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### Index

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

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