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# SPDX-License-Identifier: GPL-2.0-or-later
# homalg: A homological algebra meta-package for computable Abelian categories
#
# Declarations
#
## Declarations for objects of (Abelian) categories.
####################################
#
# categories:
#
####################################
## <#GAPDoc Label="IsHomalgObject">
## <ManSection>
## <Filt Type="Category" Arg="F" Name="IsHomalgObject"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## This is the super &GAP;-category which will include the &GAP;-categories
## <Ref Filt="IsHomalgStaticObject"/>, <Ref Filt="IsHomalgComplex"/>, <Ref Filt="IsHomalgBicomplex"/>,
## <Ref Filt="IsHomalgBigradedObject"/>, and <Ref Filt="IsHomalgSpectralSequence"/>.
## We need this &GAP;-category to be able to build complexes with *objects*
## being objects of &homalg; categories or again complexes.
## <Listing Type="Code"><![CDATA[
DeclareCategory( "IsHomalgObject",
IsHomalgObjectOrMorphism and
IsStructureObjectOrObject and
IsAdditiveElementWithZero );
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="IsHomalgStaticObject">
## <ManSection>
## <Filt Type="Category" Arg="F" Name="IsHomalgStaticObject"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## This is the super &GAP;-category which will include the &GAP;-categories
## <C>IsHomalgModule</C>, etc.
## <Listing Type="Code"><![CDATA[
DeclareCategory( "IsHomalgStaticObject",
IsHomalgStaticObjectOrMorphism and
IsHomalgObject );
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
####################################
#
# properties:
#
####################################
## <#GAPDoc Label="IsFree">
## <ManSection>
## <Prop Arg="M" Name="IsFree"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is free.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsFree",
IsHomalgObject );
## <#GAPDoc Label="IsStablyFree">
## <ManSection>
## <Prop Arg="M" Name="IsStablyFree"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is stably free.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsStablyFree",
IsHomalgObject );
## <#GAPDoc Label="IsProjective">
## <ManSection>
## <Prop Arg="M" Name="IsProjective"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is projective.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsProjective",
IsHomalgObject );
## <#GAPDoc Label="IsProjectiveOfConstantRank">
## <ManSection>
## <Prop Arg="M" Name="IsProjectiveOfConstantRank"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is projective of constant rank.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsProjectiveOfConstantRank",
IsHomalgObject );
## <#GAPDoc Label="FiniteFreeResolutionExists">
## <ManSection>
## <Prop Arg="M" Name="FiniteFreeResolutionExists"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> allows a finite free resolution. <Br/>
## (no method installed)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "FiniteFreeResolutionExists",
IsHomalgObject );
## <#GAPDoc Label="IsReflexive">
## <ManSection>
## <Prop Arg="M" Name="IsReflexive"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is reflexive.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsReflexive",
IsHomalgObject );
## <#GAPDoc Label="IsTorsionFree">
## <ManSection>
## <Prop Arg="M" Name="IsTorsionFree"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is torsion-free.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsTorsionFree",
IsHomalgObject );
## <#GAPDoc Label="IsArtinian">
## <ManSection>
## <Prop Arg="M" Name="IsArtinian"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is artinian.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsArtinian",
IsHomalgObject );
## <#GAPDoc Label="IsTorsion">
## <ManSection>
## <Prop Arg="M" Name="IsTorsion"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is torsion.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsTorsion",
IsHomalgObject );
## <#GAPDoc Label="IsPure">
## <ManSection>
## <Prop Arg="M" Name="IsPure"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is pure.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsPure",
IsHomalgObject );
## <#GAPDoc Label="IsInjective">
## <ManSection>
## <Prop Arg="M" Name="IsInjective"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is (marked) injective.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsInjective",
IsHomalgObject );
## <#GAPDoc Label="IsInjectiveCogenerator">
## <ManSection>
## <Prop Arg="M" Name="IsInjectiveCogenerator"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is (marked) an injective cogenerator.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsInjectiveCogenerator",
IsHomalgObject );
## <#GAPDoc Label="IsCohenMacaulay">
## <ManSection>
## <Prop Arg="M" Name="IsCohenMacaulay"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is Cohen-Macaulay (depends on the specific Abelian category).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsCohenMacaulay",
IsHomalgObject );
## <#GAPDoc Label="IsGorenstein">
## <ManSection>
## <Prop Arg="M" Name="IsGorenstein"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is Gorenstein (depends on the specific Abelian category).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsGorenstein",
IsHomalgObject );
## <#GAPDoc Label="IsKoszul">
## <ManSection>
## <Prop Arg="M" Name="IsKoszul"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> is Koszul (depends on the specific Abelian category).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsKoszul",
IsHomalgObject );
## <#GAPDoc Label="HasConstantRank">
## <ManSection>
## <Prop Arg="M" Name="HasConstantRank"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; object <A>M</A> has constant rank. <Br/>
## (no method installed)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "HasConstantRank",
IsHomalgObject );
####################################
#
# attributes:
#
####################################
DeclareAttribute( "AFiniteFreeResolution",
IsHomalgObject, "mutable" );
## <#GAPDoc Label="TorsionSubobject">
## <ManSection>
## <Attr Arg="M" Name="TorsionSubobject"/>
## <Returns>a &homalg; subobject</Returns>
## <Description>
## This constructor returns the finitely generated torsion subobject of the &homalg; object <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareAttribute( "TorsionSubobject",
IsHomalgObject );
## <#GAPDoc Label="TheMorphismToZero">
## <ManSection>
## <Attr Arg="M" Name="TheMorphismToZero"/>
## <Returns>a &homalg; map</Returns>
## <Description>
## The zero morphism from the &homalg; object <A>M</A> to zero.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "TheMorphismToZero",
IsHomalgObject );
## <#GAPDoc Label="TheIdentityMorphism">
## <ManSection>
## <Attr Arg="M" Name="TheIdentityMorphism"/>
## <Returns>a &homalg; map</Returns>
## <Description>
## The identity automorphism of the &homalg; object <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "TheIdentityMorphism",
IsHomalgObject );
DeclareAttribute( "Genesis",
IsHomalgObject, "mutable" );
## <#GAPDoc Label="FullSubobject">
## <ManSection>
## <Attr Arg="M" Name="FullSubobject"/>
## <Returns>a &homalg; subobject</Returns>
## <Description>
## The &homalg; object <A>M</A> as a subobject of itself.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "FullSubobject",
IsHomalgObject );
## <#GAPDoc Label="ZeroSubobject">
## <ManSection>
## <Attr Arg="M" Name="ZeroSubobject"/>
## <Returns>a &homalg; subobject</Returns>
## <Description>
## The zero subobject of the &homalg; object <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ZeroSubobject",
IsHomalgObject );
## <#GAPDoc Label="UnderlyingSubobject">
## <ManSection>
## <Attr Arg="M" Name="UnderlyingSubobject"/>
## <Returns>a &homalg; subobject</Returns>
## <Description>
## In case <A>M</A> was defined as the object underlying a subobject <M>L</M> then <M>L</M> is returned. <Br/>
## (no method installed)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "UnderlyingSubobject",
IsHomalgObject );
## <#GAPDoc Label="Annihilator:objects">
## <ManSection>
## <Attr Arg="M" Name="Annihilator" Label="for static objects"/>
## <Returns>a &homalg; subobject</Returns>
## <Description>
## The annihilator of the object <A>M</A> as a subobject of the structure object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "Annihilator",
IsHomalgStaticObject );
## <#GAPDoc Label="EndomorphismRing">
## <ManSection>
## <Attr Arg="M" Name="EndomorphismRing" Label="for static objects"/>
## <Returns>a &homalg; object</Returns>
## <Description>
## The endomorphism ring of the object <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "EndomorphismRing",
IsHomalgStaticObject );
## <#GAPDoc Label="UnitObject">
## <ManSection>
## <Prop Arg="M" Name="UnitObject"/>
## <Returns>a Chern character</Returns>
## <Description>
## <A>M</A> is a &homalg; object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "UnitObject",
IsHomalgStaticObject );
DeclareAttribute( "TheZeroElement",
IsHomalgStaticObject );
##
## the attributes below are intrinsic:
##
## !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
## should all be added by hand to LIOBJ.intrinsic_attributes
## !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
## <#GAPDoc Label="RankOfObject">
## <ManSection>
## <Attr Arg="M" Name="RankOfObject"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## The projective rank of the &homalg; object <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "RankOfObject",
IsStructureObjectOrObject );
## <#GAPDoc Label="ProjectiveDimension">
## <ManSection>
## <Attr Arg="M" Name="ProjectiveDimension"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## The projective dimension of the &homalg; object <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ProjectiveDimension",
IsHomalgObject );
## <#GAPDoc Label="DegreeOfTorsionFreeness">
## <ManSection>
## <Attr Arg="M" Name="DegreeOfTorsionFreeness"/>
## <Returns>a nonnegative integer of infinity</Returns>
## <Description>
## Auslander's degree of torsion-freeness of the &homalg; object <A>M</A>.
## It is set to infinity only for <A>M</A><M>=0</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "DegreeOfTorsionFreeness",
IsHomalgObject );
## <#GAPDoc Label="Grade">
## <ManSection>
## <Attr Arg="M" Name="Grade"/>
## <Returns>a nonnegative integer of infinity</Returns>
## <Description>
## The grade of the &homalg; object <A>M</A>.
## It is set to infinity if <A>M</A><M>=0</M>.
## Another name for this operation is <C>Depth</C>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "Grade",
IsHomalgObject );
## <#GAPDoc Label="PurityFiltration">
## <ManSection>
## <Attr Arg="M" Name="PurityFiltration"/>
## <Returns>a &homalg; filtration</Returns>
## <Description>
## The purity filtration of the &homalg; object <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "PurityFiltration",
IsHomalgObject );
## <#GAPDoc Label="CodegreeOfPurity">
## <ManSection>
## <Attr Arg="M" Name="CodegreeOfPurity"/>
## <Returns>a list of nonnegative integers</Returns>
## <Description>
## The codegree of purity of the &homalg; object <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "CodegreeOfPurity",
IsHomalgObject );
## <#GAPDoc Label="HilbertPolynomial">
## <ManSection>
## <Attr Arg="M" Name="HilbertPolynomial"/>
## <Returns>a univariate polynomial with rational coefficients</Returns>
## <Description>
## <A>M</A> is a &homalg; object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "HilbertPolynomial",
IsStructureObjectOrObject );
## <#GAPDoc Label="AffineDimension">
## <ManSection>
## <Attr Arg="M" Name="AffineDimension"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## <A>M</A> is a &homalg; object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "AffineDimension",
IsStructureObjectOrObject );
## <#GAPDoc Label="ProjectiveDegree">
## <ManSection>
## <Attr Arg="M" Name="ProjectiveDegree"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## <A>M</A> is a &homalg; object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ProjectiveDegree",
IsStructureObjectOrObject );
## <#GAPDoc Label="ConstantTermOfHilbertPolynomial">
## <ManSection>
## <Attr Arg="M" Name="ConstantTermOfHilbertPolynomialn"/>
## <Returns>an integer</Returns>
## <Description>
## <A>M</A> is a &homalg; object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ConstantTermOfHilbertPolynomial",
IsStructureObjectOrObject );
## <#GAPDoc Label="ElementOfGrothendieckGroup">
## <ManSection>
## <Prop Arg="M" Name="ElementOfGrothendieckGroup"/>
## <Returns>an element of the Grothendieck group of a projective space</Returns>
## <Description>
## <A>M</A> is a &homalg; object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ElementOfGrothendieckGroup",
IsStructureObjectOrObject );
## <#GAPDoc Label="ChernPolynomial">
## <ManSection>
## <Prop Arg="M" Name="ChernPolynomial"/>
## <Returns>a Chern polynomial with rank</Returns>
## <Description>
## <A>M</A> is a &homalg; object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ChernPolynomial",
IsStructureObjectOrObject );
## <#GAPDoc Label="ChernCharacter">
## <ManSection>
## <Prop Arg="M" Name="ChernCharacter"/>
## <Returns>a Chern character</Returns>
## <Description>
## <A>M</A> is a &homalg; object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ChernCharacter",
IsStructureObjectOrObject );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareOperation( "Pullback",
[ IsStructureObjectMorphism, IsHomalgObject ] );
DeclareOperation( "*",
[ IsStructureObject, IsHomalgStaticObject ] );
DeclareOperation( "*",
[ IsHomalgStaticObject, IsStructureObject ] );
# basic operations:
DeclareOperation( "StructureObject",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "HomalgCategory",
[ IsObject ] );
DeclareOperation( "MorphismConstructor",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "MorphismConstructor",
[ IsObject, IsObject ] );
DeclareOperation( "MorphismConstructor",
[ IsObject, IsHomalgStaticObject, IsHomalgStaticObject ] );
DeclareOperation( "FunctorOfGenesis",
[ IsHomalgObjectOrMorphism, IsInt ] );
DeclareOperation( "FunctorOfGenesis",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "FunctorsOfGenesis",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "ArgumentsOfGenesis",
[ IsHomalgObjectOrMorphism, IsInt ] );
DeclareOperation( "ArgumentsOfGenesis",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "PartOfPresentationRelevantForOutputOfFunctors",
[ IsHomalgStaticObject, IsObject ] );
DeclareOperation( "ComparePresentationsForOutputOfFunctors",
[ IsHomalgStaticObject, IsObject, IsObject ] );
DeclareOperation( "End",
[ IsHomalgStaticObject ] );
DeclareGlobalFunction( "Grade_UsingInternalExtForObjects" );
DeclareOperation( "Grade",
[ IsHomalgStaticObject, IsStructureObjectOrObjectOrMorphism, IsInt ] );
DeclareOperation( "Grade",
[ IsHomalgStaticObject, IsStructureObjectOrObjectOrMorphism ] );
DeclareOperation( "Grade",
[ IsHomalgStaticObject, IsInt ] );
## Depth is already declared as an operation in GAP
## so we cannot declare it as a synonym for Grade;
## not doing so keeps us more flexible but requires
## explicit declarations and installations
DeclareOperation( "Depth",
[ IsHomalgStaticObject, IsStructureObjectOrObjectOrMorphism, IsInt ] );
DeclareOperation( "Depth",
[ IsHomalgStaticObject, IsStructureObjectOrObjectOrMorphism ] );
DeclareOperation( "Depth",
[ IsHomalgStaticObject, IsInt ] );
## corresponds to the above declaration of Grade as an attribute
DeclareOperation( "Depth",
[ IsHomalgStaticObject ] );
DeclareOperation( "SetUpperBoundForProjectiveDimension",
[ IsHomalgObject, IsInt ] );
DeclareOperation( "SetUpperBoundForProjectiveDimension",
[ IsHomalgObject, IsInfinity ] );
DeclareOperation( "LockObjectOnCertainPresentation",
[ IsHomalgStaticObject, IsObject ] );
DeclareOperation( "LockObjectOnCertainPresentation",
[ IsHomalgStaticObject ] );
DeclareOperation( "UnlockObject",
[ IsHomalgStaticObject ] );
DeclareOperation( "IsLockedObject",
[ IsHomalgStaticObject ] );
DeclareOperation( "SetPositionOfTheDefaultPresentation",
[ IsHomalgStaticObject, IsObject ] );
DeclareOperation( "DecideZero",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "ByASmallerPresentation",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "OnPresentationByFirstMorphismOfResolution",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "Display",
[ IsHomalgObjectOrMorphism, IsString ] );
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