<, for two elements in a PathAlgebraModule 6.7-12<, for two elements in a path algebra 4.5-2<, for two elements of a path algebra 4.13-4<, for two paths in a quiver 3.7-7* 3.7-5., for a path algebra 4.4-4., for quiver 3.5-1/ 6.7-131stSyzygy 8.1-1= 3.7-6\* (maps) 7.2-3\+ (maps) 7.2-2\=, for two path algebra matrix modules 6.1-3\= (maps) 7.2-1\^ 10.2-6\in, elt. in path alg. and ideal 4.7-6^, a PathAlgebraMatModule element and a PathAlgebra element 6.3-1^, a PathAlgebraModule element and a PathAlgebra element 6.7-11AddNthPowerToRelations 4.7-5AdjacencyMatrixOfQuiver 3.5-4AdmitsFinitelyManyNontips 5.3-1AlgebraAsModuleOverEnvelopingAlgebra 4.16-11AlgebraAsQuiverAlgebra 4.17-1AllComplementsOfAlmostCompleteCotiltingModule 8.1-2AllComplementsOfAlmostCompleteTiltingModule 8.1-2AlmostSplitSequence 9.1-1AnnihilatorOfModule 6.4-1ARQuiverNumerical 13.3-1ARQuiverNumerical 13.3-1ARQuiverNumerical 13.3-1ARQuiverNumerical 13.3-1ArrowsOfQuiver 3.5-3AssignGeneratorVariables 4.6-1AssociatedMonomialAlgebra 4.4-1BasicVersionOfModule 6.4-2BasisOfProjectives 6.5-1BilinearFormOfUnitForm 12.2-2BlockDecompositionOfModule 6.4-3BlockSplittingIdempotents 6.4-4BoundariesOfComplex 10.5-6BrutalTruncation 10.6-6BrutalTruncationAbove 10.6-5BrutalTruncationBelow 10.6-4CanonicalAlgebra 4.14-1CartanMatrix 4.12-1CatOfComplex 10.5-1CatOfRightAlgebraModules 10.3-2Centre/Center 4.12-2ChainMap 10.7-2Coefficients 4.13-2CoKernel 7.3-1CoKernelOfWhat 7.2-4CoKernelProjection 7.3-2CommonDirectSummand 6.4-5ComparisonLifting 10.7-8ComparisonLiftingToProjectiveResolution 10.7-9CompletelyReduce 5.3-2CompletelyReduceGroebnerBasis 5.3-3CompletelyReduceGroebnerBasisForModule 6.7-2Complex 10.4-3ComplexAndChainMaps 10.7-5ComplexityOfAlgebra 4.12-3ComplexityOfModule 6.4-6ConnectedComponentsOfQuiver 3.5-11ConstantInfList 10.2-25CosyzygyTruncation 10.6-8CotiltingModule 8.1-3CoxeterMatrix 4.12-4CoxeterPolynomial 4.12-5Cut 10.2-20CyclesOfComplex 10.5-5DecomposeModule 6.4-7DecomposeModuleWithMultiplicities 6.4-8DegOrderDirectPredecessors 13.5-3DegOrderDirectSuccessors 13.5-6DegOrderLEQ 13.4-6DegOrderLEQNC 13.4-7DegOrderPredecessors 13.5-2DegOrderPredecessorsWithDirect 13.5-4DegOrderSuccessors 13.5-5DegOrderSuccessorsWithDirect 13.5-7DifferentialOfComplex 10.5-3DifferentialsOfComplex 10.5-4DimEnd 13.4-3Dimension 4.12-6Dimension, for a PathAlgebraMatModule 6.4-9DimensionVector 6.4-10DimensionVector, DimVectFT 13.4-1DimHom 13.4-2Direction 10.2-9DirectSumInclusions 6.4-12DirectSumOfQPAModules 6.4-11DirectSumProjections 6.4-13DominantDimensionOfAlgebra 8.1-4DominantDimensionOfModule 8.1-5DTr 6.6-3DualOfAlgebraAsModuleOverEnvelopingAlgebra 4.16-12DualOfModule 6.6-1DualOfModuleHomomorphism 6.6-2DualOfTranspose 6.6-3DynkinQuiver, DynkinQuiver 3.2-2ElementFunction 10.2-12ElementOfPathAlgebra 4.5-1ElementOfQuotientOfPathAlgebra 4.13-5EndModuloProjOverAlgebra 7.3-3EndOfModuleAsQuiverAlgebra 7.3-4EndOverAlgebra 7.3-5Enumerator 5.3-4EnvelopingAlgebra 4.16-9EulerBilinearFormOfAlgebra 12.2-9ExtAlgebraGenerators 8.1-6ExtOverAlgebra 8.1-7FaithfulDimension 8.1-8FiniteChainMap 10.7-4FiniteComplex 10.4-5FiniteInfList 10.2-26FinitePartAsList 10.2-36ForEveryDegree 10.5-17FromEndMToHomMM 7.3-6FromHomMMToEndM 7.3-7FullSubquiver 3.5-10FunctionInfList 10.2-24GeneratorsOfQuiver 3.5-5GlobalDimension 4.12-7GlobalDimensionOfAlgebra 8.1-9GorensteinDimension 8.1-10GorensteinDimensionOfAlgebra 8.1-11GroebnerBasis 5.1-2GroebnerBasisOfIdeal 4.10-1HalfInfList 10.2-21HaveFiniteCoresolutionInAddM 8.1-12HaveFiniteResolutionInAddM 8.1-13HighestKnownDegree 10.5-12HighestKnownPosition 10.2-32HighestKnownValue 10.2-18HomFactoringThroughProjOverAlgebra 7.3-8HomFromProjective 7.3-9HomologyOfComplex 10.5-7HomomorphismFromImages 7.2-27HomOverAlgebra 7.3-10Ideal 4.7-1IdealOfQuotient 4.7-2IdentityMapping 7.2-5Image 7.3-11ImageElm 7.2-6ImageInclusion 7.3-12ImageOfWhat 7.2-8ImageProjection 7.3-13ImageProjectionInclusion 7.3-14ImagesSet 7.2-7IncludeInProductQuiver 4.16-4IncomingArrowsOfVertex 3.8-1IndecInjectiveModules 6.5-2IndecProjectiveModules 6.5-3InDegreeOfVertex 3.8-3InfConcatenation 10.2-41InfList 10.2-42InfListType 10.2-10InfoGroebnerBasis 5.1-1InfoQuiver 3.1-1InitialValue 10.2-16InjDimension 8.1-14InjDimensionOfModule 8.1-15InjectiveEnvelope 8.1-16InjectiveResolution 11.1-1IntegersList 10.2-43IntersectionOfSubmodules 6.4-14IsAcyclicQuiver 3.3-2IsAdmissibleIdeal 4.8-1IsAdmissibleQuotientOfPathAlgebra 4.11-1IsARQuiverNumerical 13.3-2IsArrow 3.6-3IsBasicAlgebra 4.17-2IsCanonicalAlgebra 4.11-4IsCat 10.3-1IsChainMap 10.7-1IsCompleteGroebnerBasis 5.2-2IsCompletelyReducedGroebnerBasis 5.2-1IsConnectedQuiver 3.3-4IsCotiltingModule 8.1-17IsDirectSummand 6.4-15IsDirectSumOfModules 6.4-16IsDistributiveAlgebra 4.11-5IsDynkinQuiver 3.3-6IsElementaryAlgebra 4.17-3IsElementOfQuotientOfPathAlgebra 4.13-1IsEnvelopingAlgebra 4.16-10IsExactInDegree 10.5-15IsExactSequence 10.5-14IsExceptionalModule 6.4-17IsFiniteComplex 10.5-8IsFiniteDimensional 4.11-3IsFiniteGlobalDimensionAlgebra 4.11-6IsFiniteTypeAlgebra 4.11-23IsGentleAlgebra 4.11-7IsGorensteinAlgebra 4.11-8IsGroebnerBasis 5.2-3IsHalfInfList 10.2-5IsHereditaryAlgebra 4.11-9IsHomogeneousGroebnerBasis 5.2-4IsIdealInPathAlgebra 4.8-2IsInAdditiveClosure 6.4-19IsIndecomposableModule 6.4-18IsInfiniteNumber 10.2-1IsInfList 10.2-4IsInjective 7.2-9IsInjectiveComplex 11.1-3IsInjectiveModule 6.4-20IsIsomorphism 7.2-10IsKroneckerAlgebra 4.11-10IsLeftDivisible 6.7-3IsLeftMinimal 7.2-11IsLeftUniform 4.5-3IsMonomialAlgebra 4.11-11IsMonomialIdeal 4.8-3IsNakayamaAlgebra 4.11-12IsNormalForm 4.13-3IsOmegaPeriodic 8.1-18IsomorphicModules 6.4-21IsomorphismOfModules 7.3-15IsPath 3.6-1IsPathAlgebra 4.3-1IsPathAlgebraMatModule 6.2-1IsPathAlgebraModule 6.7-4IsPathAlgebraModuleHomomorphism 7.1-1IsPathAlgebraVector 6.7-5IsPrefixOfTipInTipIdeal 5.3-5IsProjectiveComplex 11.1-2IsProjectiveModule 6.4-22IsQPAComplex 10.4-1IsQuadraticIdeal 4.8-4IsQuiver 3.3-1IsQuiverAlgebra 4.11-13IsQuiverProductDecomposition 4.16-3IsQuiverVertex 3.6-2IsQuotientOfPathAlgebra 4.11-2IsRadicalSquareZeroAlgebra 4.11-14IsRepeating 10.2-15IsRightGroebnerBasis 5.4-1IsRightMinimal 7.2-12IsRightUniform 4.5-4IsRigidModule 6.4-23IsSchurianAlgebra 4.11-15IsSelfinjectiveAlgebra 4.11-16IsSemicommutativeAlgebra 4.11-17IsSemisimpleAlgebra 4.11-18IsSemisimpleModule 6.4-24IsShortExactSequence 10.5-16IsSimpleQPAModule 6.4-25IsSpecialBiserialAlgebra 4.11-19IsSpecialBiserialQuiver 4.14-5IsSplitEpimorphism 7.2-13IsSplitMonomorphism 7.2-14IsStoringValues 10.2-13IsStringAlgebra 4.11-20IsSurjective 7.2-15IsSymmetricAlgebra 4.11-21IsTauPeriodic 9.1-2IsTauRigidModule 6.4-26IsTipReducedGroebnerBasis 5.2-5IsTreeQuiver 3.3-5IsTtiltingModule 8.1-19IsUAcyclicQuiver 3.3-3IsUniform 4.5-5IsUnitForm 12.2-1IsWeaklyNonnegativeUnitForm 12.2-3IsWeaklyPositiveUnitForm 12.2-4IsWeaklySymmetricAlgebra 4.11-22IsZero 6.4-28IsZero 7.2-16IsZeroComplex 10.4-2IsZeroPath 3.6-4Iterator 5.3-6IyamaGenerator 8.1-20Kernel 7.3-16KernelInclusion 7.3-16KernelOfWhat 7.2-17KroneckerAlgebra 4.14-2LeadingCoefficient 4.5-7LeadingCoefficient (of PathAlgebraVector) 6.7-6LeadingComponent 6.7-7LeadingMonomial 4.5-8LeadingPosition 6.7-8LeadingTerm 4.5-6LeadingTerm (of PathAlgebraVector) 6.7-9LeftApproximationByAddTHat 8.1-21LeftDivision 6.7-10LeftFacMApproximation 8.1-22LeftInverseOfHomomorphism 7.2-18LeftMinimalVersion 7.3-17LeftMutationOfCotiltingModuleComplement 8.1-23LeftMutationOfTiltingModuleComplement 8.1-23LeftSubMApproximation 8.1-24LengthOfComplex 10.5-11LengthOfPath 3.7-3LiftingCompleteSetOfOrthogonalIdempotents 4.18-1LiftingIdempotent 4.18-2LiftingInclusionMorphisms 8.1-25LiftingMorphismFromProjective 8.1-26LoewyLength 4.12-8LoewyLength, for a PathAlgebraMatModule 6.4-27LowerBound 10.2-35LowerBound 10.5-10LowestKnownDegree 10.5-13LowestKnownPosition 10.2-17LowestKnownPosition 10.2-33MakeHalfInfList 10.2-7MakeInfList 10.2-23MakeInfListFromHalfInfLists 10.2-22MakeUniformOnRight 4.5-9MappedExpression 4.5-10MappingCone 10.7-10MatricesOfPathAlgebraMatModuleHomomorphism 7.2-19MatricesOfPathAlgebraModule 6.4-29MaximalCommonDirectSummand 6.4-30MiddleEnd 10.2-28MiddlePart 10.2-29MiddleStart 10.2-27MinimalGeneratingSetOfModule 6.4-32MinimalLeftAddMApproximation 8.1-27MinimalLeftApproximation 8.1-27MinimalLeftFacMApproximation 8.1-22MinimalLeftSubMApproximation 8.1-24MinimalRightAddMApproximation 8.1-28MinimalRightApproximation 8.1-28MinimalRightFacMApproximation 8.1-40MinimalRightSubMApproximation 8.1-42ModulesOfDimVect 13.5-1MorphismOfChainMap 10.7-6MorphismOnCoKernel 8.1-29MorphismOnImage 8.1-29MorphismOnKernel 8.1-29MorphismsOfChainMap 10.7-7N_RigidModule 8.1-43NakayamaAlgebra 4.14-3NakayamaAutomorphism 4.12-9NakayamaFunctorOfModule 6.6-4NakayamaFunctorOfModuleHomomorphism 6.6-5NakayamaPermutation 4.12-10NegativeInfinity 10.2-3NegativePart 10.2-31NegativePartFrom 10.2-38NeighborsOfVertex 3.8-5NewValueCallback 10.2-14Nontips 5.3-7NontipSize 5.3-8NthPowerOfArrowIdeal 4.7-4NthSyzygy 8.1-30NthSyzygyNC 8.1-31NumberOfArrows 3.5-7NumberOfComplementsOfAlmostCompleteCotiltingModule 8.1-32NumberOfComplementsOfAlmostCompleteTiltingModule 8.1-32NumberOfIndecomposables 13.3-3NumberOfNonIsoDirSummands 6.4-31NumberOfProjectives 13.3-4NumberOfVertices 3.5-6ObjectOfComplex 10.5-2OppositePath 4.15-1OppositePathAlgebra 4.15-2OppositePathAlgebraElement 4.15-3OppositeQuiver 3.5-9OrbitCodim 13.4-5OrbitDim 13.4-4OrderedBy 3.2-3OrderingOfAlgebra 4.4-3OrderingOfQuiver 3.5-8OrderOfNakayamaAutomorphism 4.12-11OriginalPathAlgebra 4.13-6OutDegreeOfVertex 3.8-4OutgoingArrowsOfVertex 3.8-2PathAlgebra 4.2-1PathAlgebraOfMatModuleMap 7.2-20PathAlgebraVector 6.7-14PathsOfLengthTwo 4.7-3PositiveInfinity 10.2-2PositivePart 10.2-30PositivePartFrom 10.2-37PositiveRootsOfUnitForm 12.2-5PredecessorOfModule 9.1-3PreImagesRepresentative 7.2-21PrimitiveIdempotents 4.17-4PrintMultiplicityVector 13.4-8PrintMultiplicityVectors 13.4-9ProductOfIdeals 4.9-1ProjDimension 8.1-33ProjDimensionOfModule 8.1-34ProjectFromProductQuiver 4.16-5ProjectiveCover 8.1-35ProjectivePathAlgebraPresentation 6.7-15ProjectiveResolution 11.1-4ProjectiveResolutionOfComplex 11.2-1ProjectiveResolutionOfPathAlgebraModule 8.1-36ProjectiveToInjectiveComplex 11.2-2ProjectiveToInjectiveFiniteComplex 11.2-2PullBack 8.1-37PushOut 8.1-38QuadraticFormOfUnitForm 12.2-6QuadraticPerpOfPathAlgebraIdeal 4.9-2Quiver, adjacenymatrix 3.2-1Quiver, lists of vertices and arrows 3.2-1Quiver, no. of vertices, list of arrows 3.2-1QuiverOfPathAlgebra 4.4-2QuiverProduct 4.16-1QuiverProductDecomposition 4.16-2RadicalOfModule 6.4-33RadicalOfModuleInclusion 7.3-19RadicalSeries 6.4-34RadicalSeriesOfAlgebra 4.12-12Range 7.2-22ReadAlgebra 4.19-1RejectOfModule 7.3-20RelationsOfAlgebra 4.5-12RepeatingList 10.2-11RightAlgebraModuleToPathAlgebraMatModule 6.1-2RightApproximationByPerpT 8.1-39RightFacMApproximation 8.1-40RightGroebnerBasis 5.4-2RightGroebnerBasisOfIdeal 5.4-3RightGroebnerBasisOfModule 6.7-16RightInverseOfHomomorphism 7.2-23RightMinimalVersion 7.3-18RightModuleHomOverAlgebra 7.1-2RightModuleOverPathAlgebra, no dimension vector 6.1-1RightModuleOverPathAlgebra, with dimension vector 6.1-1RightModuleOverPathAlgebraNC, no dimension vector 6.1-1RightMutationOfCotiltingModuleComplement 8.1-41RightMutationOfTiltingModuleComplement 8.1-41RightProjectiveModule 6.7-1RightSubMApproximation 8.1-42SaveAlgebra 4.19-2SeparatedQuiver 3.5-12Shift 10.2-19Shift 10.2-39Shift 10.6-1ShiftUnsigned 10.6-2ShortExactSequence 10.4-7SimpleModules 6.5-4SimpleTensor 4.16-7SocleOfModule 6.4-36SocleOfModuleInclusion 7.3-21SocleSeries 6.4-35Source 7.2-24SourceOfPath 3.7-1Splice 10.2-40StalkComplex 10.4-6StarOfMapBetweenDecompProjectives 11.2-5StarOfMapBetweenIndecProjectives 11.2-5StarOfMapBetweenProjectives 11.2-5StarOfModule 6.6-6StarOfModuleHomomorphism 6.6-7StartPosition 10.2-8SubRepresentation 6.4-37SubRepresentationInclusion 7.3-22SumOfSubmodules 6.4-38SupportModuleElement 6.4-39SymmetricMatrixOfUnitForm 12.2-7SyzygyCosyzygyTruncation 10.6-9SyzygyTruncation 10.6-7TargetOfPath 3.7-2TargetVertex 6.7-17TauOfComplex 11.2-3TensorProductDecomposition 4.16-8TensorProductOfAlgebras 4.16-6TiltingModule 8.1-44Tip 4.5-6TipCoefficient 4.5-7TipMonomial 4.5-8TipReduce 5.3-9TipReduceGroebnerBasis 5.3-10TitsUnitFormOfAlgebra 12.2-8TopOfModule 6.4-40TopOfModuleProjection 7.3-23TraceOfModule 7.3-24TransposeOfDual 6.6-8TransposeOfModule 6.6-9TrD 6.6-8TrivialExtensionOfQuiverAlgebra 4.16-13TruncatedPathAlgebra 4.14-4UniformGeneratorsOfModule 6.7-18UnitForm 12.2-10UpperBound 10.2-34UpperBound 10.5-9Vectorize 6.7-19VertexPosition 4.5-11VerticesOfQuiver 3.5-2WalkOfPath 3.7-4YonedaProduct 10.6-3Zero 7.2-25ZeroChainMap 10.7-3ZeroComplex 10.4-4ZeroMapping 7.2-26ZeroModule 6.5-5
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