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#############################################################################
##
## HAPPRIME - ringhomomorphism.gd
## Functions, Operations and Methods to implement ring homomorphisms
## Paul Smith
##
## Copyright (C) 2008
## Paul Smith
## National University of Ireland Galway
##
## This file is part of HAPprime.
##
## HAPprime is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## HAPprime is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <https://www.gnu.org/licenses/>.
##
##
#############################################################################
#####################################################################
## <#GAPDoc Label="HAPRingHomomorphismFilter_DTmanRingHomomorphismNODOC">
## <ManSection>
## <Filt Name="IsHAPRingHomomorphism" Arg="O" Type="Category"/>
## <Returns>
## <K>true</K> if the object is a <K>HAPRingHomomorphism</K>, or
## <K>false</K> otherwise
## </Returns>
## </ManSection>
## <#/GAPDoc>
#####################################################################
DeclareCategory("IsHAPRingHomomorphism", IsObject);
# Note this also defines the function IsHAPRingHomomorphism
#####################################################################
#####################################################################
## <#GAPDoc Label="HAPRingHomomorphismFamilyAttr_DTmanRingHomomorphismNODOC">
## <ManSection>
## <Fam Name="HAPRingHomomorphismFamily"/>
## <Description>
## The family to which <K>HAPRingHomomorphism</K> objects belong.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
DeclareAttribute("HAPRingHomomorphismFamily", IsFamily);
# Note this also defines the function HAPRingHomomorphismFamily
#####################################################################
#######################################################################
#
# Declarations for Operations in ringhomomorphism.gi
#
DeclareOperation("HAPRingToSubringHomomorphism",
[IsPolynomialRing, IsHomogeneousList,
IsHomogeneousList and IsRationalFunctionCollection]);
DeclareOperation("HAPSubringToRingHomomorphism",
[IsHomogeneousList and IsRationalFunctionCollection,
IsHomogeneousList, IsPolynomialRing]);
DeclareOperation("HAPSubringToRingHomomorphism",
[IsHomogeneousList and IsRationalFunctionCollection,
IsPolynomialRing, IsHomogeneousList]);
DeclareOperation("HAPRingHomomorphismByIndeterminateMap",
[IsPolynomialRing, IsHomogeneousList, IsPolynomialRing]);
DeclareOperation("HAPRingReductionHomomorphism",
[IsPolynomialRing, IsHomogeneousList, IsHomogeneousList]);
DeclareOperation("HAPRingReductionHomomorphism",
[IsHAPRingHomomorphism, IsHomogeneousList]);
DeclareOperation("HAPZeroRingHomomorphism",
[IsPolynomialRing, IsHomogeneousList]);
DeclareOperation("CompositionRingHomomorphism",
[IsHAPRingHomomorphism, IsHAPRingHomomorphism]);
DeclareAttribute("InverseRingHomomorphism", IsHAPRingHomomorphism);
DeclareAttribute("SourcePolynomialRing", IsHAPRingHomomorphism);
DeclareAttribute("SourceGenerators", IsHAPRingHomomorphism);
DeclareAttribute("SourceRelations", IsHAPRingHomomorphism);
DeclareAttribute("ImagePolynomialRing", IsHAPRingHomomorphism);
DeclareAttribute("ImageGenerators", IsHAPRingHomomorphism);
DeclareAttribute("ImageRelations", IsHAPRingHomomorphism);
DeclareOperation("ImageOfRingHomomorphism",
[IsHAPRingHomomorphism, IsHomogeneousList and IsRationalFunctionCollection]);
DeclareOperation("PreimageOfRingHomomorphism",
[IsHAPRingHomomorphism, IsHomogeneousList and IsRationalFunctionCollection]);
DeclareGlobalFunction("HAPPRIME_MakeEliminationOrdering");
DeclareGlobalFunction("HAPPRIME_RingHomomorphismsAreComposable");
#####################################################################
## <#GAPDoc Label="SourceGenerators_DTmanRingHomomorphism_Dat">
## <ManSection>
## <Attr Name="SourceGenerators" Arg="phi"/>
## <Returns>
## List
## </Returns>
## <Description>
## A list of generators for the source ring <M>R/I</M> of the ring
## homomorphism.
## <A>phi</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
## <#GAPDoc Label="SourceRelations_DTmanRingHomomorphism_Dat">
## <ManSection>
## <Attr Name="SourceRelations" Arg="phi"/>
## <Returns>
## List
## </Returns>
## <Description>
## A list of the relations that generate the ideal <M>I</M> of in the source
## ring of the ring homomorphism <A>phi</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
## <#GAPDoc Label="SourcePolynomialRing_DTmanRingHomomorphism_Dat">
## <ManSection>
## <Attr Name="SourcePolynomialRing" Arg="phi"/>
## <Returns>
## <K>PolynomialRing</K>
## </Returns>
## <Description>
## Returns the polynomial ring which contains the source ring of the
## ring homomorphism <A>phi</A>.
## Polynomials to be mapped by <A>phi</A> must be in this ring.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
## <#GAPDoc Label="ImageGenerators_DTmanRingHomomorphism_Dat">
## <ManSection>
## <Attr Name="ImageGenerators" Arg="phi"/>
## <Returns>
## List
## </Returns>
## <Description>
## A list of generators for the image ring <M>S/J</M> of the ring
## homomorphism <A>phi</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
## <#GAPDoc Label="ImageRelations_DTmanRingHomomorphism_Dat">
## <ManSection>
## <Attr Name="ImageRelations" Arg="phi"/>
## <Returns>
## List
## </Returns>
## <Description>
## A list of the relations that generate the ideal <M>J</M> of in the image
## ring of the ring homomorphism <A>phi</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
## <#GAPDoc Label="ImagePolynomialRing_DTmanRingHomomorphism_Dat">
## <ManSection>
## <Attr Name="ImagePolynomialRing" Arg="phi"/>
## <Returns>
## <K>PolynomialRing</K>
## </Returns>
## <Description>
## Returns the polynomial ring which contains the image of the
## ring homomorphism <A>phi></A>. All polynomials mapped by <A>phi</A> will
## be in this ring.
## </Description>
## </ManSection>
## <#/GAPDoc>
#####################################################################
|
