentityFromSCTable}{62.4.7}{X78B633CE7A5B9F9A} 4514\makelabel{ref:QuotientFromSCTable}{62.4.8}{X7F2A71608602635D} 4515\makelabel{ref:QuaternionAlgebra}{62.5.1}{X83DF4BCC7CE494FC} 4516\makelabel{ref:ComplexificationQuat for a vector}{62.5.2}{X7B807702782F56FF} 4517\makelabel{ref:ComplexificationQuat for a matrix}{62.5.2}{X7B807702782F56FF} 4518\makelabel{ref:OctaveAlgebra}{62.5.3}{X78C88A38853A8443} 4519\makelabel{ref:FullMatrixAlgebra}{62.5.4}{X7D88E42B7DE087B0} 4520\makelabel{ref:MatrixAlgebra}{62.5.4}{X7D88E42B7DE087B0} 4521\makelabel{ref:MatAlgebra}{62.5.4}{X7D88E42B7DE087B0} 4522\makelabel{ref:NullAlgebra}{62.5.5}{X78B8BA77869DAA13} 4523\makelabel{ref:Subalgebra}{62.6.1}{X8396643D7A49EEAD} 4524\makelabel{ref:SubalgebraNC}{62.6.2}{X7C6B08657BD836C3} 4525\makelabel{ref:SubalgebraWithOne}{62.6.3}{X83ECF489846F00B0} 4526\makelabel{ref:SubalgebraWithOneNC}{62.6.4}{X7A11B177868E76AA} 4527\makelabel{ref:TrivialSubalgebra}{62.6.5}{X7FDD953A84CFC3D2} 4528\makelabel{ref:IsFLMLOR}{62.8.1}{X7FEDFAA383AB20D2} 4529\makelabel{ref:IsFLMLORWithOne}{62.8.2}{X85C1E13A877DF2C8} 4530\makelabel{ref:IsAlgebra}{62.8.3}{X801ED693808F6C84} 4531\makelabel{ref:IsAlgebraWithOne}{62.8.4}{X80B21AC27DE6D068} 4532\makelabel{ref:IsLieAlgebra}{62.8.5}{X839BAC687B4E1A1D} 4533\makelabel{ref:IsSimpleAlgebra}{62.8.6}{X877DF13387831A6A} 4534\makelabel{ref:IsFiniteDimensional for matrix algebras}{62.8.7}{X7C5AECE87D79D075} 4535\makelabel{ref:IsQuaternion}{62.8.8}{X82B3A9077D0CB453} 4536\makelabel{ref:IsQuaternionCollection}{62.8.8}{X82B3A9077D0CB453} 4537\makelabel{ref:IsQuaternionCollColl}{62.8.8}{X82B3A9077D0CB453} 4538\makelabel{ref:GeneratorsOfAlgebra}{62.9.1}{X83B055F37EBF2438} 4539\makelabel{ref:GeneratorsOfAlgebraWithOne}{62.9.2}{X7FA408307A5A420E} 4540\makelabel{ref:ProductSpace}{62.9.3}{X7D309FD37D94B196} 4541\makelabel{ref:PowerSubalgebraSeries}{62.9.4}{X875CD2B37EE9A8A2} 4542\makelabel{ref:AdjointBasis}{62.9.5}{X788F4E6184E5C863} 4543\makelabel{ref:IndicesOfAdjointBasis}{62.9.6}{X800A410B8536E6DD} 4544\makelabel{ref:AsAlgebra}{62.9.7}{X7BA35CB28062D407} 4545\makelabel{ref:AsAlgebraWithOne}{62.9.8}{X878323367D0B68EB} 4546\makelabel{ref:AsSubalgebra}{62.9.9}{X7A922D26805AFF99} 4547\makelabel{ref:AsSubalgebraWithOne}{62.9.10}{X7B964BC37A975E48} 4548\makelabel{ref:MutableBasisOfClosureUnderAction}{62.9.11}{X7C280DAC7F840B60} 4549\makelabel{ref:MutableBasisOfNonassociativeAlgebra}{62.9.12}{X7BA1739D7F8B3A2B} 4550\makelabel{ref:MutableBasisOfIdealInNonassociativeAlgebra}{62.9.13}{X8467B687823371F9} 4551\makelabel{ref:DirectSumOfAlgebras for two algebras}{62.9.14}{X7C591B7C7DEA7EEB} 4552\makelabel{ref:DirectSumOfAlgebras for a list of algebras}{62.9.14}{X7C591B7C7DEA7EEB} 4553\makelabel{ref:FullMatrixAlgebraCentralizer}{62.9.15}{X7D0EB1437D3D9495} 4554\makelabel{ref:RadicalOfAlgebra}{62.9.16}{X850C29907A509533} 4555\makelabel{ref:CentralIdempotentsOfAlgebra}{62.9.17}{X82571785846CF05C} 4556\makelabel{ref:DirectSumDecomposition for lie algebras}{62.9.18}{X7CFB230582C26DAA} 4557\makelabel{ref:LeviMalcevDecomposition for lie algebras}{62.9.19}{X85C58364833E014C} 4558\makelabel{ref:Grading}{62.9.20}{X7DCA2568870A2D34} 4559\makelabel{ref:AlgebraGeneralMappingByImages}{62.10.1}{X83CE798C7D39E368} 4560\makelabel{ref:AlgebraHomomorphismByImages}{62.10.2}{X7A7F97ED8608C882} 4561\makelabel{ref:AlgebraHomomorphismByImagesNC}{62.10.3}{X8326D1BD79725462} 4562\makelabel{ref:AlgebraWithOneGeneralMappingByImages}{62.10.4}{X8057E55B864567AD} 4563\makelabel{ref:AlgebraWithOneHomomorphismByImages}{62.10.5}{X866F32B5846E5857} 4564\makelabel{ref:AlgebraWithOneHomomorphismByImagesNC}{62.10.6}{X80BF4D6A7FDC959A} 4565\makelabel{ref:NaturalHomomorphismByIdeal for an algebra and an ideal}{62.10.7}{X8712E5C1861CC32C} 4566\makelabel{ref:OperationAlgebraHomomorphism action w.r.t. a basis of the module}{62.10.8}{X8705A9C68102FEA3} 4567\makelabel{ref:OperationAlgebraHomomorphism action on a free left module}{62.10.8}{X8705A9C68102FEA3} 4568\makelabel{ref:NiceAlgebraMonomorphism}{62.10.9}{X7B249E8E86D895F0} 4569\makelabel{ref:IsomorphismFpAlgebra}{62.10.10}{X79D770777D873F80} 4570\makelabel{ref:IsomorphismMatrixAlgebra}{62.10.11}{X7FB760F9813B0789} 4571\makelabel{ref:IsomorphismSCAlgebra w.r.t. a given basis}{62.10.12}{X7F8D3DF2863EC50D} 4572\makelabel{ref:IsomorphismSCAlgebra for an algebra}{62.10.12}{X7F8D3DF2863EC50D} 4573\makelabel{ref:RepresentativeLinearOperation}{62.10.13}{X7F34244B81979696} 4574\makelabel{ref:LeftAlgebraModuleByGenerators}{62.11.1}{X8055B87F7ADBD66B} 4575\makelabel{ref:RightAlgebraModuleByGenerators}{62.11.2}{X8026B99B7955A355} 4576\makelabel{ref:BiAlgebraModuleByGenerators}{62.11.3}{X7F28A47E876427E0} 4577\makelabel{ref:LeftAlgebraModule}{62.11.4}{X852524F581613359} 4578\makelabel{ref:RightAlgebraModule}{62.11.5}{X8222F2B67D753036} 4579\makelabel{ref:BiAlgebraModule}{62.11.6}{X84517770868DDA02} 4580\makelabel{ref:GeneratorsOfAlgebraModule}{62.11.7}{X79AAB50D83A14A43} 4581\makelabel{ref:IsAlgebraModuleElement}{62.11.8}{X82B708BD84F3DAB1} 4582\makelabel{ref:IsAlgebraModuleElementCollection}{62.11.8}{X82B708BD84F3DAB1} 4583\makelabel{ref:IsAlgebraModuleElementFamily}{62.11.8}{X82B708BD84F3DAB1} 4584\makelabel{ref:IsLeftAlgebraModuleElement}{62.11.9}{X80E786467F9163F9} 4585\makelabel{ref:IsLeftAlgebraModuleElementCollection}{62.11.9}{X80E786467F9163F9} 4586\makelabel{ref:IsRightAlgebraModuleElement}{62.11.10}{X863756787E2B6E75} 4587\makelabel{ref:IsRightAlgebraModuleElementCollection}{62.11.10}{X863756787E2B6E75} 4588\makelabel{ref:LeftActingAlgebra}{62.11.11}{X85654EF07F708AC3} 4589\makelabel{ref:RightActingAlgebra}{62.11.12}{X826298B37E1B1520} 4590\makelabel{ref:ActingAlgebra}{62.11.13}{X8308408D86CFC3C9} 4591\makelabel{ref:IsBasisOfAlgebraModuleElementSpace}{62.11.14}{X7C325A507EC9BA18} 4592\makelabel{ref:MatrixOfAction}{62.11.15}{X789863037B0E35D2} 4593\makelabel{ref:SubAlgebraModule}{62.11.16}{X8742A7D27F26AFAB} 4594\makelabel{ref:LeftModuleByHomomorphismToMatAlg}{62.11.17}{X86E0515987192F0E} 4595\makelabel{ref:RightModuleByHomomorphismToMatAlg}{62.11.18}{X7EE41297867E41A8} 4596\makelabel{ref:AdjointModule}{62.11.19}{X8729F0A678A4A09C} 4597\makelabel{ref:FaithfulModule for lie algebras}{62.11.20}{X84813BCD80BDF3C4} 4598\makelabel{ref:ModuleByRestriction}{62.11.21}{X7E16630185CE2C10} 4599\makelabel{ref:NaturalHomomorphismBySubAlgebraModule}{62.11.22}{X7885AAC87FDCF649} 4600\makelabel{ref:DirectSumOfAlgebraModules for a list of lie algebra modules}{62.11.23}{X85D0F3758551DADC} 4601\makelabel{ref:DirectSumOfAlgebraModules for two lie algebra modules}{62.11.23}{X85D0F3758551DADC} 4602\makelabel{ref:TranslatorSubalgebra}{62.11.24}{X7D7A6486803B15CE} 4603\makelabel{ref:LieObject}{64.1.1}{X87F121978775AF48} 4604\makelabel{ref:IsLieObject}{64.1.2}{X83E5DD4381D9A65D} 4605\makelabel{ref:IsLieObjectCollection}{64.1.2}{X83E5DD4381D9A65D} 4606\makelabel{ref:IsRestrictedLieObject}{64.1.2}{X83E5DD4381D9A65D} 4607\makelabel{ref:IsRestrictedLieObjectCollection}{64.1.2}{X83E5DD4381D9A65D} 4608\makelabel{ref:LieFamily}{64.1.3}{X8725993C7BF386EE} 4609\makelabel{ref:Embedding for Lie algebras}{64.1.3}{X8725993C7BF386EE} 4610\makelabel{ref:UnderlyingFamily}{64.1.4}{X81D9F5C6876FE93B} 4611\makelabel{ref:UnderlyingRingElement}{64.1.5}{X874B2B2A7F5A9A78} 4612\makelabel{ref:LieAlgebraByStructureConstants}{64.2.1}{X7D362350824FA115} 4613\makelabel{ref:RestrictedLieAlgebraByStructureConstants}{64.2.2}{X7EEB79EE855E124C} 4614\makelabel{ref:LieAlgebra for an associative algebra}{64.2.3}{X7C840A9F85D28C81} 4615\makelabel{ref:LieAlgebra for field and generators}{64.2.3}{X7C840A9F85D28C81} 4616\makelabel{ref:FreeLieAlgebra for ring, rank (and name)}{64.2.4}{X7F7B34BD80F0F1C8} 4617\makelabel{ref:FreeLieAlgebra for ring and several names}{64.2.4}{X7F7B34BD80F0F1C8} 4618\makelabel{ref:FullMatrixLieAlgebra}{64.2.5}{X8735EE937A0081F0} 4619\makelabel{ref:MatrixLieAlgebra}{64.2.5}{X8735EE937A0081F0} 4620\makelabel{ref:MatLieAlgebra}{64.2.5}{X8735EE937A0081F0} 4621\makelabel{ref:RightDerivations}{64.2.6}{X821B6C197C08878B} 4622\makelabel{ref:LeftDerivations}{64.2.6}{X821B6C197C08878B} 4623\makelabel{ref:Derivations}{64.2.6}{X821B6C197C08878B} 4624\makelabel{ref:SimpleLieAlgebra}{64.2.7}{X7933F05F7DE342AB} 4625\makelabel{ref:LieCentre}{64.3.1}{X8111F58E7DE3E25C} 4626\makelabel{ref:LieCenter}{64.3.1}{X8111F58E7DE3E25C} 4627\makelabel{ref:LieCentralizer}{64.3.2}{X811444717EEDCC34} 4628\makelabel{ref:LieNormalizer}{64.3.3}{X7E62B6B37A75E09D} 4629\makelabel{ref:LieDerivedSubalgebra}{64.3.4}{X7C95C0057C977747} 4630\makelabel{ref:LieNilRadical}{64.3.5}{X7D072F6D7A3D0BAF} 4631\makelabel{ref:LieSolvableRadical}{64.3.6}{X8445C9F17F7CBEA1} 4632\makelabel{ref:CartanSubalgebra}{64.3.7}{X86114F157DFF6523} 4633\makelabel{ref:LieDerivedSeries}{64.4.1}{X7DEF89A8869809F5} 4634\makelabel{ref:LieLowerCentralSeries}{64.4.2}{X7900D17E7BA26A48} 4635\makelabel{ref:LieUpperCentralSeries}{64.4.3}{X86A8701C868828C7} 4636\makelabel{ref:IsLieAbelian}{64.5.1}{X7F97D08F7B738ADE} 4637\makelabel{ref:IsLieNilpotent}{64.5.2}{X78452F4E875A62A8} 4638\makelabel{ref:IsLieSolvable}{64.5.3}{X859FF1B3812B8FCC} 4639\makelabel{ref:SemiSimpleType}{64.6.1}{X8401CDC2859F8A85} 4640\makelabel{ref:ChevalleyBasis}{64.6.2}{X82EBF10A7B3B6F6E} 4641\makelabel{ref:IsRootSystem}{64.6.3}{X79B5D27681193625} 4642\makelabel{ref:IsRootSystemFromLieAlgebra}{64.6.4}{X7D64D49479CBB203} 4643\makelabel{ref:RootSystem}{64.6.5}{X80D15C027BB8029B} 4644\makelabel{ref:UnderlyingLieAlgebra}{64.6.6}{X7CA021E28527763E} 4645\makelabel{ref:PositiveRoots}{64.6.7}{X7B6B0BBD8035D7E5} 4646\makelabel{ref:NegativeRoots}{64.6.8}{X81F9E0E67DD2688F} 4647\makelabel{ref:PositiveRootVectors}{64.6.9}{X829C78427A442C23} 4648\makelabel{ref:NegativeRootVectors}{64.6.10}{X7AB374DC87A39349} 4649\makelabel{ref:SimpleSystem}{64.6.11}{X7DBD179E7CCF6699} 4650\makelabel{ref:CartanMatrix}{64.6.12}{X84E3FEF587CB66C3} 4651\makelabel{ref:BilinearFormMat}{64.6.13}{X878644D68571BF44} 4652\makelabel{ref:CanonicalGenerators}{64.6.14}{X7FAE45B37C5779A0} 4653\makelabel{ref:IsWeylGroup}{64.7.1}{X82AA29DD7969A935} 4654\makelabel{ref:SparseCartanMatrix}{64.7.2}{X81EF01E57E5DC18A} 4655\makelabel{ref:WeylGroup}{64.7.3}{X86BED5098322EBEF} 4656\makelabel{ref:ApplySimpleReflection}{64.7.4}{X7829BC4D7F253649} 4657\makelabel{ref:LongestWeylWordPerm}{64.7.5}{X80A7204F7D40D80F} 4658\makelabel{ref:ConjugateDominantWeight}{64.7.6}{X7D4E213F82F73857} 4659\makelabel{ref:ConjugateDominantWeightWithWord}{64.7.6}{X7D4E213F82F73857} 4660\makelabel{ref:WeylOrbitIterator}{64.7.7}{X7E000FA97949BFD5} 4661\makelabel{ref:IsRestrictedLieAlgebra}{64.8.1}{X81F28B1D830F28EB} 4662\makelabel{ref:PthPowerImages}{64.8.2}{X7D7BD5908016461B} 4663\makelabel{ref:PthPowerImage for basis and element}{64.8.3}{X879BB01782E7D7A9} 4664\makelabel{ref:PthPowerImage for element}{64.8.3}{X879BB01782E7D7A9} 4665\makelabel{ref:PthPowerImage for element and integer}{64.8.3}{X879BB01782E7D7A9} 4666\makelabel{ref:JenningsLieAlgebra}{64.8.4}{X8692ADD581359CA1} 4667\makelabel{ref:PCentralLieAlgebra}{64.8.5}{X785251E879E1BFC6} 4668\makelabel{ref:NaturalHomomorphismOfLieAlgebraFromNilpotentGroup}{64.8.6}{X781ADBEC850C7DE7} 4669\makelabel{ref:AdjointMatrix}{64.9.1}{X786886D882795F78} 4670\makelabel{ref:AdjointAssociativeAlgebra}{64.9.2}{X873A64307AC6C63E} 4671\makelabel{ref:KillingMatrix}{64.9.3}{X877CCFD5832E035D} 4672\makelabel{ref:KappaPerp}{64.9.4}{X8234046083B60F6E} 4673\makelabel{ref:IsNilpotentElement}{64.9.5}{X7A00601387A060CF} 4674\makelabel{ref:NonNilpotentElement}{64.9.6}{X86EF3E6F7BC0A8AD} 4675\makelabel{ref:FindSl2}{64.9.7}{X7A912D9E7B3BA874} 4676\makelabel{ref:UniversalEnvelopingAlgebra}{64.10.1}{X8226CD1680207A5F} 4677\makelabel{ref:FpLieAlgebraByCartanMatrix}{64.11.1}{X780A5B457A051110} 4678\makelabel{ref:NilpotentQuotientOfFpLieAlgebra}{64.11.2}{X79FD70C487EA9438} 4679\makelabel{ref:IsCochain}{64.12.1}{X82CC31CF79F59FEE} 4680\makelabel{ref:IsCochainCollection}{64.12.1}{X82CC31CF79F59FEE} 4681\makelabel{ref:Cochain}{64.12.2}{X79F3DF0D8791C2E3} 4682\makelabel{ref:CochainSpace}{64.12.3}{X7CF2919081600A3D} 4683\makelabel{ref:ValueCochain}{64.12.4}{X7D6760DA84683011} 4684\makelabel{ref:LieCoboundaryOperator}{64.12.5}{X851F5EF47FA90CBC} 4685\makelabel{ref:Cocycles for lie algebra module}{64.12.6}{X7FB815F38143939E} 4686\makelabel{ref:Coboundaries}{64.12.7}{X7C4F372C7AE2F739} 4687\makelabel{ref:DominantWeights}{64.13.1}{X7D8522E37ED1024A} 4688\makelabel{ref:DominantCharacter for a semisimple lie algebra and a highest weight}{64.13.2}{X79AAC71E8267E9F8} 4689\makelabel{ref:DominantCharacter for a root system and a highest weight}{64.13.2}{X79AAC71E8267E9F8} 4690\makelabel{ref:DecomposeTensorProduct}{64.13.3}{X7BE7129384B012DF} 4691\makelabel{ref:DimensionOfHighestWeightModule}{64.13.4}{X7D67A9BC7E4714D9} 4692\makelabel{ref:IsUEALatticeElement}{64.14.1}{X86E6722379576746} 4693\makelabel{ref:IsUEALatticeElementCollection}{64.14.1}{X86E6722379576746} 4694\makelabel{ref:IsUEALatticeElementFamily}{64.14.1}{X86E6722379576746} 4695\makelabel{ref:LatticeGeneratorsInUEA}{64.14.2}{X79F4F58B7888B0A5} 4696\makelabel{ref:ObjByExtRep for creating a uealattice element}{64.14.3}{X875FD1627F3B72DB} 4697\makelabel{ref:IsWeightRepElement}{64.14.4}{X8248DB547B02B0FA} 4698\makelabel{ref:IsWeightRepElementCollection}{64.14.4}{X8248DB547B02B0FA} 4699\makelabel{ref:IsWeightRepElementFamily}{64.14.4}{X8248DB547B02B0FA} 4700\makelabel{ref:HighestWeightModule}{64.14.5}{X7FB14F7F80EFF33F} 4701\makelabel{ref:TensorProductOfAlgebraModules for a list of algebra modules}{64.15.1}{X7A1E0AC4800E7FDA} 4702\makelabel{ref:TensorProductOfAlgebraModules for two algebra modules}{64.15.1}{X7A1E0AC4800E7FDA} 4703\makelabel{ref:ExteriorPowerOfAlgebraModule}{64.15.2}{X7F4AB6A1863E8FB2} 4704\makelabel{ref:SymmetricPowerOfAlgebraModule}{64.15.3}{X842DF85687D61A56} 4705\makelabel{ref:group algebra}{65}{X825897DC7A16E07D} 4706\makelabel{ref:group ring}{65}{X825897DC7A16E07D} 4707\makelabel{ref:FreeMagmaRing}{65.1.1}{X7B9AF0A47F44E4B4} 4708\makelabel{ref:GroupRing}{65.1.2}{X86D2CA90847C091B} 4709\makelabel{ref:IsFreeMagmaRing}{65.1.3}{X7A24B95C8210BD09} 4710\makelabel{ref:IsFreeMagmaRingWithOne}{65.1.4}{X8382ED697A28CE67} 4711\makelabel{ref:IsGroupRing}{65.1.5}{X82C63644805EB1EE} 4712\makelabel{ref:UnderlyingMagma}{65.1.6}{X848D60417DFF7947} 4713\makelabel{ref:AugmentationIdeal}{65.1.7}{X7B21DB3E7CD80983} 4714\makelabel{ref:IsMagmaRingObjDefaultRep}{65.2.1}{X827B2D7D7E41780C} 4715\makelabel{ref:IsElementOfFreeMagmaRing}{65.2.2}{X7D9C684A81E66310} 4716\makelabel{ref:IsElementOfFreeMagmaRingCollection}{65.2.2}{X7D9C684A81E66310} 4717\makelabel{ref:IsElementOfFreeMagmaRingFamily}{65.2.3}{X869768AF7B444BF8} 4718\makelabel{ref:CoefficientsAndMagmaElements}{65.2.4}{X843D1D8578C33513} 4719\makelabel{ref:ZeroCoefficient}{65.2.5}{X78C3DB417E353390} 4720\makelabel{ref:ElementOfMagmaRing}{65.2.6}{X8671DE0A81BEEFB0} 4721\makelabel{ref:Embedding for magma rings}{65.3}{X80366F1480ACD8DF} 4722\makelabel{ref:IsElementOfMagmaRingModuloRelations}{65.4.1}{X869D54847E881848} 4723\makelabel{ref:IsElementOfMagmaRingModuloRelationsCollection}{65.4.1}{X869D54847E881848} 4724\makelabel{ref:IsElementOfMagmaRingModuloRelationsFamily}{65.4.2}{X875BEB1A840FFAA4} 4725\makelabel{ref:NormalizedElementOfMagmaRingModuloRelations}{65.4.3}{X85956ED27FA6AC68} 4726\makelabel{ref:IsMagmaRingModuloRelations}{65.4.4}{X804B5AAB813E184D} 4727\makelabel{ref:IsElementOfMagmaRingModuloSpanOfZeroFamily}{65.5.1}{X7B3D45A6802B695C} 4728\makelabel{ref:IsMagmaRingModuloSpanOfZero}{65.5.2}{X872713EE84DA9B72} 4729\makelabel{ref:MagmaRingModuloSpanOfZero}{65.5.3}{X7A7F880D7D7D3722} 4730\makelabel{ref:Indeterminate for a ring (and a number)}{66.1.1}{X79D0380D7FA39F7D} 4731\makelabel{ref:Indeterminate for a ring (and a name, and an exclusion list)}{66.1.1}{X79D0380D7FA39F7D} 4732\makelabel{ref:Indeterminate for a family and a number}{66.1.1}{X79D0380D7FA39F7D} 4733\makelabel{ref:X for a ring (and a number)}{66.1.1}{X79D0380D7FA39F7D} 4734\makelabel{ref:X for a ring (and a name, and an exclusion list)}{66.1.1}{X79D0380D7FA39F7D} 4735\makelabel{ref:X for a family and a number}{66.1.1}{X79D0380D7FA39F7D} 4736\makelabel{ref:IndeterminateNumberOfUnivariateRationalFunction}{66.1.2}{X816C8D797C804380} 4737\makelabel{ref:IndeterminateOfUnivariateRationalFunction}{66.1.3}{X7A2FA46885EF403D} 4738\makelabel{ref:IndeterminateName}{66.1.4}{X7FD4AC807A1C8E27} 4739\makelabel{ref:HasIndeterminateName}{66.1.4}{X7FD4AC807A1C8E27} 4740\makelabel{ref:SetIndeterminateName}{66.1.4}{X7FD4AC807A1C8E27} 4741\makelabel{ref:CIUnivPols}{66.1.5}{X791A06E67F784328} 4742\makelabel{ref:addition rational functions}{66.2}{X86A68FD582F4F757} 4743\makelabel{ref:subtraction rational functions}{66.2}{X86A68FD582F4F757} 4744\makelabel{ref:product rational functions}{66.2}{X86A68FD582F4F757} 4745\makelabel{ref:quotient rational functions}{66.2}{X86A68FD582F4F757} 4746\makelabel{ref:mod Laurent polynomials}{66.2}{X86A68FD582F4F757} 4747\makelabel{ref:comparison rational functions}{66.3}{X824B6D328643CE04} 4748\makelabel{ref:smaller rational functions}{66.3}{X824B6D328643CE04} 4749\makelabel{ref:IsPolynomialFunction}{66.4.1}{X86C92F677DA9347F} 4750\makelabel{ref:IsRationalFunction}{66.4.1}{X86C92F677DA9347F} 4751\makelabel{ref:NumeratorOfRationalFunction}{66.4.2}{X7D7D2667803D8D8A} 4752\makelabel{ref:DenominatorOfRationalFunction}{66.4.3}{X78DC1B5B866ADB6C} 4753\makelabel{ref:IsPolynomial}{66.4.4}{X7974B0707C8DAB6C} 4754\makelabel{ref:AsPolynomial}{66.4.5}{X7914771F7C6013EF} 4755\makelabel{ref:IsUnivariateRationalFunction}{66.4.6}{X8738F73583273FCA} 4756\makelabel{ref:CoefficientsOfUnivariateRationalFunction}{66.4.7}{X7F1F67527A35A9CE} 4757\makelabel{ref:IsUnivariatePolynomial}{66.4.8}{X86A2546685D0016B} 4758\makelabel{ref:CoefficientsOfUnivariatePolynomial}{66.4.9}{X78C9524D7F2708C2} 4759\makelabel{ref:IsLaurentPolynomial}{66.4.10}{X79138FF28213B6EC} 4760\makelabel{ref:IsConstantRationalFunction}{66.4.11}{X7F2A49208341C2A8} 4761\makelabel{ref:IsPrimitivePolynomial}{66.4.12}{X834B54947FAADEA4} 4762\makelabel{ref:SplittingField}{66.4.13}{X87531E03849391C1} 4763\makelabel{ref:UnivariatePolynomial}{66.5.1}{X8379F8CB7D0076BA} 4764\makelabel{ref:UnivariatePolynomialByCoefficients}{66.5.2}{X85178A3E7B4F11E0} 4765\makelabel{ref:DegreeOfLaurentPolynomial}{66.5.3}{X78AF77C383245254} 4766\makelabel{ref:RootsOfPolynomial}{66.5.4}{X7CBB760C87B04F75} 4767\makelabel{ref:RootsOfUPol}{66.5.5}{X80CEB10D7879767F} 4768\makelabel{ref:QuotRemLaurpols}{66.5.6}{X7887FBC78149BB0C} 4769\makelabel{ref:UnivariatenessTestRationalFunction}{66.5.7}{X7DDADF157879EFBF} 4770\makelabel{ref:InfoPoly}{66.5.8}{X7A3BC96B7A50DE98} 4771\makelabel{ref:DegreeIndeterminate}{66.6.1}{X826B99B17ABD11BE} 4772\makelabel{ref:PolynomialCoefficientsOfPolynomial}{66.6.2}{X85646FD07F9C60F5} 4773\makelabel{ref:LeadingCoefficient}{66.6.3}{X80710E9B7D8340BD} 4774\makelabel{ref:LeadingMonomial}{66.6.4}{X7B3EAE41795598A5} 4775\makelabel{ref:Derivative}{66.6.5}{X7B57CEE2780D0E0B} 4776\makelabel{ref:Discriminant}{66.6.6}{X7C7D790A7D6E11AD} 4777\makelabel{ref:Resultant}{66.6.7}{X857AD5587EF49029} 4778\makelabel{ref:Value for rat. function, a list of indeterminates, a value (and a one)}{66.7.1}{X7A70769C7F52CD2D} 4779\makelabel{ref:Value for a univariate rat. function, a value (and a one)}{66.7.1}{X7A70769C7F52CD2D} 4780\makelabel{ref:MinimalPolynomial over a ring}{66.8}{X7ED3E7D17C7AC732} 4781\makelabel{ref:MinimalPolynomial}{66.8.1}{X8643915A8424DAF8} 4782\makelabel{ref:CyclotomicPolynomial}{66.9.1}{X827FC7FE81EE4C02} 4783\makelabel{ref:Factors of polynomial}{66.10.1}{X83511D517B544F36} 4784\makelabel{ref:FactorsSquarefree}{66.10.2}{X7F5A4ACB7AF9E329} 4785\makelabel{ref:PrimitivePolynomial}{66.11.1}{X7E66494B7B05A055} 4786\makelabel{ref:PolynomialModP}{66.11.2}{X7A73A3877EB73566} 4787\makelabel{ref:GaloisType}{66.11.3}{X7AB9A6257ED694EC} 4788\makelabel{ref:ProbabilityShapes}{66.11.4}{X7EB610D37D156DC6} 4789\makelabel{ref:BombieriNorm}{66.12.1}{X8723075C81D2CCA6} 4790\makelabel{ref:MinimizedBombieriNorm}{66.12.2}{X856D769D878AF7AE} 4791\makelabel{ref:HenselBound}{66.12.3}{X8139BB0F87399F2C} 4792\makelabel{ref:OneFactorBound}{66.12.4}{X79CC9C8D7C9F6B6A} 4793\makelabel{ref:LaurentPolynomialByCoefficients}{66.13.1}{X8467263B7EFA013E} 4794\makelabel{ref:CoefficientsOfLaurentPolynomial}{66.13.2}{X86D58AB67F86469F} 4795\makelabel{ref:IndeterminateNumberOfLaurentPolynomial}{66.13.3}{X8381E1B582F38C85} 4796\makelabel{ref:UnivariateRationalFunctionByCoefficients}{66.14.1}{X83DD411179888783} 4797\makelabel{ref:PolynomialRing for a ring and a rank (and an exclusion list)}{66.15.1}{X7D2F16E480060330} 4798\makelabel{ref:PolynomialRing for a ring and a list of names (and an exclusion list)}{66.15.1}{X7D2F16E480060330} 4799\makelabel{ref:PolynomialRing for a ring and a list of indeterminates}{66.15.1}{X7D2F16E480060330} 4800\makelabel{ref:PolynomialRing for a ring and a list of indeterminate numbers}{66.15.1}{X7D2F16E480060330} 4801\makelabel{ref:IndeterminatesOfPolynomialRing}{66.15.2}{X80D585E1793D4552} 4802\makelabel{ref:IndeterminatesOfFunctionField}{66.15.2}{X80D585E1793D4552} 4803\makelabel{ref:CoefficientsRing}{66.15.3}{X8235D10781BE8003} 4804\makelabel{ref:IsPolynomialRing}{66.15.4}{X7D631ACC86C584B7} 4805\makelabel{ref:IsFiniteFieldPolynomialRing}{66.15.5}{X86F391237A76D804} 4806\makelabel{ref:IsAbelianNumberFieldPolynomialRing}{66.15.6}{X782D07F77BCF67C1} 4807\makelabel{ref:IsRationalsPolynomialRing}{66.15.7}{X7D45213A8642033B} 4808\makelabel{ref:FunctionField for an integral ring and a rank (and an exclusion list)}{66.15.8}{X812E801484E3624E} 4809\makelabel{ref:FunctionField for an integral ring and a list of names (and an exclusion list)}{66.15.8}{X812E801484E3624E} 4810\makelabel{ref:FunctionField for an integral ring and a list of indeterminates}{66.15.8}{X812E801484E3624E} 4811\makelabel{ref:FunctionField for an integral ring and a list of indeterminate numbers}{66.15.8}{X812E801484E3624E} 4812\makelabel{ref:IsFunctionField}{66.15.9}{X8090C9EC85201AAC} 4813\makelabel{ref:UnivariatePolynomialRing for a ring (and an indeterminate number)}{66.16.1}{X84DC2A59797A26DE} 4814\makelabel{ref:UnivariatePolynomialRing for a ring (and a name and an exclusion list)}{66.16.1}{X84DC2A59797A26DE} 4815\makelabel{ref:IsUnivariatePolynomialRing}{66.16.2}{X7A43D74B812401CA} 4816\makelabel{ref:IsMonomialOrdering}{66.17.1}{X79D4CBBF820EA204} 4817\makelabel{ref:LeadingMonomialOfPolynomial}{66.17.2}{X7D052A017A73E91E} 4818\makelabel{ref:LeadingTermOfPolynomial}{66.17.3}{X7B6231137BA8B95F} 4819\makelabel{ref:LeadingCoefficientOfPolynomial}{66.17.4}{X798E707D86141087} 4820\makelabel{ref:MonomialComparisonFunction}{66.17.5}{X7EDE941781BA7F8B} 4821\makelabel{ref:MonomialExtrepComparisonFun}{66.17.6}{X7EDC3A457E7B591E} 4822\makelabel{ref:MonomialLexOrdering}{66.17.7}{X852D7BB37ECE98E1} 4823\makelabel{ref:MonomialGrlexOrdering}{66.17.8}{X786C866C824D2688} 4824\makelabel{ref:MonomialGrevlexOrdering}{66.17.9}{X8094C733808D1799} 4825\makelabel{ref:EliminationOrdering}{66.17.10}{X84AC871283A74EC0} 4826\makelabel{ref:PolynomialReduction}{66.17.11}{X7C99593584D478D7} 4827\makelabel{ref:PolynomialReducedRemainder}{66.17.12}{X7DE7D4467EBAD916} 4828\makelabel{ref:PolynomialDivisionAlgorithm}{66.17.13}{X7C8239057FD4EC03} 4829\makelabel{ref:MonomialExtGrlexLess}{66.17.14}{X7A30E10B820311D1} 4830\makelabel{ref:GroebnerBasis for a list and a monomial ordering}{66.18.1}{X7A43611E876B7560} 4831\makelabel{ref:GroebnerBasis for an ideal and a monomial ordering}{66.18.1}{X7A43611E876B7560} 4832\makelabel{ref:GroebnerBasisNC}{66.18.1}{X7A43611E876B7560} 4833\makelabel{ref:ReducedGroebnerBasis for a list and a monomial ordering}{66.18.2}{X7DEF286384967C9E} 4834\makelabel{ref:ReducedGroebnerBasis for an ideal and a monomial ordering}{66.18.2}{X7DEF286384967C9E} 4835\makelabel{ref:StoredGroebnerBasis}{66.18.3}{X7FC1EFE78498C17C} 4836\makelabel{ref:InfoGroebner}{66.18.4}{X7C55702786D284A7} 4837\makelabel{ref:RationalFunctionsFamily}{66.19.1}{X855DD73C78A90BC3} 4838\makelabel{ref:IsPolynomialFunctionsFamily}{66.19.2}{X86E097307D188D3B} 4839\makelabel{ref:IsRationalFunctionsFamily}{66.19.2}{X86E097307D188D3B} 4840\makelabel{ref:CoefficientsFamily}{66.19.3}{X7AADCA45826866FB} 4841\makelabel{ref:Expanded form of monomials}{66.21}{X7F44CF87801DB965} 4842\makelabel{ref:External representation of polynomials}{66.21}{X7F44CF87801DB965} 4843\makelabel{ref:IsRationalFunctionDefaultRep}{66.21.1}{X791E16C67A352263} 4844\makelabel{ref:ExtRepNumeratorRatFun}{66.21.2}{X7DF955C87CBFC12B} 4845\makelabel{ref:ExtRepDenominatorRatFun}{66.21.3}{X8059E74D7DCABDBC} 4846\makelabel{ref:ZeroCoefficientRatFun}{66.21.4}{X84F546F87B5ECFE0} 4847\makelabel{ref:IsPolynomialDefaultRep}{66.21.5}{X833CE16579AB26E0} 4848\makelabel{ref:ExtRepPolynomialRatFun}{66.21.6}{X8406EE2E8775FBAB} 4849\makelabel{ref:IsLaurentPolynomialDefaultRep}{66.21.7}{X7E1B98CC7BADAF56} 4850\makelabel{ref:RationalFunctionByExtRep}{66.22.1}{X81297E4587A9F2A6} 4851\makelabel{ref:RationalFunctionByExtRepNC}{66.22.1}{X81297E4587A9F2A6} 4852\makelabel{ref:PolynomialByExtRep}{66.22.2}{X79E445AF7849F48A} 4853\makelabel{ref:PolynomialByExtRepNC}{66.22.2}{X79E445AF7849F48A} 4854\makelabel{ref:LaurentPolynomialByExtRep}{66.22.3}{X7E2A46D68472F492} 4855\makelabel{ref:LaurentPolynomialByExtRepNC}{66.22.3}{X7E2A46D68472F492} 4856\makelabel{ref:ZippedSum}{66.23.1}{X855094857A78ABF9} 4857\makelabel{ref:ZippedProduct}{66.23.2}{X7B911136782F0F6D} 4858\makelabel{ref:QuotientPolynomialsExtRep}{66.23.3}{X87E5EB8985AF04CD} 4859\makelabel{ref:RationalFunctionByExtRepWithCancellation}{66.24.1}{X878A1AC87B492E3D} 4860\makelabel{ref:TryGcdCancelExtRepPolynomials}{66.24.2}{X7BFB55887A153003} 4861\makelabel{ref:HeuristicCancelPolynomialsExtRep}{66.24.3}{X8477D7337C4A98AB} 4862\makelabel{ref:AlgebraicExtension}{67.1.1}{X7CDA90537D2BAC8A} 4863\makelabel{ref:AlgebraicExtensionNC}{67.1.1}{X7CDA90537D2BAC8A} 4864\makelabel{ref:IsAlgebraicExtension}{67.1.2}{X811F10217F12B3F9} 4865\makelabel{ref:Operations for algebraic elements}{67.2}{X819C7E6F78817F1E} 4866\makelabel{ref:IsAlgebraicElement}{67.2.1}{X79695C887FD0AEAB} 4867\makelabel{ref:IdealDecompositionsOfPolynomial}{67.3.1}{X7FCAEFBC87651BDD} 4868\makelabel{ref:PurePadicNumberFamily}{68.1.1}{X82D1AD1D872B480D} 4869\makelabel{ref:PadicNumber for pure padics}{68.1.2}{X84A79ED87B47CC07} 4870\makelabel{ref:Valuation}{68.1.3}{X80D67BB67A509A56} 4871\makelabel{ref:ShiftedPadicNumber}{68.1.4}{X79059A9E876C8198} 4872\makelabel{ref:IsPurePadicNumber}{68.1.5}{X7AD7FA3786AF9F0E} 4873\makelabel{ref:IsPurePadicNumberFamily}{68.1.6}{X83B2BA4586ECAA5C} 4874\makelabel{ref:PadicExtensionNumberFamily}{68.2.1}{X83EE630D7885DB3D} 4875\makelabel{ref:PadicNumber for a p-adic extension family and a rational}{68.2.2}{X7C6F2F018084AFC4} 4876\makelabel{ref:PadicNumber for a pure p-adic numbers family and a list}{68.2.2}{X7C6F2F018084AFC4} 4877\makelabel{ref:PadicNumber for a p-adic extension family and a list}{68.2.2}{X7C6F2F018084AFC4} 4878\makelabel{ref:IsPadicExtensionNumber}{68.2.3}{X7923FC147BDCC810} 4879\makelabel{ref:IsPadicExtensionNumberFamily}{68.2.4}{X868807D487DAF713} 4880\makelabel{ref:GModuleByMats for generators and a field}{69.1.1}{X801022027B066497} 4881\makelabel{ref:GModuleByMats for empty list, the dimension, and a field}{69.1.1}{X801022027B066497} 4882\makelabel{ref:PermutationGModule}{69.2.1}{X8233134A81D58DA3} 4883\makelabel{ref:TensorProductGModule}{69.2.2}{X80A50F717B206C98} 4884\makelabel{ref:WedgeGModule}{69.2.3}{X7ABC0E98832FEA69} 4885\makelabel{ref:MTX}{69.3.1}{X7C2352A17B505AF6} 4886\makelabel{ref:MTX.Generators}{69.4.1}{X78E61F7287BF1D0C} 4887\makelabel{ref:MTX.Dimension}{69.4.2}{X7DF2D6C07D7B09CD} 4888\makelabel{ref:MTX.Field}{69.4.3}{X830C00887CE9323C} 4889\makelabel{ref:MTX.IsIrreducible}{69.5.1}{X83BEDF86784A6491} 4890\makelabel{ref:MTX.IsAbsolutelyIrreducible}{69.5.2}{X876810D679926679} 4891\makelabel{ref:MTX.DegreeSplittingField}{69.5.3}{X7E84E1927EBFD483} 4892\makelabel{ref:MTX.IsIndecomposable}{69.6.1}{X7D9B5B4E7F5A5FBD} 4893\makelabel{ref:MTX.Indecomposition}{69.6.2}{X781772FD865B9F9C} 4894\makelabel{ref:MTX.HomogeneousComponents}{69.6.3}{X7F00E49484FBA7B8} 4895\makelabel{ref:MTX.SubmoduleGModule}{69.7.1}{X80FFB229852B24E9} 4896\makelabel{ref:MTX.SubGModule}{69.7.1}{X80FFB229852B24E9} 4897\makelabel{ref:MTX.ProperSubmoduleBasis}{69.7.2}{X81326D84845C206F} 4898\makelabel{ref:MTX.BasesSubmodules}{69.7.3}{X84604D867983DD41} 4899\makelabel{ref:MTX.BasesMinimalSubmodules}{69.7.4}{X871D9AF87FABFB00} 4900\makelabel{ref:MTX.BasesMaximalSubmodules}{69.7.5}{X864527B77A359195} 4901\makelabel{ref:MTX.BasisRadical}{69.7.6}{X830500CE7ABF6039} 4902\makelabel{ref:MTX.BasisSocle}{69.7.7}{X86A5197D8154A63C} 4903\makelabel{ref:MTX.BasesMinimalSupermodules}{69.7.8}{X7F7FB6687ADE3FD8} 4904\makelabel{ref:MTX.BasesCompositionSeries}{69.7.9}{X79B704998400B9FC} 4905\makelabel{ref:MTX.CompositionFactors}{69.7.10}{X7E77F9A97EA855E2} 4906\makelabel{ref:MTX.CollectedFactors}{69.7.11}{X7E5038F384DBCAEC} 4907\makelabel{ref:MTX.NormedBasisAndBaseChange}{69.8.1}{X79EA05D4822C2668} 4908\makelabel{ref:MTX.InducedActionSubmodule}{69.8.2}{X7812D644850D7AED} 4909\makelabel{ref:MTX.InducedActionSubmoduleNB}{69.8.2}{X7812D644850D7AED} 4910\makelabel{ref:MTX.InducedActionFactorModule}{69.8.3}{X7EAC61B381385A99} 4911\makelabel{ref:MTX.InducedActionSubMatrix}{69.8.4}{X8753A03A7C7CBFF1} 4912\makelabel{ref:MTX.InducedActionSubMatrixNB}{69.8.4}{X8753A03A7C7CBFF1} 4913\makelabel{ref:MTX.InducedActionFactorMatrix}{69.8.4}{X8753A03A7C7CBFF1} 4914\makelabel{ref:MTX.InducedAction}{69.8.5}{X7B137BE5877A7FA1} 4915\makelabel{ref:MTX.BasisModuleHomomorphisms}{69.9.1}{X8292535D8533671C} 4916\makelabel{ref:MTX.BasisModuleEndomorphisms}{69.9.2}{X78EE1274825D9E03} 4917\makelabel{ref:MTX.IsomorphismModules}{69.9.3}{X8519B3C486AC8C7E} 4918\makelabel{ref:MTX.ModuleAutomorphisms}{69.9.4}{X8442D91F7C4D724F} 4919\makelabel{ref:MTX.IsEquivalent}{69.10.1}{X858D2B0D7AE032D5} 4920\makelabel{ref:MTX.IsomorphismIrred}{69.10.2}{X7E86F5B67CBD7C41} 4921\makelabel{ref:MTX.Homomorphism}{69.10.3}{X807AE3AC7E9B7CFF} 4922\makelabel{ref:MTX.Homomorphisms}{69.10.4}{X7BC612D2860C582B} 4923\makelabel{ref:MTX.Distinguish}{69.10.5}{X81A6ECB078D4441C} 4924\makelabel{ref:MTX.InvariantBilinearForm}{69.11.1}{X78B114E78227EA37} 4925\makelabel{ref:MTX.InvariantSesquilinearForm}{69.11.2}{X7E1F430278A334E1} 4926\makelabel{ref:MTX.InvariantQuadraticForm}{69.11.3}{X7ADE65997F16EE63} 4927\makelabel{ref:MTX.BasisInOrbit}{69.11.4}{X78E60EFE802AEBC1} 4928\makelabel{ref:MTX.OrthogonalSign}{69.11.5}{X8168EB348474046B} 4929\makelabel{ref:SMTX.RandomIrreducibleSubGModule}{69.12.1}{X7E78525883E715E1} 4930\makelabel{ref:SMTX.GoodElementGModule}{69.12.2}{X7EA698517A19D35B} 4931\makelabel{ref:SMTX.SortHomGModule}{69.12.3}{X811339547D341BBE} 4932\makelabel{ref:SMTX.MinimalSubGModules}{69.12.4}{X86B6092681221D7A} 4933\makelabel{ref:SMTX.Setter}{69.12.5}{X87E49FCD867983B5} 4934\makelabel{ref:SMTX.Getter}{69.12.6}{X7E60EBC57FFDF7BD} 4935\makelabel{ref:SMTX.IrreducibilityTest}{69.12.7}{X808345D784E0AC85} 4936\makelabel{ref:SMTX.AbsoluteIrreducibilityTest}{69.12.8}{X7E692DC97AFB661E} 4937\makelabel{ref:SMTX.MinimalSubGModule}{69.12.9}{X80BC392285994DA8} 4938\makelabel{ref:SMTX.MatrixSum}{69.12.10}{X79EF16677C2EE095} 4939\makelabel{ref:SMTX.CompleteBasis}{69.12.11}{X7D1471077A774C81} 4940\makelabel{ref:SMTX.Subbasis}{69.13.1}{X84A93AC482A1946D} 4941\makelabel{ref:SMTX.AlgEl}{69.13.2}{X7ABCD69880772B2D} 4942\makelabel{ref:SMTX.AlgElMat}{69.13.3}{X7D6C947A7C8C14B2} 4943\makelabel{ref:SMTX.AlgElCharPol}{69.13.4}{X8417F86A7A20F128} 4944\makelabel{ref:SMTX.AlgElCharPolFac}{69.13.5}{X79A82FED785BFB6D} 4945\makelabel{ref:SMTX.AlgElNullspaceVec}{69.13.6}{X8367B4A17EC39ABD} 4946\makelabel{ref:SMTX.AlgElNullspaceDimension}{69.13.7}{X877F1AB77DC1E12C} 4947\makelabel{ref:SMTX.CentMat}{69.13.8}{X78A6B95686671067} 4948\makelabel{ref:SMTX.CentMatMinPoly}{69.13.9}{X7D199DB6804F5D8F} 4949\makelabel{ref:TableOfMarks for a group}{70.3.1}{X85B262AB7E219C34} 4950\makelabel{ref:TableOfMarks for a string}{70.3.1}{X85B262AB7E219C34} 4951\makelabel{ref:TableOfMarks for a matrix}{70.3.1}{X85B262AB7E219C34} 4952\makelabel{ref:TableOfMarksByLattice}{70.3.2}{X7B30FF3A79CCB0DF} 4953\makelabel{ref:LatticeSubgroupsByTom}{70.3.3}{X79ABFA0A833DDCFE} 4954\makelabel{ref:ViewObj for a table of marks}{70.4.1}{X7DC656517D8335DC} 4955\makelabel{ref:PrintObj for a table of marks}{70.4.2}{X86379C0D7D17AD92} 4956\makelabel{ref:Display for a table of marks}{70.4.3}{X821F9438839F445D} 4957\makelabel{ref:SortedTom}{70.5.1}{X786A948E82C36F0E} 4958\makelabel{ref:PermutationTom}{70.5.2}{X7EFD937D804662F6} 4959\makelabel{ref:InfoTom}{70.6.1}{X870985C58547FED4} 4960\makelabel{ref:IsTableOfMarks}{70.6.2}{X7AC1A73D8100C7EC} 4961\makelabel{ref:TableOfMarksFamily}{70.6.3}{X7ACF943D84BDF89E} 4962\makelabel{ref:TableOfMarksComponents}{70.6.4}{X87789FD27831B2A2} 4963\makelabel{ref:ConvertToTableOfMarks}{70.6.5}{X8491CDBF8543A7D5} 4964\makelabel{ref:MarksTom}{70.7.1}{X78F486A28561D006} 4965\makelabel{ref:SubsTom}{70.7.1}{X78F486A28561D006} 4966\makelabel{ref:NrSubsTom}{70.7.2}{X82E5DA217A5D1134} 4967\makelabel{ref:OrdersTom}{70.7.2}{X82E5DA217A5D1134} 4968\makelabel{ref:LengthsTom}{70.7.3}{X781AA1B28178AE9A} 4969\makelabel{ref:ClassTypesTom}{70.7.4}{X7A33C7C38083CC09} 4970\makelabel{ref:ClassNamesTom}{70.7.5}{X7A53E923819FE173} 4971\makelabel{ref:FusionsTom}{70.7.6}{X86B9891C788D5107} 4972\makelabel{ref:UnderlyingGroup for tables of marks}{70.7.7}{X81E41D3880FA6C4C} 4973\makelabel{ref:IdempotentsTom}{70.7.8}{X817238FB79A3462F} 4974\makelabel{ref:IdempotentsTomInfo}{70.7.8}{X817238FB79A3462F} 4975\makelabel{ref:Identifier for tables of marks}{70.7.9}{X810E53597B5BB4F8} 4976\makelabel{ref:MatTom}{70.7.10}{X8463272986781E17} 4977\makelabel{ref:MoebiusTom}{70.7.11}{X7D32C8B0786D16C1} 4978\makelabel{ref:WeightsTom}{70.7.12}{X78525D04849A48EA} 4979\makelabel{ref:IsAbelianTom}{70.8.1}{X7C93BAEC78B7C2B4} 4980\makelabel{ref:IsCyclicTom}{70.8.1}{X7C93BAEC78B7C2B4} 4981\makelabel{ref:IsNilpotentTom}{70.8.1}{X7C93BAEC78B7C2B4} 4982\makelabel{ref:IsPerfectTom}{70.8.1}{X7C93BAEC78B7C2B4} 4983\makelabel{ref:IsSolvableTom}{70.8.1}{X7C93BAEC78B7C2B4} 4984\makelabel{ref:IsInternallyConsistent for tables of marks}{70.9.1}{X7D8B4BE08094B137} 4985\makelabel{ref:DerivedSubgroupTom}{70.9.2}{X8528D9397FFAF477} 4986\makelabel{ref:DerivedSubgroupsTom}{70.9.2}{X8528D9397FFAF477} 4987\makelabel{ref:DerivedSubgroupsTomPossible}{70.9.3}{X7C29BD438127DFBE} 4988\makelabel{ref:DerivedSubgroupsTomUnique}{70.9.3}{X7C29BD438127DFBE} 4989\makelabel{ref:NormalizerTom}{70.9.4}{X7CE6C45881F7F7D4} 4990\makelabel{ref:NormalizersTom}{70.9.4}{X7CE6C45881F7F7D4} 4991\makelabel{ref:ContainedTom}{70.9.5}{X7F87B2797827E5DE} 4992\makelabel{ref:ContainingTom}{70.9.6}{X7EE050FB87D6F0E7} 4993\makelabel{ref:CyclicExtensionsTom for a prime}{70.9.7}{X838DE06B823C19CA} 4994\makelabel{ref:CyclicExtensionsTom for a list of primes}{70.9.7}{X838DE06B823C19CA} 4995\makelabel{ref:DecomposedFixedPointVector}{70.9.8}{X80890C247EB1E35C} 4996\makelabel{ref:EulerianFunctionByTom}{70.9.9}{X7B1C1A7C867A4082} 4997\makelabel{ref:IntersectionsTom}{70.9.10}{X8224E51382FDB912} 4998\makelabel{ref:FactorGroupTom}{70.9.11}{X859F069C8428B598} 4999\makelabel{ref:MaximalSubgroupsTom}{70.9.12}{X8325811586C00ECF} 5000\makelabel{ref:MinimalSupergroupsTom}{70.9.13}{X7923B19D7C47BF63} 5001\makelabel{ref:GeneratorsSubgroupsTom}{70.10.1}{X7B0B6FDD806E9734} 5002\makelabel{ref:StraightLineProgramsTom}{70.10.2}{X7898BE7284E47FF3} 5003\makelabel{ref:IsTableOfMarksWithGens}{70.10.3}{X7889DB6D790593B9} 5004\makelabel{ref:RepresentativeTom}{70.10.4}{X7F625AB880B73AC3} 5005\makelabel{ref:RepresentativeTomByGenerators}{70.10.4}{X7F625AB880B73AC3} 5006\makelabel{ref:RepresentativeTomByGeneratorsNC}{70.10.4}{X7F625AB880B73AC3} 5007\makelabel{ref:FusionCharTableTom}{70.11.1}{X7A82CB487DBDDC53} 5008\makelabel{ref:PossibleFusionsCharTableTom}{70.11.1}{X7A82CB487DBDDC53} 5009\makelabel{ref:PermCharsTom via fusion map}{70.11.2}{X8016499282F0BA37} 5010\makelabel{ref:PermCharsTom from a character table}{70.11.2}{X8016499282F0BA37} 5011\makelabel{ref:TableOfMarksCyclic}{70.12.1}{X7CAA5B6C85CB9A8D} 5012\makelabel{ref:TableOfMarksDihedral}{70.12.2}{X7AADB47B8079C99E} 5013\makelabel{ref:TableOfMarksFrobenius}{70.12.3}{X78E9DDF885E12687} 5014\makelabel{ref:tables}{71}{X7B7A9EE881E01C10} 5015\makelabel{ref:tables}{71.3}{X8701174D86B586AF} 5016\makelabel{ref:character tables}{71.3}{X8701174D86B586AF} 5017\makelabel{ref:library tables}{71.3}{X8701174D86B586AF} 5018\makelabel{ref:character tables access to}{71.3}{X8701174D86B586AF} 5019\makelabel{ref:character tables calculate}{71.3}{X8701174D86B586AF} 5020\makelabel{ref:character tables of groups}{71.3}{X8701174D86B586AF} 5021\makelabel{ref:CharacterTable for a group}{71.3.1}{X7FCA7A7A822BDA33} 5022\makelabel{ref:CharacterTable for an ordinary character table}{71.3.1}{X7FCA7A7A822BDA33} 5023\makelabel{ref:CharacterTable for a string}{71.3.1}{X7FCA7A7A822BDA33} 5024\makelabel{ref:BrauerTable for a character table, and a prime integer}{71.3.2}{X8476B25A79D7A7FC} 5025\makelabel{ref:BrauerTable for a group, and a prime integer}{71.3.2}{X8476B25A79D7A7FC} 5026\makelabel{ref:BrauerTableOp}{71.3.2}{X8476B25A79D7A7FC} 5027\makelabel{ref:ComputedBrauerTables}{71.3.2}{X8476B25A79D7A7FC} 5028\makelabel{ref:CharacterTableRegular}{71.3.3}{X85DB8AE7786A2DB5} 5029\makelabel{ref:SupportedCharacterTableInfo}{71.3.4}{X7DBEF4BF87F10CD6} 5030\makelabel{ref:ConvertToCharacterTable}{71.3.5}{X8195BC057B1DFAD5} 5031\makelabel{ref:ConvertToCharacterTableNC}{71.3.5}{X8195BC057B1DFAD5} 5032\makelabel{ref:IsNearlyCharacterTable}{71.4.1}{X82FF82C87CF82ADF} 5033\makelabel{ref:IsCharacterTable}{71.4.1}{X82FF82C87CF82ADF} 5034\makelabel{ref:IsOrdinaryTable}{71.4.1}{X82FF82C87CF82ADF} 5035\makelabel{ref:IsBrauerTable}{71.4.1}{X82FF82C87CF82ADF} 5036\makelabel{ref:IsCharacterTableInProgress}{71.4.1}{X82FF82C87CF82ADF} 5037\makelabel{ref:InfoCharacterTable}{71.4.2}{X7C6F3D947E5188D1} 5038\makelabel{ref:NearlyCharacterTablesFamily}{71.4.3}{X7FA867637EBB30F9} 5039\makelabel{ref:UnderlyingGroup for character tables}{71.6.1}{X7FF4826A82B667AF} 5040\makelabel{ref:ConjugacyClasses for character tables}{71.6.2}{X849A38F887F6EC86} 5041\makelabel{ref:IdentificationOfConjugacyClasses}{71.6.3}{X84DC12AA804C8085} 5042\makelabel{ref:CharacterTableWithStoredGroup}{71.6.4}{X8788C6C7829C1ADE} 5043\makelabel{ref:CompatibleConjugacyClasses}{71.6.5}{X790019E87CFDDB98} 5044\makelabel{ref:mod for character tables}{71.7}{X7CADCBC9824CB624} 5045\makelabel{ref:character tables infix operators}{71.7}{X7CADCBC9824CB624} 5046\makelabel{ref:CharacterDegrees for a group}{71.8.1}{X81FEFF768134481A} 5047\makelabel{ref:CharacterDegrees for a character table}{71.8.1}{X81FEFF768134481A} 5048\makelabel{ref:Irr for a group}{71.8.2}{X873B3CC57E9A5492} 5049\makelabel{ref:Irr for a character table}{71.8.2}{X873B3CC57E9A5492} 5050\makelabel{ref:LinearCharacters for a group}{71.8.3}{X8549899A7DE206BA} 5051\makelabel{ref:LinearCharacters for a character table}{71.8.3}{X8549899A7DE206BA} 5052\makelabel{ref:OrdinaryCharacterTable for a group}{71.8.4}{X8011EEB684848039} 5053\makelabel{ref:OrdinaryCharacterTable for a character table}{71.8.4}{X8011EEB684848039} 5054\makelabel{ref:AbelianInvariants for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5055\makelabel{ref:CommutatorLength for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5056\makelabel{ref:Exponent for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5057\makelabel{ref:IsAbelian for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5058\makelabel{ref:IsAlmostSimple for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5059\makelabel{ref:IsCyclic for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5060\makelabel{ref:IsElementaryAbelian for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5061\makelabel{ref:IsFinite for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5062\makelabel{ref:IsMonomial for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5063\makelabel{ref:IsNilpotent for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5064\makelabel{ref:IsPerfect for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5065\makelabel{ref:IsSimple for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5066\makelabel{ref:IsSolvable for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5067\makelabel{ref:IsSporadicSimple for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5068\makelabel{ref:IsSupersolvable for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5069\makelabel{ref:IsomorphismTypeInfoFiniteSimpleGroup for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5070\makelabel{ref:NrConjugacyClasses for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5071\makelabel{ref:Size for a character table}{71.8.5}{X81EFD9FE804AC6EE} 5072\makelabel{ref:OrdersClassRepresentatives}{71.9.1}{X86F455DA7A9C30EE} 5073\makelabel{ref:SizesCentralizers}{71.9.2}{X7CF7907F790A5DE6} 5074\makelabel{ref:SizesCentralisers}{71.9.2}{X7CF7907F790A5DE6} 5075\makelabel{ref:SizesConjugacyClasses}{71.9.3}{X7D9D2A45879A6A62} 5076\makelabel{ref:AutomorphismsOfTable}{71.9.4}{X7C2753DE8094F4BA} 5077\makelabel{ref:UnderlyingCharacteristic for a character table}{71.9.5}{X7F58A82F7D88000A} 5078\makelabel{ref:UnderlyingCharacteristic for a character}{71.9.5}{X7F58A82F7D88000A} 5079\makelabel{ref:ClassNames}{71.9.6}{X804CFD597C795801} 5080\makelabel{ref:CharacterNames}{71.9.6}{X804CFD597C795801} 5081\makelabel{ref:ClassParameters}{71.9.7}{X8333E8038308947E} 5082\makelabel{ref:CharacterParameters}{71.9.7}{X8333E8038308947E} 5083\makelabel{ref:Identifier for character tables}{71.9.8}{X79C40EE97890202F} 5084\makelabel{ref:InfoText for character tables}{71.9.9}{X7932C35180C80953} 5085\makelabel{ref:InverseClasses}{71.9.10}{X7919E2897BE8234A} 5086\makelabel{ref:RealClasses}{71.9.11}{X87FF547981456932} 5087\makelabel{ref:classes real}{71.9.11}{X87FF547981456932} 5088\makelabel{ref:ClassOrbit}{71.9.12}{X7ABB007C799F7C49} 5089\makelabel{ref:ClassRoots}{71.9.13}{X7F863B15804E0835} 5090\makelabel{ref:ClassPositionsOfNormalSubgroups}{71.10.1}{X850C7D947B3DBFA2} 5091\makelabel{ref:ClassPositionsOfMaximalNormalSubgroups}{71.10.1}{X850C7D947B3DBFA2} 5092\makelabel{ref:ClassPositionsOfMinimalNormalSubgroups}{71.10.1}{X850C7D947B3DBFA2} 5093\makelabel{ref:ClassPositionsOfAgemo}{71.10.2}{X8491DA0981D6F264} 5094\makelabel{ref:ClassPositionsOfCentre for a character table}{71.10.3}{X7A6B1F8A84A495DC} 5095\makelabel{ref:ClassPositionsOfCenter for a character table}{71.10.3}{X7A6B1F8A84A495DC} 5096\makelabel{ref:ClassPositionsOfDirectProductDecompositions}{71.10.4}{X7D53F60785AB22B1} 5097\makelabel{ref:ClassPositionsOfDerivedSubgroup}{71.10.5}{X79EE7BE17BD343D5} 5098\makelabel{ref:ClassPositionsOfElementaryAbelianSeries}{71.10.6}{X86ABB2E179D7F6E1} 5099\makelabel{ref:ClassPositionsOfFittingSubgroup}{71.10.7}{X7D2A55A584F955DB} 5100\makelabel{ref:ClassPositionsOfLowerCentralSeries}{71.10.8}{X79AEFC4384769B72} 5101\makelabel{ref:ClassPositionsOfUpperCentralSeries}{71.10.9}{X86065D217A36CD9B} 5102\makelabel{ref:ClassPositionsOfSolvableRadical}{71.10.10}{X877FDE8A84A9F52C} 5103\makelabel{ref:ClassPositionsOfSupersolvableResiduum}{71.10.11}{X8392DD5B813250A4} 5104\makelabel{ref:ClassPositionsOfPCore}{71.10.12}{X7BBE7EBA7A64A6B0} 5105\makelabel{ref:ClassPositionsOfNormalClosure}{71.10.13}{X7FCF905D7FD7CC40} 5106\makelabel{ref:PrimeBlocks}{71.11.1}{X7ACB9306804F4E3F} 5107\makelabel{ref:PrimeBlocksOp}{71.11.1}{X7ACB9306804F4E3F} 5108\makelabel{ref:ComputedPrimeBlockss}{71.11.1}{X7ACB9306804F4E3F} 5109\makelabel{ref:SameBlock}{71.11.2}{X7E80E35985275F35} 5110\makelabel{ref:BlocksInfo}{71.11.3}{X7FF4CE4A7A272F88} 5111\makelabel{ref:DecompositionMatrix}{71.11.4}{X84701640811D2345} 5112\makelabel{ref:LaTeX for a decomposition matrix}{71.11.4}{X84701640811D2345} 5113\makelabel{ref:LaTeXStringDecompositionMatrix}{71.11.5}{X83EC921380AF9B3B} 5114\makelabel{ref:Index for two character tables}{71.12.1}{X8441983C845F2176} 5115\makelabel{ref:IsInternallyConsistent for character tables}{71.12.2}{X8123650E817926FC} 5116\makelabel{ref:IsPSolvableCharacterTable}{71.12.3}{X7A0CBD1884276882} 5117\makelabel{ref:IsPSolubleCharacterTable}{71.12.3}{X7A0CBD1884276882} 5118\makelabel{ref:IsPSolvableCharacterTableOp}{71.12.3}{X7A0CBD1884276882} 5119\makelabel{ref:IsPSolubleCharacterTableOp}{71.12.3}{X7A0CBD1884276882} 5120\makelabel{ref:ComputedIsPSolvableCharacterTables}{71.12.3}{X7A0CBD1884276882} 5121\makelabel{ref:ComputedIsPSolubleCharacterTables}{71.12.3}{X7A0CBD1884276882} 5122\makelabel{ref:IsClassFusionOfNormalSubgroup}{71.12.4}{X82F523E8784B3752} 5123\makelabel{ref:Indicator}{71.12.5}{X7FD3D3047DE6381E} 5124\makelabel{ref:IndicatorOp}{71.12.5}{X7FD3D3047DE6381E} 5125\makelabel{ref:ComputedIndicators}{71.12.5}{X7FD3D3047DE6381E} 5126\makelabel{ref:NrPolyhedralSubgroups}{71.12.6}{X83AE05BF8085B3C8} 5127\makelabel{ref:subgroups polyhedral}{71.12.6}{X83AE05BF8085B3C8} 5128\makelabel{ref:ClassMultiplicationCoefficient for character tables}{71.12.7}{X7E2EA9FE7D3062D3} 5129\makelabel{ref:ClassMultiplicationCoefficient for character tables}{71.12.7}{X7E2EA9FE7D3062D3} 5130\makelabel{ref:class multiplication coefficient}{71.12.7}{X7E2EA9FE7D3062D3} 5131\makelabel{ref:structure constant}{71.12.7}{X7E2EA9FE7D3062D3} 5132\makelabel{ref:ClassStructureCharTable}{71.12.8}{X7A19F56C7FD5EFC7} 5133\makelabel{ref:class multiplication coefficient}{71.12.8}{X7A19F56C7FD5EFC7} 5134\makelabel{ref:structure constant}{71.12.8}{X7A19F56C7FD5EFC7} 5135\makelabel{ref:MatClassMultCoeffsCharTable}{71.12.9}{X809E67E57D4933B3} 5136\makelabel{ref:structure constant}{71.12.9}{X809E67E57D4933B3} 5137\makelabel{ref:class multiplication coefficient}{71.12.9}{X809E67E57D4933B3} 5138\makelabel{ref:ViewObj for a character table}{71.13.1}{X7D45224B86D802E5} 5139\makelabel{ref:PrintObj for a character table}{71.13.2}{X836554207C678D41} 5140\makelabel{ref:Display for a character table}{71.13.3}{X7B41F36478C47364} 5141\makelabel{ref:DisplayOptions}{71.13.4}{X85E883A87A190AA4} 5142\makelabel{ref:PrintCharacterTable}{71.13.5}{X79EC9603833AA2AB} 5143\makelabel{ref:IrrDixonSchneider}{71.14.1}{X7ED39DB680BFEA96} 5144\makelabel{ref:IrrConlon}{71.14.2}{X7E81BCD686561DF0} 5145\makelabel{ref:IrrBaumClausen}{71.14.3}{X7BF15729839203FC} 5146\makelabel{ref:IrreducibleRepresentations}{71.14.4}{X7F29C5447B5DC102} 5147\makelabel{ref:IrreducibleRepresentationsDixon}{71.14.5}{X8493ED7A86FFCB8A} 5148\makelabel{ref:IrreducibleModules}{71.15.1}{X87E82F8085745523} 5149\makelabel{ref:AbsolutelyIrreducibleModules}{71.15.2}{X7D0BD5337D1C069B} 5150\makelabel{ref:AbsoluteIrreducibleModules}{71.15.2}{X7D0BD5337D1C069B} 5151\makelabel{ref:AbsolutIrreducibleModules}{71.15.2}{X7D0BD5337D1C069B} 5152\makelabel{ref:RegularModule}{71.15.3}{X7EB88B2E87AF5556} 5153\makelabel{ref:Dixon-Schneider algorithm}{71.16}{X86CDA4007A5EF704} 5154\makelabel{ref:irreducible characters computation}{71.17}{X7C083207868066C1} 5155\makelabel{ref:DixonRecord}{71.17.1}{X7C398F2680C8616B} 5156\makelabel{ref:DixonInit}{71.17.2}{X7E33C03E7BDDC9B0} 5157\makelabel{ref:DixontinI}{71.17.3}{X868476037907918F} 5158\makelabel{ref:DixonSplit}{71.17.4}{X87ABE0B081DAD476} 5159\makelabel{ref:BestSplittingMatrix}{71.17.5}{X7BFD4C1A821731FB} 5160\makelabel{ref:DxIncludeIrreducibles}{71.17.6}{X7C85B56C80BFA2E3} 5161\makelabel{ref:SplitCharacters}{71.17.7}{X87A5B5C77F7F348E} 5162\makelabel{ref:IsDxLargeGroup}{71.17.8}{X8089009E7EA85BC8} 5163\makelabel{ref:CharacterTableDirectProduct}{71.20.1}{X7BE1572D7BBC6AC8} 5164\makelabel{ref:FactorsOfDirectProduct}{71.20.2}{X7C97CF727FBDFCAB} 5165\makelabel{ref:CharacterTableFactorGroup}{71.20.3}{X7C3A4E5283B240BE} 5166\makelabel{ref:CharacterTableIsoclinic}{71.20.4}{X85BE46F784B83938} 5167\makelabel{ref:CharacterTableIsoclinic for a character table and one or two lists}{71.20.4}{X85BE46F784B83938} 5168\makelabel{ref:CharacterTableIsoclinic for a brauer table and an ordinary table}{71.20.4}{X85BE46F784B83938} 5169\makelabel{ref:SourceOfIsoclinicTable}{71.20.4}{X85BE46F784B83938} 5170\makelabel{ref:CharacterTableOfNormalSubgroup}{71.20.5}{X806E55A58397B11B} 5171\makelabel{ref:CharacterTableWreathSymmetric}{71.20.6}{X79B75C8582426BC5} 5172\makelabel{ref:CharacterValueWreathSymmetric}{71.20.7}{X83E71B1F7FA70134} 5173\makelabel{ref:CharacterTableWithSortedCharacters}{71.21.1}{X7D9C4A7F8086F671} 5174\makelabel{ref:SortedCharacters}{71.21.2}{X87E3CF317D8E4EC7} 5175\makelabel{ref:CharacterTableWithSortedClasses}{71.21.3}{X7E3DE0A47E62BE6B} 5176\makelabel{ref:SortedCharacterTable w.r.t. a normal subgroup}{71.21.4}{X82DCAAA882416E24} 5177\makelabel{ref:SortedCharacterTable w.r.t. a series of normal subgroups}{71.21.4}{X82DCAAA882416E24} 5178\makelabel{ref:SortedCharacterTable relative to the table of a factor group}{71.21.4}{X82DCAAA882416E24} 5179\makelabel{ref:ClassPermutation}{71.21.5}{X8099FEDC7DE03AEE} 5180\makelabel{ref:MatrixAutomorphisms}{71.22.1}{X84353BB884AF0365} 5181\makelabel{ref:TableAutomorphisms}{71.22.2}{X8082DD827C673138} 5182\makelabel{ref:TransformingPermutations}{71.22.3}{X7D721E3D7AA319F5} 5183\makelabel{ref:TransformingPermutationsCharacterTables}{71.22.4}{X849731AA7EC9FA73} 5184\makelabel{ref:FamiliesOfRows}{71.22.5}{X8117D940835B0B47} 5185\makelabel{ref:NormalSubgroupClassesInfo}{71.23.1}{X7E66174C7C7A8C0C} 5186\makelabel{ref:ClassPositionsOfNormalSubgroup}{71.23.2}{X7C2A87E085111090} 5187\makelabel{ref:NormalSubgroupClasses}{71.23.3}{X87E7391F7F92377C} 5188\makelabel{ref:FactorGroupNormalSubgroupClasses}{71.23.4}{X79D451F0808EB252} 5189\makelabel{ref:characters}{72}{X7C91D0D17850E564} 5190\makelabel{ref:group characters}{72}{X7C91D0D17850E564} 5191\makelabel{ref:virtual characters}{72}{X7C91D0D17850E564} 5192\makelabel{ref:generalized characters}{72}{X7C91D0D17850E564} 5193\makelabel{ref:IsClassFunction}{72.1.1}{X7E75A70F7BF00A0D} 5194\makelabel{ref:class function}{72.1.1}{X7E75A70F7BF00A0D} 5195\makelabel{ref:class function objects}{72.1.1}{X7E75A70F7BF00A0D} 5196\makelabel{ref:UnderlyingCharacterTable}{72.2.1}{X81B55C067D123B76} 5197\makelabel{ref:ValuesOfClassFunction}{72.2.2}{X7FE14712843C6486} 5198\makelabel{ref:class functions as ring elements}{72.4}{X83B9F0C5871A5F7F} 5199\makelabel{ref:inverse of class function}{72.4}{X83B9F0C5871A5F7F} 5200\makelabel{ref:character value of group element using powering operator}{72.4}{X83B9F0C5871A5F7F} 5201\makelabel{ref:power meaning for class functions}{72.4}{X83B9F0C5871A5F7F} 5202\makelabel{ref: for class functions}{72.4}{X83B9F0C5871A5F7F} 5203\makelabel{ref:Characteristic for a class function}{72.4.1}{X83AAD5527BBAFA03} 5204\makelabel{ref:ComplexConjugate for a class function}{72.4.2}{X856AB97E785E0B04} 5205\makelabel{ref:GaloisCyc for a class function}{72.4.2}{X856AB97E785E0B04} 5206\makelabel{ref:Permuted for a class function}{72.4.2}{X856AB97E785E0B04} 5207\makelabel{ref:Order for a class function}{72.4.3}{X7BCE99B88285EB39} 5208\makelabel{ref:ViewObj for class functions}{72.5.1}{X7BDD2D4A7F7FB3B1} 5209\makelabel{ref:PrintObj for class functions}{72.5.2}{X871160B98595D4BA} 5210\makelabel{ref:Display for class functions}{72.5.3}{X8430D31B8163C230} 5211\makelabel{ref:ClassFunction for a character table and a list}{72.6.1}{X78F4E23985FCA259} 5212\makelabel{ref:ClassFunction for a group and a list}{72.6.1}{X78F4E23985FCA259} 5213\makelabel{ref:VirtualCharacter for a character table and a list}{72.6.2}{X7805AFF77EFC3306} 5214\makelabel{ref:VirtualCharacter for a group and a list}{72.6.2}{X7805AFF77EFC3306} 5215\makelabel{ref:Character for a character table and a list}{72.6.3}{X849DD34C7968206C} 5216\makelabel{ref:Character for a group and a list}{72.6.3}{X849DD34C7968206C} 5217\makelabel{ref:ClassFunctionSameType}{72.6.4}{X7B38035981D71B1B} 5218\makelabel{ref:TrivialCharacter for a character table}{72.7.1}{X86129DC37C55E4D6} 5219\makelabel{ref:TrivialCharacter for a group}{72.7.1}{X86129DC37C55E4D6} 5220\makelabel{ref:NaturalCharacter for a group}{72.7.2}{X82C01DDB82D751A9} 5221\makelabel{ref:NaturalCharacter for a homomorphism}{72.7.2}{X82C01DDB82D751A9} 5222\makelabel{ref:PermutationCharacter for a group, an action domain, and a function}{72.7.3}{X7938621F81B65E03} 5223\makelabel{ref:PermutationCharacter for two groups}{72.7.3}{X7938621F81B65E03} 5224\makelabel{ref:IsCharacter}{72.8.1}{X7FE3CD08794051F8} 5225\makelabel{ref:ordinary character}{72.8.1}{X7FE3CD08794051F8} 5226\makelabel{ref:Brauer character}{72.8.1}{X7FE3CD08794051F8} 5227\makelabel{ref:IsVirtualCharacter}{72.8.2}{X788DD05C86CB7030} 5228\makelabel{ref:virtual character}{72.8.2}{X788DD05C86CB7030} 5229\makelabel{ref:IsIrreducibleCharacter}{72.8.3}{X79A4B1D3870C8807} 5230\makelabel{ref:irreducible character}{72.8.3}{X79A4B1D3870C8807} 5231\makelabel{ref:DegreeOfCharacter}{72.8.4}{X7802BC157C69DD75} 5232\makelabel{ref:ScalarProduct for characters}{72.8.5}{X855FD9F983D275CD} 5233\makelabel{ref:constituent of a group character}{72.8.5}{X855FD9F983D275CD} 5234\makelabel{ref:decompose a group character}{72.8.5}{X855FD9F983D275CD} 5235\makelabel{ref:multiplicity of constituents of a group character}{72.8.5}{X855FD9F983D275CD} 5236\makelabel{ref:inner product of group characters}{72.8.5}{X855FD9F983D275CD} 5237\makelabel{ref:MatScalarProducts}{72.8.6}{X858DF4E67EBB99DA} 5238\makelabel{ref:Norm for a class function}{72.8.7}{X8572B18A7BAED73E} 5239\makelabel{ref:Norm of character}{72.8.7}{X8572B18A7BAED73E} 5240\makelabel{ref:ConstituentsOfCharacter}{72.8.8}{X78550D7087DB1181} 5241\makelabel{ref:KernelOfCharacter}{72.8.9}{X7E0A24498710F12B} 5242\makelabel{ref:ClassPositionsOfKernel}{72.8.10}{X7B4708B47D9C05B3} 5243\makelabel{ref:CentreOfCharacter}{72.8.11}{X7E77D4147A0836D3} 5244\makelabel{ref:centre of a character}{72.8.11}{X7E77D4147A0836D3} 5245\makelabel{ref:ClassPositionsOfCentre for a character}{72.8.12}{X7CE5B4137B399274} 5246\makelabel{ref:InertiaSubgroup}{72.8.13}{X7C3187387C2D9938} 5247\makelabel{ref:CycleStructureClass}{72.8.14}{X8269BE0079A64D43} 5248\makelabel{ref:IsTransitive for a character}{72.8.15}{X86EDB4047C5AD6E7} 5249\makelabel{ref:Transitivity for a character}{72.8.16}{X801DC07B8029841B} 5250\makelabel{ref:CentralCharacter}{72.8.17}{X7DD8FDCF7FB7834A} 5251\makelabel{ref:central character}{72.8.17}{X7DD8FDCF7FB7834A} 5252\makelabel{ref:DeterminantOfCharacter}{72.8.18}{X7A292A58827B95B8} 5253\makelabel{ref:determinant character}{72.8.18}{X7A292A58827B95B8} 5254\makelabel{ref:EigenvaluesChar}{72.8.19}{X861B435C7F68AE7D} 5255\makelabel{ref:Tensored}{72.8.20}{X7A106BE281EFD953} 5256\makelabel{ref:inflated class functions}{72.9}{X854A4E3A85C5F89B} 5257\makelabel{ref:RestrictedClassFunction}{72.9.1}{X86BABEA6841A40CF} 5258\makelabel{ref:RestrictedClassFunctions}{72.9.2}{X86DB64F08035D219} 5259\makelabel{ref:InducedClassFunction for a supergroup}{72.9.3}{X7FE39D3D78855D3B} 5260\makelabel{ref:InducedClassFunction for a given monomorphism}{72.9.3}{X7FE39D3D78855D3B} 5261\makelabel{ref:InducedClassFunction for the character table of a supergroup}{72.9.3}{X7FE39D3D78855D3B} 5262\makelabel{ref:InducedClassFunctions}{72.9.4}{X8484C0F985AD2D28} 5263\makelabel{ref:InducedClassFunctionsByFusionMap}{72.9.5}{X7C72003880743D28} 5264\makelabel{ref:InducedCyclic}{72.9.6}{X7C055F327C99CE71} 5265\makelabel{ref:ReducedClassFunctions}{72.10.1}{X86F360D983343C2A} 5266\makelabel{ref:ReducedCharacters}{72.10.2}{X7B7138ED8586F09E} 5267\makelabel{ref:IrreducibleDifferences}{72.10.3}{X7D3289BB865BCF98} 5268\makelabel{ref:LLL}{72.10.4}{X85B360C085B360C0} 5269\makelabel{ref:LLL algorithm for virtual characters}{72.10.4}{X85B360C085B360C0} 5270\makelabel{ref:short vectors spanning a lattice}{72.10.4}{X85B360C085B360C0} 5271\makelabel{ref:lattice basis reduction for virtual characters}{72.10.4}{X85B360C085B360C0} 5272\makelabel{ref:Extract}{72.10.5}{X808D71A57D104ED7} 5273\makelabel{ref:OrthogonalEmbeddingsSpecialDimension}{72.10.6}{X7F97B34A879D11BA} 5274\makelabel{ref:Decreased}{72.10.7}{X8799AB967C58C0E9} 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5507\makelabel{ref:InstallMethodWithRandomSource}{78.3.3}{X78CA646678B0539F} 5508\makelabel{ref:InstallOtherMethodWithRandomSource}{78.3.3}{X78CA646678B0539F} 5509\makelabel{ref:TryNextMethod}{78.5.1}{X7EED949B83046A7F} 5510\makelabel{ref:RedispatchOnCondition}{78.6.1}{X7D4A46CE7BCFCCF5} 5511\makelabel{ref:InstallImmediateMethod}{78.7.1}{X87B47AC0849611F8} 5512\makelabel{ref:InstallTrueMethod}{78.8.1}{X860B8B707995CFE3} 5513\makelabel{ref:SuspendMethodReordering}{78.8.2}{X7B26BDF68754DF7A} 5514\makelabel{ref:ResumeMethodReordering}{78.8.2}{X7B26BDF68754DF7A} 5515\makelabel{ref:ResetMethodReordering}{78.8.2}{X7B26BDF68754DF7A} 5516\makelabel{ref:overload}{78.9}{X855FE25783FB0D4E} 5517\makelabel{ref:Objectify}{79.1.1}{X7CB5C12E813F512B} 5518\makelabel{ref:ObjectifyWithAttributes}{79.1.2}{X85377AC07E775066} 5519\makelabel{ref:NamesOfComponents}{79.2.1}{X823965BF7DFDACC9} 5520\makelabel{ref:ExtRepOfObj}{79.8.1}{X8542B32A8206118C} 5521\makelabel{ref:ObjByExtRep}{79.8.1}{X8542B32A8206118C} 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5536\makelabel{ref:DeclareAttribute!example}{80.8.3}{X782AC35979925C71} 5537\makelabel{ref:ArithmeticElementCreator}{80.9.1}{X87A88E3D7F6E2A7C} 5538\makelabel{ref:HELPADDBOOK}{84.1.1}{X7CD0B8507A3D231D} 5539\makelabel{ref:HELPREMOVEBOOK}{84.1.2}{X7BDEB25D7AFC4322} 5540\makelabel{ref:document formats!for help books}{84.3}{X7AD7541E7C30D5B3} 5541\makelabel{ref:HELPVIEWERINFO}{84.4.1}{X84B011847A4D90F0} 5542\makelabel{ref:FOA triples}{85}{X8350247A8501969F} 5543\makelabel{ref:KeyDependentOperation}{85.1.1}{X7CABFDAA8596757E} 5544\makelabel{ref:InParentFOA}{85.2.1}{X7C0E62D8813A4EE6} 5545\makelabel{ref:ExternalSet computing orbits}{85.3}{X7CD4A0867BD825F7} 5546\makelabel{ref:G-sets computing orbits}{85.3}{X7CD4A0867BD825F7} 5547\makelabel{ref:Orbits as attributes for external sets}{85.3}{X7CD4A0867BD825F7} 5548\makelabel{ref:OrbitsishOperation}{85.3.1}{X7CA3826A7EBDE208} 5549\makelabel{ref:OrbitishFO}{85.3.2}{X7B23C48482ADB237} 5550\makelabel{ref:WeakPointerObj}{86.1.1}{X8155EE1386F46063} 5551\makelabel{ref:ElmWPObj}{86.2}{X7F4476958497F239} 5552\makelabel{ref:SetElmWPObj}{86.2.1}{X7B9748ED7BAAA379} 5553\makelabel{ref:UnbindElmWPObj}{86.2.1}{X7B9748ED7BAAA379} 5554\makelabel{ref:ElmWPObj}{86.2.1}{X7B9748ED7BAAA379} 5555\makelabel{ref:IsBoundElmWPObj}{86.2.1}{X7B9748ED7BAAA379} 5556\makelabel{ref:LengthWPObj}{86.2.1}{X7B9748ED7BAAA379} 5557\makelabel{ref:generalized conjugation technique}{87.1}{X870717BA831A0365} 5558\makelabel{ref:ordered partitions internal representation}{87.2.1}{X82E18F38824B5856} 5559\makelabel{ref:meet strategy}{87.2.4}{X86CCA2B384A74856} 5560