|
# SPDX-License-Identifier: GPL-2.0-or-later
# Modules: A homalg based package for the Abelian category of finitely presented modules over computable rings
#
# Declarations
#
## Declaration stuff for a set of relations.
####################################
#
# categories:
#
####################################
# A new GAP-category:
## <#GAPDoc Label="IsHomalgRelations">
## <ManSection>
## <Filt Type="Category" Arg="rel" Name="IsHomalgRelations"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; relations.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgRelations",
IsAttributeStoringRep );
## CAUTION: in the code the following two categories are the only ones for sets of generators,
## i.e. IsHomalgRelations and not IsHomalgRelationsOfLeftModule => IsHomalgRelationsOfRightModule
## <#GAPDoc Label="IsHomalgRelationsOfLeftModule">
## <ManSection>
## <Filt Type="Category" Arg="rel" Name="IsHomalgRelationsOfLeftModule"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; relations of a left module. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgRelations</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgRelationsOfLeftModule",
IsHomalgRelations );
## <#GAPDoc Label="IsHomalgRelationsOfRightModule">
## <ManSection>
## <Filt Type="Category" Arg="rel" Name="IsHomalgRelationsOfRightModule"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; relations of a right module. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgRelations</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgRelationsOfRightModule",
IsHomalgRelations );
####################################
#
# properties:
#
####################################
## <#GAPDoc Label="CanBeUsedToDecideZeroEffectively">
## <ManSection>
## <Prop Arg="rel" Name="CanBeUsedToDecideZeroEffectively"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; set of relations <A>rel</A> can be used for normal form reductions. <Br/>
## (no method installed)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "CanBeUsedToDecideZeroEffectively",
IsHomalgRelations );
## <#GAPDoc Label="IsInjectivePresentation">
## <ManSection>
## <Prop Arg="rel" Name="IsInjectivePresentation"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; set of relations <A>rel</A> has zero syzygies.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsInjectivePresentation",
IsHomalgRelations );
##
DeclareProperty( "IsTorsion",
IsHomalgRelations );
DeclareAttribute( "NrGeneratorsForRelations",
IsHomalgRelations );
DeclareAttribute( "NrRelationsForRelations",
IsHomalgRelations );
####################################
#
# attributes:
#
####################################
##
DeclareAttribute( "EvalMatrixOfRelations",
IsHomalgRelations );
##
DeclareAttribute( "EvaluatedMatrixOfRelations",
IsHomalgRelations );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareGlobalFunction( "_HomalgRelationsForLeftModule" );
DeclareOperation( "HomalgRelationsForLeftModule",
[ IsObject, IsObject ] );
DeclareOperation( "HomalgRelationsForLeftModule",
[ IsObject ] );
DeclareGlobalFunction( "_HomalgRelationsForRightModule" );
DeclareOperation( "HomalgRelationsForRightModule",
[ IsObject, IsObject ] );
DeclareOperation( "HomalgRelationsForRightModule",
[ IsObject ] );
# basic operations:
DeclareGlobalFunction( "INSTALL_TODO_LIST_ENTRIES_FOR_MATRICES_OF_RELATIONS" );
DeclareGlobalFunction( "INSTALL_TODO_LIST_ENTRIES_FOR_RELATIONS_OF_MODULES" );
DeclareOperation( "MatrixOfRelations",
[ IsHomalgRelations ] );
DeclareOperation( "HomalgRing",
[ IsHomalgRelations ] );
DeclareOperation( "HasNrGenerators",
[ IsHomalgRelations ] );
DeclareOperation( "NrGenerators",
[ IsHomalgRelations ] );
DeclareOperation( "HasNrRelations",
[ IsHomalgRelations ] );
DeclareOperation( "NrRelations",
[ IsHomalgRelations ] );
DeclareOperation( "CertainRelations",
[ IsHomalgRelations, IsList ] );
DeclareOperation( "UnionOfRelations",
[ IsHomalgRelations, IsHomalgRelations ] );
DeclareOperation( "UnionOfRelations",
[ IsHomalgMatrix, IsHomalgRelations ] );
DeclareOperation( "UnionOfRelations",
[ IsHomalgRelations, IsHomalgMatrix ] );
DeclareOperation( "BasisOfModule",
[ IsHomalgRelations ] );
DeclareOperation( "DecideZero",
[ IsHomalgMatrix, IsHomalgRelations ] );
DeclareOperation( "DecideZero",
[ IsHomalgRelations, IsHomalgRelations ] );
DeclareOperation( "BasisCoeff",
[ IsHomalgRelations ] );
DeclareOperation( "RightDivide",
[ IsHomalgMatrix, IsHomalgMatrix, IsHomalgRelations ] );
DeclareOperation( "LeftDivide",
[ IsHomalgMatrix, IsHomalgMatrix, IsHomalgRelations ] );
DeclareOperation( "SyzygiesGenerators",
[ IsHomalgRelations ] );
DeclareOperation( "SyzygiesGenerators",
[ IsHomalgMatrix, IsHomalgRelations ] );
DeclareOperation( "ReducedSyzygiesGenerators",
[ IsHomalgRelations ] );
DeclareOperation( "ReducedSyzygiesGenerators",
[ IsHomalgMatrix, IsHomalgRelations ] );
DeclareOperation( "NonZeroGenerators",
[ IsHomalgRelations ] );
DeclareOperation( "GetRidOfObsoleteRelations",
[ IsHomalgRelations ] );
DeclareOperation( "GetIndependentUnitPositions",
[ IsHomalgRelations, IsHomogeneousList ] );
DeclareOperation( "GetIndependentUnitPositions",
[ IsHomalgRelations ] );
DeclareOperation( "^",
[ IsHomalgRelations, IsHomalgMatrix ] );
DeclareOperation( "*",
[ IsHomalgRelations, IsHomalgMatrix ] );
####################################
#
# synonyms:
#
####################################
DeclareSynonym ( "BetterBasis",
GetRidOfObsoleteRelations );
[ Dauer der Verarbeitung: 0.15 Sekunden
(vorverarbeitet)
]
|
