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# SPDX-License-Identifier: GPL-2.0-or-later
# MatricesForHomalg: Matrices for the homalg project
#
# Declarations
#
####################################
#
# categories:
#
####################################
# two new GAP-categories:
## <#GAPDoc Label="IsHomalgRingMap">
## <ManSection>
## <Filt Type="Category" Arg="phi" Name="IsHomalgRingMap"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of ring maps.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgRingMap",
IsStructureObjectMorphism );
## <#GAPDoc Label="IsHomalgRingSelfMap">
## <ManSection>
## <Filt Type="Category" Arg="phi" Name="IsHomalgRingSelfMap"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of ring self-maps. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgRingMap</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgRingSelfMap",
IsHomalgRingMap );
####################################
#
# properties:
#
####################################
## <#GAPDoc Label="IsMorphism:ringmap">
## <ManSection>
## <Prop Arg="phi" Name="IsMorphism" Label="for ring maps"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if <A>phi</A> is a well-defined map, i.e. independent of all involved presentations.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsMorphism",
IsHomalgRingMap );
## <#GAPDoc Label="IsIdentityMorphism:ringmap">
## <ManSection>
## <Prop Arg="phi" Name="IsIdentityMorphism" Label="for ring maps"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; ring map <A>phi</A> is the identity morphism.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsIdentityMorphism",
IsHomalgRingMap );
## <#GAPDoc Label="IsMonomorphism:ringmap">
## <ManSection>
## <Prop Arg="phi" Name="IsMonomorphism" Label="for ring maps"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; ring map <A>phi</A> is a monomorphism.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsMonomorphism",
IsHomalgRingMap );
## <#GAPDoc Label="IsEpimorphism:ringmap">
## <ManSection>
## <Prop Arg="phi" Name="IsEpimorphism" Label="for ring maps"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; ring map <A>phi</A> is an epimorphism.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsEpimorphism",
IsHomalgRingMap );
## <#GAPDoc Label="IsIsomorphism:ringmap">
## <ManSection>
## <Prop Arg="phi" Name="IsIsomorphism" Label="for ring maps"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; ring map <A>phi</A> is an isomorphism.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsIsomorphism",
IsHomalgRingMap );
## <#GAPDoc Label="IsAutomorphism:ringmap">
## <ManSection>
## <Prop Arg="phi" Name="IsAutomorphism" Label="for ring maps"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; ring map <A>phi</A> is an automorphism.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsAutomorphism", ## do not make an ``and''-filter out of this property (I hope the other GAP packages respect this)
IsHomalgRingMap );
####################################
#
# attributes:
#
####################################
## <#GAPDoc Label="Source:ringmap">
## <ManSection>
## <Attr Arg="phi" Name="Source" Label="for ring maps"/>
## <Returns>a &homalg; ring</Returns>
## <Description>
## The source of the &homalg; ring map <A>phi</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "Source",
IsHomalgRingMap );
## <#GAPDoc Label="Range:ringmap">
## <ManSection>
## <Attr Arg="phi" Name="Range" Label="for ring maps"/>
## <Returns>a &homalg; ring</Returns>
## <Description>
## The target (range) of the &homalg; ring map <A>phi</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "Range",
IsHomalgRingMap );
## <#GAPDoc Label="DegreeOfMorphism:ringmap">
## <ManSection>
## <Attr Arg="phi" Name="DegreeOfMorphism" Label="for ring maps"/>
## <Returns>an integer</Returns>
## <Description>
## The degree of the morphism <A>phi</A> of graded rings. <Br/>
## (no method installed)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "DegreeOfMorphism",
IsHomalgRingMap );
## <#GAPDoc Label="CoordinateRingOfGraph">
## <ManSection>
## <Attr Arg="phi" Name="CoordinateRingOfGraph" Label="for ring maps"/>
## <Returns>a &homalg; ring</Returns>
## <Description>
## The coordinate ring of the graph of the ring map <A>phi</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "CoordinateRingOfGraph",
IsHomalgRingMap );
## <#GAPDoc Label="GeneratorsOfKernelOfRingMap:ringmap">
## <ManSection>
## <Attr Arg="phi" Name="GeneratorsOfKernelOfRingMap" Label="for ring maps"/>
## <Returns>a &homalg; submodule</Returns>
## <Description>
## The kernel ideal of the ring map <A>phi</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "GeneratorsOfKernelOfRingMap",
IsHomalgRingMap );
## intrinsic attributes:
##
## !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
## should all be added by hand to LIMAP.intrinsic_attributes
## !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareOperation( "RingMap",
[ IsHomalgMatrix, IsHomalgRing, IsHomalgRing ] );
DeclareOperation( "RingMap",
[ IsList, IsHomalgRing, IsHomalgRing ] );
DeclareOperation( "RingMap",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "RingMap",
[ IsHomalgMatrix ] );
DeclareOperation( "RingMap",
[ IsHomalgRing ] );
# attributes
DeclareAttribute( "ImagesOfRingMap",
IsHomalgRingMap );
DeclareAttribute( "ImagesOfRingMapAsColumnMatrix",
IsHomalgRingMap );
DeclareAttribute( "DataOfCoordinateRingOfGraph",
IsHomalgRingMap );
# basic operations:
if false then ## keep for future documentation
DeclareOperation( "Pullback",
[ IsHomalgRingMap, IsHomalgMatrix ] );
fi;
DeclareOperation( "Pullback",
[ IsHomalgRingMap, IsRingElement ] );
DeclareOperation( "PreCompose",
[ IsHomalgRingMap, IsHomalgRingMap ] );
[ Dauer der Verarbeitung: 0.21 Sekunden
(vorverarbeitet)
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