DONE-QPA1.txt

Functions that have changed names
============================================================

AlgebraAsModuleOverEnvelopingAlgebra( A ) -> AlgebraAsBimodule( A ) (undocumented)
AllComplementsOfAlmostCompleteTiltingModule( <M>, <X> ) -> AllComplementsOfAlmostCompleteTiltingRepresentation( <R>, <X> )
AllComplementsOfAlmostCompleteCoiltingModule( <M>, <X> ) -> AllComplementsOfAlmostCompleteCotiltingRepresentation( <R>, <X> )
AnnihilatorOfModule( M ) -> AnnihilatorOfModule( M ) and AnnihilatorOfRepresentation( R )
ArrowsOfQuiver( quiver )   -> Arrows( quiver )

BasicVersionOfModule( M ) -> BasicVersionOfRepresentation( R )
BlockDecompositionOfModule( M ) -> BlockDecompositionOfModule( M ) and BlockDecompositionOfRepresentation( R )

CoKernel( f ) -> CokernelObject( f ) (from CAP, undocumented in QPA)
CoKernelProjection( f ) -> CokernelProjection( f ) (from CAP, undocumented in QPA)
CompletelyReduce( GB, a ) -> Reduce( e, divisors ) # divisors is a list containing the elements of GB
ComplexityOfModule( M, n ) ->  ComplexityOfModule( M, n )  and ComplexityOfRepresentation( R, n )
ConnectedComponentsOfQuiver( quiver ) -- ConnectedComponents( quiver )
CotiltingModule( M, n ) -> CotiltingRepresentation( R, n )

DecomposeModule( M ) -> DecomposeModule( M )  and DecomposeRepresentation( R )
DecomposeModuleWithMultiplicities( M ) -> DecomposeModuleWithMultiplicities( M )  and  DecomposeRepresentationWithMultiplicities( R ) 
DirectSumOfQPAModules( L ) -> DirectSum( L ) (CAP operation, undocumented in QPA)
DirectSumInclusions( M ) -- use CAP operation InjectionOfCofactorOfDirectSum
DirectSumProjections( M ) -- use CAP operation ProjectionInFactorOfDirectSum
DominantDimensionOfModule( <M>, <n> ) -> DominantDimensionOfRepresentation( M, n )
DualOfAlgebraAsModuleOverEnvelopingAlgebra( A ) -> 
					    DualOfAlgebraAsLeftModule( A ), DualOfAlgebraAsRightModule( A ),
					    DualOfAlgebraAsBimodule( A ), DualOfAlgebraAsModule( side, A )
DualOfModule( M ) -> DualOfModule( M ), DualOfRepresentation( R )
DualOfModuleHomomorphism( f ) -> DualOfRepresentationHomomorphism
DynkinQuiver( Delta, n, orientation) --> DynkinQuiver( args ), LeftDynkinQuiver( Delta, n, orientation ),
	      	     		     	 	       	       			 RightDynkinQuiver( Delta, n, orientation )

ElementOfPathAlgebra( PA, path ) -> PathAsAlgebraElement( PA, path )
ElementOfQuotientOfPathAlgebra( family, element, computenormal ) -> QuotientOfPathAlgebraElement( A, element )
EndOverAlgebra( M ) -> EndomorphismAlgebra( M ), EndomorphismAlgebra( R )
EndModuloProjOverAlgebra( M ) -> StableEndomorphismAlgebraModuleProj( R )

f * g -> PreCompose( f, g ) (from CAP, undocumented in QPA)
FromEndMToHomMM( f ) -> FromEndMToHomMM( f ), FromEndRToHomRR( f )
FromHomMMToEndM( f ) -> FromHomRRToEndR( f )

GeneratorsOfQuiver( quiver ) -> PrimitivePaths( quiver )
GroebnerBasis( I, rels ) -> GroebnerBasis( I )
GroebnerBasisOfIdeal( I ) -> GroebnerBasis( I )

HaveFiniteResolutionInAddM( <N>, <M>, <n> ) -> FiniteResolutionInAddR( N, M, n )
HaveFiniteCoresolutionInAddM( <N>, <M>, <n> ) -> FiniteCoresolutionInAddR( N, M, n )
HomFactoringThroughProjOverAlgebra( M, N ) -> HomFactoringThroughProj( M, N )
HomOverAlgebra( M, N ) -> Hom( M, N ) # returns vector space instead of list

Ideal( FQ, elems ) -> QuiverAlgebraTwoSidedIdeal( FQ, elems )
IdentityMapping( M ) -> IdentityMorphism( M ) (from CAP, undocumented in QPA)
Image( f ) -> ImageObject( f ) (from CAP, undocumented in QPA)
ImageInclusion( f ) -> ImageEmbedding( f ) (from CAP, undocumented in QPA)
ImageProjection( f ) -> CoastrictionToImage( f ) (from CAP, undocumented in QPA)
IncludeInProductQuiver( L, Q ) -> PathInProductQuiver( Q, L )
IncomingArrowsOfVertex( vertex ) -> IncomingArrows( vertex )
IndecInjectiveModules( A ) -> IndecInjRepresentations( A ) and IndecInjModule( side, A), IndecInjLeftModules( A ),
		       	      			       	 IndecInjRightModules( A ), IndecInjBimodules( A )
IndecProjectiveModules( A ) -> IndecProjRepresentations( A ) and IndecProjModule( side, A), IndecProjLeftModules( A ),
			       				 IndecProjRightModules( A ), IndecProjBimodules( A )
InDegreeOfVertex( vertex ) -> Indegree( vertex )
InjDimensionOfModule( <M>, <n> ) -> InjDimensionOfObject( M, n )
IntersectionOfSubmodules( list ) -- IntersectionOfModules( L ) and IntersectionOfRepresentations( L )
IsAdmissibleQuotientOfPathAlgebra( A ) -> IsAdmissibleQuiverAlgebra( A )
IsConnectedQuiver( quiver ) -> IsConnected( quiver )
IsCotiltingModule( M ) -> IsCotiltingObject( R )
IsElementOfQuotientOfPathAlgebra( obj ) -> IsQuotientOfPathAlgebraElement( obj )
IsExceptionalModule( M ) -> IsExceptionalModule( M ), IsExceptionalRepresentation( R )
IsIndecomposableModule( M ) -> IsIndecomposableModule( M )  and IsIndecomposableRepresentation( R ) 
IsInjective( f ) -> IsMonomorphism( f ) (from CAP, undocumented)
IsomorphicModules( M, N ) -> IsomorphicModules( M, N ), IsomorphicRepresentations( R1, R2 )
IsPath( obj ) -> IsPath( obj ), IsLeftPath( obj), IsRightPath( obj )
IsPathAlgebraMatModule( obj ) -> IsQuiverModule( obj ) / IsRightQuiverModule( obj )
IsPathAlgebraModuleHomomorphism( f ) -> IsQuiverModuleHomomorphism( f )
IsProjectiveModule( M ) -> IsProjectiveModule( M ), IsProjectiveRepresentation( R )
IsQuadraticIdeal( I ) -> IsQuadraticElements( list )
IsQuiver( obj )            -> IsQuiver( obj ), IsLeftQuiver, IsRightQuiver( obj )

IsRigidModule( M ) -> IsRigidObject( M )
IsSemisimpleModule( M ) -> IsSemisimpleRepresentation( R )
IsSimpleQPAModule( M ) -> IsSimpleRepresentation( R ) and IsSimpleQuiverModule( M )
IsSurjective( f ) -> IsEpimorphism( f ) (from CAP, undocumented)
IsTiltingModule( M ) -> IsTiltingObject( R )
IsUAcyclicQuiver( quiver ) -> IsUnorientedAcyclicQuiver( quiver )

KernelInclusion( f ) -> KernelEmbedding( f ) (from CAP, undocumented in QPA)

LeadingMonomial( element ), TipMonomial( element ) -> LeadingPath( element )
LeftApproximationByAddM( M, C) -> LeftApproximationByAddR( R, C )
LeftFacMApproximation( <C>, <M> ) -> LeftApproximationByFacR( C, R )
LeftMutationOfCotiltingModuleComplement( <M>, <N> ) -> LeftMutationOfCotiltingRepresentationComplement
LeftMutationOfTiltingModuleComplement( <M>, <N> ) -> LeftMutationOfTiltingRepresentationComplement
LeftSubMApproximation( <C>, <M> ) -> LeftApproximationBySubR( C, M )
LengthOfPath( path ) -> Length( path )
LiftingIdempotent( f, e ) -> LiftIdempotent( f, e )


MatricesOfPathAlgebraModule( M ) -> MatricesOfRepresentation( UnderlyingRepresentation( M ) ) # gives QPA matrices
MatricesOfPathAlgebraMatModuleHomomorphism( f ) -- MatricesOfModuleHomomorphism( f ) # gives QPA matrices,
					      	   				       	     MatricesOfRepresentationHomomorphism( f )
MinimalGeneratingSetOfModule( R ) -> MinimalGeneratingSet( R ) for representations
MinimalLeftApproximation( C, M ) -> MinimalLeftApproximationByAddR( C, R )
MinimalLeftFacMApproximation( <C>, <M> ) -> MinimalLeftApproximation( C, R )
MinimalLeftSubMApproximation( <C>, <M> ) -> MinimalLeftApproximationBySubR( C, M )
MinimalRightApproximation( M, C ) -> MinimalRightApproximationByAddR( R, C )
MinimalRightSubMApproximation( <M>, <C> ) ->MinimalRightApproximationBySubR( R, C )

NakayamaAlgebra( admiss_seq, field ) -> NakayamaAlgebra( args), LeftNakayamaAlgebra( args ),
		 	     	     			 			     RightNakayamaAlgebra( field, admiss_seq )
NeighborsOfVertex( vertex ) -> Neighbors( vertex )
N_RigidModule( <M>, <n> ) -> IsN_RigidObject( R, n )
NumberOfComplementsOfAlmostCompleteTiltingModule( <R> ) ->  NumberOfComplementsOfAlmostCompleteTiltingRepresentation( R )
NumberOfComplementsOfAlmostCompleteCotiltingModule( <R> ) ->  NumberOfComplementsOfAlmostCompleteCotiltingRepresentation( R )
NumberOfNonIsoDirSummands( M ) -> NumberOfNonIsoDirectSummands( R )

OppositePathAlgebra( A ) -> OppositeAlgebra( A )
OppositePathAlgebraElement( x ) -> OppositeAlgebraElement( x )
OutDegreeOfVertex( vertex ) -> Outdegree( vertex )
OutgoingArrowsOfVertex( vertex ) -> OutgoingArrows( vertex )

PrimitiveIdempotents( A ) -> CompleteSetOfPrimitiveIdempotents( A )
ProjDimensionOfModule( <R>, <n> ) -> ProjDimensionOfObject( M, n )
ProjectFromProductQuiver( i, p ) -> ProjectPathFromProductQuiver( i, p )

Quiver( N, arrows )        -> Quiver( args ), LeftQuiver( args ), RightQuiver( args )
Quiver( vertices, arrows ) -> RightQuiver( "Q", vertices, arrows ) # different format for arrows
Quiver( adjacencymatrix )  -> Quiver( direction, name, matrix )
QuiverOfPathAlgebra( FQ ) -> QuiverOfAlgebra( FQ )
QuiverProductDecomposition( Q ) -> ProductQuiverFactors( Q )

RadicalOfModule( M ) -> RadicalOfModule( M ), RadicalOfRepresentation( R )
RadicalOfModuleInclusion( R ) -> RadicalInclusion( R ) for representations
RejectOfModule( M, N ) -> RejectOfRepresentation( R, N )
RightAlgebraModuleToPathAlgebraMatModule( M ) -> RightAlgebraModuleToRightQuiverModule( M )
RightApproximationByAddR( C, M) -> RightApproximationByAddR( C, R )
RightModuleHomOverAlgebra( M, N, mats ) -> QuiverModuleHomomorphism( M, N, mats ) # different format for mats
RightModuleOverPathAlgebra( A, dim_vector, gens ) -> RightQuiverModule( A, dim_vector, matrices ) # different format for matrices
RightModuleOverPathAlgebra( A, mats ) -- no (use RightQuiverModule)
RightModuleOverPathAlgebraNC( A, mats ) -- no (use RightQuiverModule)
RightModuleOverPathAlgebra -> QuiverRepresentation, QuiverRepresentationNC
RightMutationOfCotiltingModuleComplement( <M>, <N> ) -> RightMutationOfCotiltingRepresentationComplement( M, N )
RightMutationOfTiltingModuleComplement( <M>, <N> ) -> RightMutationOfTiltingRepresentationComplement(M, N ) 
RightSubMApproximation( <M>, <C> ) -> RightApproximationBySubR( R, C )

SimpleModules( A ) ->  SimpleRepresentations( A) and SimpleModule( side, A), SimpleLeftModules( A ),
	       	       			      	     		   SimpleRightModules( A ), SimpleBimodules( A 
SimpleTensor( L, T ) -> ElementaryTensor( a, b, T )
SourceOfPath( path ) -> Source( path )
SocleOfModule( M ) -> SocleOfRepresentation( R )
SocleOfModuleInclusion( M ) -> SocleOfRepresentationInclusion( R )
SourceOfPath( path ) -> Source( path )
SubRepresentationInclusion( M, gens ) -> SubrepresentationInclusion( R, gens )
SumOfSubmodules( f, g ) -> SumOfSubobjects( list )
SupportModuleElement( m ) -> SupportOfElement( m ) for representations

TargetOfPath( path ) -> Target( path )
TensorAlgebrasInclusion( T, n ) -> TensorAlgebraInclusions( T )[ n ]
TensorProductDecomposition( T ) -> TensorProductFactors( T ) (undocumented)
TiltingModule( M, n ) -> TiltingRepresentation( R, n )
Tip( element ) -> LeadingTerm( element )
TipCoefficient( element ) -> LeadingCoefficient( element )
TopOfModule( M ) -> TopOfModule( M ), TopOfRepresentation( R )
TopOfModuleProjection( R ) -> TopProjection( R ) for representations
TraceOfModule( M, N ) -> TraceOfRepresentation( R, N )

VertexPosition( element ) -- can use VertexNumber( LeadingPath( element ) )
VerticesOfQuiver( quiver ) -> Vertices( quiver )

WalkOfPath( path ) -> ArrowList( path )

ZeroMapping( M, N ) -> ZeroMorphism( M ) (from CAP, undocumented in QPA)
ZeroModule( A ) -> RightZeroModule( A ), ZeroRepresentation( A )

Functions that are the same
============================================================

AddNthPowerToRelations( FQ, rels, n ) 
AdjacencyMatrixOfQuiver( quiver ) 
AlgebraAsQuiverAlgebra( A )
AlmostSplitSequence( M, side )
AssociatedMonomialAlgebra( A ) 

BasisOfProjectives( A )
BilinearFormOfUnitForm
BlockSplittingIdempotents( M ) -- for modules and representations

CanonicalAlgebra( field, weights[, relcoeff] )
CartanMatrix( A ) 
Centre( A ), Center( A )
Coefficients( B, element ) 
CommonDirectSummand( M, N ) 
ComplexityOfAlgebra( A, n )
CoxeterMatrix( A ) 
CoxeterPolynomial( A ) 

Dimension( A ) -- same (undocumented) 
Dimension( M )
DimensionVector( R )
DominantDimension( R )
DominantDimensionOfAlgebra( A, n )
DTr( M[, n ] ), DualOfTranspose( M[, n ] ) 

EnvelopingAlgebra( A )
EulerBilinearFormOfAlgebra

GlobalDimension( A ) 
GlobalDimensionOfAlgebra( A, n )
GorensteinDimension( A )
GorensteinDimensionOfAlgebra( A, n )

f = g -- (undocumented)
f + g -- (undocumented)
FaithfulDimension( M )
FullSubquiver( quiver, list )

Ideal( FQ, elems )
IdealOfQuotient( A ) 
InjDimension( M )
InjectiveEnvelope( M )
IsAcyclicQuiver( quiver ) 
IsAdmissibleIdeal( I )
IsArrow( obj ) -- same (change name to IsQuiverArrow)
IsBasicAlgebra( A )
IsCanonicalAlgebra( A ) 
IsDirectSummand( M, N )
IsDistributiveAlgebra( A )
IsDynkinQuiver( quiver )  
IsElementaryAlgebra( A )
IsFiniteDimensional( A )
IsFiniteGlobalDimensionAlgebra( A )
IsFiniteTypeAlgebra( A )
IsGentleAlgebra( A )
IsGorensteinAlgebra( A )
IsHereditaryAlgebra( A )
IsInAdditiveClosure( M, N ) 
IsIsomorphism( f ) -- (from CAP, undocumented)
IsKroneckerAlgebra( A )
IsLeftUniform( element )
IsLeftMinimal( f )
IsMonomialIdeal( I )
IsNakayamaAlgebra( A )
IsNthSyzygy( R )
IsOmegaPeriodic( M )
IsPathAlgebra( obj )
IsQuiverAlgebra( A )
IsQuiverVertex( obj ) 
IsQuotientOfPathAlgebra( object )
IsRadicalSquareZeroAlgebra( A )
IsRightMinimal( f )
IsRightUniform( element )
IsSchurianAlgebra( A ) 
IsSelfinjectiveAlgebra( A ) 
IsSemicommutativeAlgebra( A ) 
IsSemisimpleAlgebra( A )
IsSpecialBiserialQuiver( Q )
IsSpecialBiserialAlgebra( A )
IsSplitEpimorphism( f ) -- (from CAP, undocumented)
IsSplitMonomorphism( f ) -- (from CAP, undocumented)
IsStringAlgebra( A ) 
IsSymmetricAlgebra( A )
IsTauRigidModule( M )
IsTriangularReduced( A ) 
IsTreeQuiver( quiver ) 
IsUniform( element )
IsWeaklyNonnegativeUnitForm
IsWeaklyPositiveUnitForm
IsWeaklySymmetricAlgebra( A )
IsZero( f ) -- (from CAP, undocumented)
IyamaGenerator( M )

Kernel( f ) -- (from CAP, undocumented in QPA)
KroneckerAlgebra( field, n ) 

LeadingTerm( element )
LeadingCoefficient( element )
LeftApproximationByAddTHat( T, M )
LeftInverseOfHomomorphism( f )
LeftMinimalVersion( f ) 
LiftingCompleteSetOfOrthogonalIdempotents( f, e )
LoewyLength( A )
LoewyLength( M )

M = N 
m ^ p -- same (action of an element from a path algebra on a module)
MaximalCommonDirectSummand( M, N )
MinimalGeneratingSetOfIdeal( I )

NakayamaAutomorphism( A )
NakayamaFunctorOfModule( M ) 
NakayamaFunctorOfModuleHomomorphism( f ) 
NakayamaPermutation( A )
NthPowerOfArrowIdeal( FQ, n )
NthSyzygy( M, n )
NumberOfArrows( quiver )
NumberOfVertices( quiver )

OppositePath( p )
OppositeQuiver( quiver )
OrderOfNakayamaAutomorphism( A )

p * q -- same for paths
p = q -- same for paths
p < q -- same for paths (undocumented)
PartialIyamaGenerator( M )
PartialOrderOfPoset( P ) 
PathAlgebra( F, Q )
PathsOfLengthTwo( Q ) 
Poset( P, rel )
PosetAlgebra( F, P )
PosetOfPosetAlgebra( A )
PositiveRootsOfUnitForm
PreImagesRepresentative( f, elem ) --  (undocumented)
ProjectiveCover( M )
ProjDimension( M )

QuadraticFormOfUnitForm
QuiverProduct( Q1, Q1 )

RadicalSeries( M )
RadicalSeriesOfAlgebra( A )
Range( f ) --  (undocumented)
ReflectionByBilinearForm
RelationsOfAlgebra( A )
RightApproximationByPerpT( T, M )
RightInverseOfHomomorphism( f )
RightMinimalVersion( f )

SeparatedQuiver( quiver )
Size( P ) 
SocleSeries( M )
Source( f ) --  (undocumented)
StarOfModule( M ) 
StarOfModuleHomomorphism( M ) 
SymmetricMatrixOfUnitForm

TensorProductOfAlgebras( FQ1, FQ2 )
TensorProductOfModules( M, N )
TitsUnitFormOfAlgebra
TransposeOfModule( M )
TrD( M[, n ] ), TransposeOfDual( M[, n ] ) 
TruncatedPathAlgebra( F, Q, n )

UnderlyingSet( P )
UnitForm

New operations:

DeclareAttribute( "DynkinType", IsQuiver );
DeclareProperty( "IsExtendedDynkinQuiver", IsQuiver );
DeclareOperation( "NakayamaFunctor", [ IsQuiverModuleCategory ] );
DeclareOperation( "RightAlgebraModuleToRightQuiverModule", IsRightAlgebraModuleElementCollection );
DeclareOperation( "StarFunctor", [ IsQuiverModuleCategory ] );
DeclareOperation( "TransposeFunctor", [ IsQuiverModuleCategory ] );