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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 homalg elements.
####################################
#
# categories:
#
####################################
# a new GAP-category:
## <#GAPDoc Label="IsHomalgElement">
## <ManSection>
## <Filt Type="Category" Arg="M" Name="IsHomalgElement"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of object elements.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgElement",
IsAttributeStoringRep and
IsAdditiveElementWithInverse );
####################################
#
# properties:
#
####################################
##
DeclareProperty( "Twitter",
IsHomalgElement );
## <#GAPDoc Label="IsZero:element">
## <ManSection>
## <Prop Arg="m" Name="IsZero" Label="for elements"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the object element <A>m</A> is zero.
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="IsCyclicGenerator">
## <ManSection>
## <Prop Arg="m" Name="IsCyclicGenerator"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the object element <A>m</A> is a cyclic generator.
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareProperty( "IsCyclicGenerator",
IsHomalgElement );
## <#GAPDoc Label="IsTorsion:element" Label="for elements">
## <ManSection>
## <Prop Arg="m" Name="IsTorsion"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the object element <A>m</A> is a torsion element.
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareProperty( "IsTorsion",
IsHomalgElement );
####################################
#
# attributes:
#
####################################
## <#GAPDoc Label="UnderlyingMorphism">
## <ManSection>
## <Attr Arg="m" Name="UnderlyingMorphism"/>
## <Returns>a &homalg; object</Returns>
## <Description>
## The morphism underlying the element <A>m</A> is the morphism from the structure object in the category
## to the <C>SuperObject</C><M>(</M><A>m</A><M>)</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "UnderlyingMorphism",
IsHomalgElement );
## <#GAPDoc Label="SuperObject:elements">
## <ManSection>
## <Attr Arg="m" Name="SuperObject" Label="for object elements"/>
## <Returns>a &homalg; object</Returns>
## <Description>
## The object <A>M</A> containing the element <A>m</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "SuperObject",
IsHomalgElement );
## <#GAPDoc Label="Annihilator:elements">
## <ManSection>
## <Attr Arg="e" Name="Annihilator" Label="for elements"/>
## <Returns>a &homalg; subobject</Returns>
## <Description>
## The annihilator of the object element <A>e</A> as a subobject of the structure object.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "Annihilator",
IsHomalgElement );
DeclareAttribute( "One",
IsHomalgElement );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareOperation( "HomalgElement",
[ IsHomalgStaticMorphism ] );
# global functions:
# basic operations:
DeclareOperation( "DecideZero",
[ IsHomalgElement ] );
DeclareOperation( "ApplyMorphismToElement",
[ IsHomalgStaticMorphism, IsHomalgElement ] );
DeclareOperation( "^",
[ IsObject, IsHomalgElement ] );
DeclareOperation( "*",
[ IsInt, IsHomalgElement ] );
DeclareOperation( "*",
[ IsHomalgElement, IsHomalgMorphism ] );
DeclareOperation( "*",
[ IsHomalgMorphism, IsHomalgElement ] );
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