|
# SPDX-License-Identifier: GPL-2.0-or-later
# GradedModules: A homalg based package for the Abelian category of finitely presented graded modules over computable graded rings
#
# Declarations
#
## Declarations for graded homalg modules.
# our info classes:
DeclareInfoClass( "InfoGradedModules" );
SetInfoLevel( InfoGradedModules, 1 );
# a central place for configurations:
DeclareGlobalVariable( "HOMALG_GRADED_MODULES" );
####################################
#
# categories:
#
####################################
## <#GAPDoc Label="IsHomalgGradedModule">
## <ManSection>
## <Filt Type="Category" Arg="M" Name="IsHomalgGradedModule"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; graded modules. <P/>
## (It is a subcategory of the &GAP; categories
## <C>IsHomalgModule</C></C>.)
## <Listing Type="Code"><![CDATA[
DeclareCategory( "IsHomalgGradedModule",
IsHomalgModule );
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareCategory( "IsCategoryOfGradedModules",
IsCategoryOfModules );
####################################
#
# properties:
#
####################################
##
DeclareProperty( "Twitter",
IsHomalgGradedModule );
##
DeclareProperty( "TrivialArtinianSubmodule",
IsHomalgGradedModule );
####################################
#
# attributes:
#
####################################
##
## the attributes below are intrinsic:
##
## !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
## should all be added by hand to LIGrMOD.intrinsic_attributes
## !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
## what was that again ;)
DeclareAttribute( "ZerothRegularity",
IsHomalgGradedModule );
## <#GAPDoc Label="BettiTable:module">
## <ManSection>
## <Attr Arg="M" Name="BettiTable" Label="for modules"/>
## <Returns>a &homalg; diagram</Returns>
## <Description>
## The Betti diagram of the &homalg; graded module <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "BettiTable",
IsHomalgGradedModule );
## <#GAPDoc Label="CastelnuovoMumfordRegularity">
## <ManSection>
## <Attr Arg="M" Name="CastelnuovoMumfordRegularity"/>
## <Returns>an integer</Returns>
## <Description>
## The Castelnuovo-Mumford regularity of the &homalg; graded module <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "CastelnuovoMumfordRegularity",
IsHomalgGradedModule );
## <#GAPDoc Label="CastelnuovoMumfordRegularityOfSheafification">
## <ManSection>
## <Attr Arg="M" Name="CastelnuovoMumfordRegularityOfSheafification"/>
## <Returns>an integer</Returns>
## <Description>
## The Castelnuovo-Mumford regularity of the sheafification of &homalg; graded module <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "CastelnuovoMumfordRegularityOfSheafification",
IsHomalgGradedModule );
## <#GAPDoc Label="LinearRegularityInterval">
## <ManSection>
## <Attr Arg="M" Name="LinearRegularityInterval"/>
## <Returns>an integer or -infinity</Returns>
## <Description>
## The linear regularity interval of the &homalg; graded module <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "LinearRegularityInterval",
IsHomalgGradedModule );
## <#GAPDoc Label="LinearRegularity">
## <ManSection>
## <Attr Arg="M" Name="LinearRegularity"/>
## <Returns>an integer or -infinity</Returns>
## <Description>
## The linear regularity of the &homalg; graded module <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "LinearRegularity",
IsHomalgGradedModule );
DeclareGlobalFunction( "LinearRegularityIntervalViaMinimalResolution" );
DeclareGlobalFunction( "LinearRegularityIntervalViaExt01OverBaseField" );
DeclareAttribute( "GradedTorsionFreeFactor",
IsHomalgGradedModule );
DeclareAttribute( "SaturateToDegreeZero",
IsHomalgGradedModule );
####################################
#
# global functions and operations:
#
####################################
# basic operations
DeclareOperation( "RandomMatrix",
[ IsHomalgModule, IsHomalgModule ] );
DeclareOperation( "MonomialMap",
[ IsInt, IsHomalgModule ] );
DeclareOperation( "MonomialMap",
[ IsHomalgElement, IsHomalgModule ] );
DeclareOperation( "DegreesOfGenerators",
[ IsHomalgModule ] );
DeclareOperation( "DegreesOfGenerators",
[ IsHomalgModule, IsPosInt ] );
DeclareOperation( "CompleteComplexByLinearResolution",
[ IsInt, IsHomalgComplex ] );
# constructors:
DeclareOperation( "GradedModule",
[ IsHomalgModule, IsInt, IsHomalgGradedRing ] );
DeclareOperation( "GradedModule",
[ IsHomalgModule, IsHomalgElement, IsHomalgGradedRing ] );
DeclareOperation( "GradedModule",
[ IsHomalgModule, IsHomalgGradedRing ] );
DeclareOperation( "GradedModule",
[ IsHomalgModule, IsList, IsHomalgGradedRing ] );
DeclareOperation( "LeftPresentationWithDegrees",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "LeftPresentationWithDegrees",
[ IsHomalgMatrix, IsInt ] );
DeclareOperation( "LeftPresentationWithDegrees",
[ IsHomalgMatrix, IsHomalgElement ] );
DeclareOperation( "LeftPresentationWithDegrees",
[ IsHomalgMatrix ] );
DeclareOperation( "RightPresentationWithDegrees",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "RightPresentationWithDegrees",
[ IsHomalgMatrix, IsInt ] );
DeclareOperation( "RightPresentationWithDegrees",
[ IsHomalgMatrix, IsHomalgElement ] );
DeclareOperation( "RightPresentationWithDegrees",
[ IsHomalgMatrix ] );
DeclareOperation( "LeftPresentationWithDegrees",
[ IsHomalgMatrix, IsList, IsHomalgGradedRing ] );
DeclareOperation( "LeftPresentationWithDegrees",
[ IsHomalgMatrix, IsInt, IsHomalgGradedRing ] );
DeclareOperation( "LeftPresentationWithDegrees",
[ IsHomalgMatrix, IsHomalgElement, IsHomalgGradedRing ] );
DeclareOperation( "LeftPresentationWithDegrees",
[ IsHomalgMatrix, IsHomalgGradedRing ] );
DeclareOperation( "RightPresentationWithDegrees",
[ IsHomalgMatrix, IsList, IsHomalgGradedRing ] );
DeclareOperation( "RightPresentationWithDegrees",
[ IsHomalgMatrix, IsInt, IsHomalgGradedRing ] );
DeclareOperation( "RightPresentationWithDegrees",
[ IsHomalgMatrix, IsHomalgElement, IsHomalgGradedRing ] );
DeclareOperation( "RightPresentationWithDegrees",
[ IsHomalgMatrix, IsHomalgGradedRing ] );
DeclareOperation( "FreeLeftModuleWithDegrees",
[ IsHomalgRing, IsList ] );
DeclareOperation( "FreeLeftModuleWithDegrees",
[ IsHomalgRing, IsHomalgElement ] );
DeclareOperation( "FreeLeftModuleWithDegrees",
[ IsList, IsHomalgRing ] );
DeclareOperation( "FreeLeftModuleWithDegrees",
[ IsInt, IsHomalgRing, IsInt ] );
DeclareOperation( "FreeLeftModuleWithDegrees",
[ IsInt, IsHomalgRing, IsHomalgElement ] );
DeclareOperation( "FreeLeftModuleWithDegrees",
[ IsInt, IsHomalgRing ] );
DeclareOperation( "FreeRightModuleWithDegrees",
[ IsHomalgRing, IsList ] );
DeclareOperation( "FreeRightModuleWithDegrees",
[ IsList, IsHomalgRing ] );
DeclareOperation( "FreeRightModuleWithDegrees",
[ IsInt, IsHomalgRing, IsInt ] );
DeclareOperation( "FreeRightModuleWithDegrees",
[ IsInt, IsHomalgRing, IsHomalgElement ] );
DeclareOperation( "FreeRightModuleWithDegrees",
[ IsInt, IsHomalgRing ] );
DeclareOperation( "PresentationWithDegrees",
[ IsHomalgGenerators, IsHomalgRelations, IsList, IsHomalgGradedRing] );
DeclareOperation( "PresentationWithDegrees",
[ IsHomalgGenerators, IsHomalgRelations, IsInt, IsHomalgGradedRing] );
DeclareOperation( "PresentationWithDegrees",
[ IsHomalgGenerators, IsHomalgRelations, IsHomalgElement, IsHomalgGradedRing] );
DeclareOperation( "PresentationWithDegrees",
[ IsHomalgGenerators, IsHomalgRelations, IsHomalgGradedRing] );
DeclareOperation( "^",
[ IsHomalgModule, IsInt ] );
DeclareOperation( "^",
[ IsHomalgModule, IsList ] );
#DeclareOperation( "^",
# [ IsHomalgModule, IsHomalgElement ] );
DeclareOperation( "^",
[ IsHomalgRing, IsInt ] );
DeclareOperation( "^",
[ IsHomalgRing, IsList ] );
#DeclareOperation( "^",
# [ IsHomalgRing, IsHomalgElement ] );
# global functions:
DeclareGlobalFunction( "HilbertPoincareSeries_ViaBettiTableOfMinimalFreeResolution" );
DeclareGlobalFunction( "CoefficientsOfNumeratorOfHilbertPoincareSeries_ViaBettiTableOfMinimalFreeResolution" );
DeclareGlobalFunction( "HilbertPolynomial_ViaBettiTableOfMinimalFreeResolution" );
# basic operations:
DeclareOperation( "SetOfDegreesOfGenerators",
[ IsHomalgGradedModule ] );
# attributes
DeclareAttribute( "UnderlyingModule",
IsHomalgGradedModule );
####################################
#
# synonyms:
#
####################################
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
]
|
