1# GAP Declarations 2# This file was generated from 3# $Id: algpath.gd,v 1.7 2012/08/01 16:01:10 sunnyquiver Exp $ 4DeclareProperty( "IsPathRing", IsMagmaRingModuloSpanOfZero ); 5DeclareProperty( "IsPathRing", IsAlgebra ); 6DeclareSynonym( "IsPathAlgebra", IsAlgebra and IsPathRing ); 7DeclareFilter("IsElementOfPathRing"); 8DeclareGlobalFunction( "PathRing" ); 9DeclareGlobalFunction( "PathAlgebra" ); 10DeclareAttribute( "QuiverOfPathRing", IsPathRing ); 11DeclareSynonymAttr( "QuiverOfPathAlgebra", QuiverOfPathRing ); 12DeclareGlobalFunction("FactorPathAlgebraByRelators"); 13DeclareCategory( "IsQuiverAlgebra", IsAlgebra ); 14InstallTrueMethod( IsQuiverAlgebra, IsPathAlgebra ); 15 16DeclareOperation( "LeadingTerm", [IsRingElement] ); 17DeclareSynonym("Tip", LeadingTerm); 18DeclareSynonym( "TipCoefficient", LeadingCoefficient ); 19DeclareSynonym( "TipMonomial", LeadingMonomial ); 20 21DeclareOperation( "IsLeftUniform", [IsRingElement]); 22DeclareOperation( "IsLeftUniform", [IsList,IsPath]); 23DeclareOperation( "IsRightUniform", [IsRingElement]); 24DeclareOperation( "IsRightUniform", [IsList,IsPath]); 25DeclareOperation( "IsUniform", [IsRingElement]); 26 27DeclareCategory( "IsQuotientOfPathAlgebra", IsQuiverAlgebra ); 28DeclareAttribute( "OrderingOfAlgebra", IsAlgebra ); 29DeclareAttribute( "GroebnerBasisOfIdeal", IsRing ); 30DeclareAttribute( "GroebnerBasisOfLeftIdeal", IsRing ); 31DeclareAttribute( "GroebnerBasisOfRightIdeal", IsRing ); 32 33DeclareCategory( "IsElementOfQuotientOfPathAlgebra", IsRingElement ); 34DeclareCategoryCollections( "IsElementOfQuotientOfPathAlgebra" ); 35DeclareCategoryFamily( "IsElementOfQuotientOfPathAlgebra" ); 36 37DeclareInfoClass( "InfoElementOfQuotientOfPathAlgebra" ); 38DeclareProperty("IsFullFpPathAlgebra", 39 IsFLMLOR and IsElementOfQuotientOfPathAlgebraCollection ); 40DeclareAttribute( "RelatorsOfFpAlgebra", 41 IsQuotientOfPathAlgebra and IsFullFpPathAlgebra); 42DeclareAttribute( "RelationsOfAlgebra", IsQuiverAlgebra); 43DeclareAttribute( "IdealOfQuotient", IsQuiverAlgebra); 44DeclareAttribute( "GroebnerBasisFunction", IsQuiverAlgebra ); 45DeclareAttribute( "NormalFormFunction", IsFamily ); 46DeclareOperation( "ElementOfQuotientOfPathAlgebra", 47 [ IsElementOfQuotientOfPathAlgebraFamily, IsRingElement, IsBool ] ); 48 49DeclareOperation( "ElementOfPathAlgebra", 50 [ IsPathAlgebra, IsPath ] ); 51 52 53DeclareHandlingByNiceBasis( "IsFpPathAlgebraElementsSpace", 54 "for spaces of f.p. path algebras" ); 55 56DeclareOperation( "BasisOfDomain", [IsQuotientOfPathAlgebra]); 57 58 59# (This should have been an operation with argument filters 60# [ IsElementOfPathAlgebra ], but that filter does not exist). 61DeclareGlobalFunction( "PathAlgebraContainingElement"); 62 63DeclareAttribute( "OriginalPathAlgebra", IsQuiverAlgebra ); 64DeclareOperation( "MakeUniformOnRight", [ IsHomogeneousList ] ); 65DeclareOperation( "GeneratorsTimesArrowsOnRight", [ IsHomogeneousList ] ); 66DeclareOperation( "NthPowerOfArrowIdeal", [ IsPathAlgebra, IS_INT ] ); 67DeclareOperation( "TruncatedPathAlgebra", [ IsField, IsQuiver, IS_INT ] ); 68DeclareOperation( "AddNthPowerToRelations", [ IsPathAlgebra, IsHomogeneousList, IS_INT ] ); 69 70DeclareAttribute( "OppositePathAlgebra", IsAlgebra ); 71DeclareGlobalFunction( "OppositePathAlgebraElement"); # should be operation with args [ IsElementOfPathAlgebra ] 72DeclareOperation( "OppositeRelations", [ IsDenseList ] ); 73DeclareOperation( "VertexPosition", [ IsElementOfQuotientOfPathAlgebra ] ); 74 75DeclareProperty( "IsSelfinjectiveAlgebra", IsQuiverAlgebra ); 76DeclareProperty( "IsSymmetricAlgebra", IsQuiverAlgebra ); 77DeclareProperty( "IsWeaklySymmetricAlgebra", IsQuiverAlgebra ); 78DeclareProperty( "IsSchurianAlgebra", IsQuiverAlgebra ); 79DeclareProperty( "IsSemicommutativeAlgebra", IsPathAlgebra); 80DeclareProperty( "IsSemicommutativeAlgebra", IsQuotientOfPathAlgebra); 81InstallTrueMethod( IsHereditaryAlgebra, IsPathAlgebra ); 82InstallTrueMethod( IsFiniteGlobalDimensionAlgebra, IsPathAlgebra ); 83 84DeclareAttribute( "CoxeterPolynomial", IsQuiverAlgebra ); 85DeclareAttribute( "CoxeterMatrix", IsQuiverAlgebra ); 86DeclareOperation( "TipMonomialandCoefficientOfVector", [ IsQuiverAlgebra, IsCollection ] ); 87DeclareOperation( "TipReduceVectors", [ IsQuiverAlgebra, IsCollection ] ); 88DeclareOperation( "CoefficientsOfVectors", [ IsAlgebra, IsCollection, IsList ] ); 89DeclareProperty( "IsDistributiveAlgebra", IsQuotientOfPathAlgebra ); 90DeclareAttribute( "NakayamaAutomorphism", IsQuotientOfPathAlgebra ); 91DeclareAttribute( "NakayamaPermutation", IsQuotientOfPathAlgebra ); 92DeclareAttribute( "OrderOfNakayamaAutomorphism", IsQuotientOfPathAlgebra ); 93DeclareAttribute( "AssociatedMonomialAlgebra", IsQuiverAlgebra ); 94DeclareProperty( "IsMonomialAlgebra", IsQuiverAlgebra ); 95DeclareOperation( "SaveAlgebra", [ IsQuiverAlgebra, IsString, IsString ]); 96DeclareOperation( "ReadAlgebra", [ IsString ]); 97DeclareProperty( "IsTriangularReduced", IsQuiverAlgebra ); 98DeclareOperation( "PathRemoval", [ IsElementOfMagmaRingModuloRelations, IsList ] ); 99DeclareOperation( "QuiverAlgebraOfAmodAeA", [ IsQuiverAlgebra, IsList ] );