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# 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
#
# Implementations
#
## LIGrHOM = Logical Implications for Graded HOMomorphisms
InstallValue( LIGrHOM,
rec(
color := "\033[4;30;46m",
intrinsic_properties := LIHOM.intrinsic_properties,
intrinsic_attributes := LIHOM.intrinsic_attributes,
exchangeable_true_properties :=
[
],
exchangeable_false_properties :=
[ "IsMorphism",
],
exchangeable_properties :=
[ "IsZero",
"IsOne",
## conditionally exchangeable attributes
[ "IsGeneralizedEpimorphism", [ "IsGeneralizedMorphismWithFullDomain" ] ],
[ "IsGeneralizedMonomorphism", [ "IsGeneralizedMorphismWithFullDomain" ] ],
[ "IsGeneralizedIsomorphism", [ "IsGeneralizedMorphismWithFullDomain" ] ],
[ "IsMonomorphism", [ "IsMorphism" ] ],
[ "IsEpimorphism", [ "IsMorphism" ] ],
[ "IsSplitMonomorphism", [ "IsMorphism" ] ],
[ "IsSplitEpimorphism", [ "IsMorphism" ] ],
[ "IsIsomorphism", [ "IsMorphism" ] ],
],
exchangeable_attributes :=
[
],
)
);
####################################
#
# immediate methods for properties:
#
####################################
##
InstallImmediateMethodToPullPropertiesOrAttributes(
IsMapOfGradedModulesRep,
IsMapOfGradedModulesRep,
LIGrHOM.exchangeable_properties,
Concatenation( LIGrHOM.intrinsic_properties, LIGrHOM.intrinsic_attributes ),
UnderlyingMorphismMutable );
##
InstallImmediateMethodToPullTrueProperties(
IsMapOfGradedModulesRep,
IsMapOfGradedModulesRep,
LIGrHOM.exchangeable_true_properties,
Concatenation( LIGrHOM.intrinsic_properties, LIGrHOM.intrinsic_attributes ),
UnderlyingMorphismMutable );
##
InstallImmediateMethodToPullFalseProperties(
IsMapOfGradedModulesRep,
IsMapOfGradedModulesRep,
LIGrHOM.exchangeable_false_properties,
Concatenation( LIGrHOM.intrinsic_properties, LIGrHOM.intrinsic_attributes ),
UnderlyingMorphismMutable );
##
InstallImmediateMethodToPushPropertiesOrAttributes( Twitter,
IsMapOfGradedModulesRep,
LIGrHOM.exchangeable_properties,
UnderlyingMorphismMutable );
##
InstallImmediateMethodToPushFalseProperties( Twitter,
IsMapOfGradedModulesRep,
LIGrHOM.exchangeable_true_properties,
UnderlyingMorphismMutable );
##
InstallImmediateMethodToPushTrueProperties( Twitter,
IsMapOfGradedModulesRep,
LIGrHOM.exchangeable_false_properties,
UnderlyingMorphismMutable );
####################################
#
# immediate methods for attributes:
#
####################################
##
InstallImmediateMethodToPullPropertiesOrAttributes(
IsMapOfGradedModulesRep,
IsMapOfGradedModulesRep,
LIGrHOM.exchangeable_attributes,
Concatenation( LIGrHOM.intrinsic_properties, LIGrHOM.intrinsic_attributes ),
UnderlyingMorphismMutable );
##
InstallImmediateMethodToPushPropertiesOrAttributes( Twitter,
IsMapOfGradedModulesRep,
LIGrHOM.exchangeable_attributes,
UnderlyingMorphismMutable );
##
InstallImmediateMethod( DegreeOfMorphism,
IsMapOfGradedModulesRep and IsMorphism, 0,
function( M )
return 0;
end );
####################################
#
# methods for attributes:
#
####################################
##
InstallMethod( KernelSubobject,
"LIGrMOR: for homalg graded module homomorphisms",
[ IsMapOfGradedModulesRep ],
function( psi )
local S, ker, emb, source, target;
S := HomalgRing( psi );
source := Source( psi );
ker := KernelSubobject( UnderlyingMorphismMutable( psi ) );
emb := EmbeddingInSuperObject( ker );
# we have to do this strange case distinction
# even for monomorphisms, the kernel object is not automatically the zero subobject
# this might happen if we compute the kernel before knowing that the morphisms is mono
if HasIsMonomorphism( psi ) and IsMonomorphism( psi ) and
IsIdenticalObj( UnderlyingObject( ker ), UnderlyingObject( UnderlyingModule( ZeroSubobject( source ) ) ) ) then
emb := GradedMap( emb, UnderlyingObject( ZeroSubobject( Source( psi ) ) ), Source( psi ), S );
else
emb := GradedMap( emb, "create", Source( psi ), S );
fi;
if HasIsMorphism( psi ) and IsMorphism( psi ) then
Assert( 4, IsMorphism( emb ) );
SetIsMorphism( emb, true );
fi;
ker := ImageSubobject( emb );
target := Range( psi );
if HasIsEpimorphism( psi ) and IsEpimorphism( psi ) then
SetCokernelEpi( ker, psi );
fi;
if HasRankOfObject( source ) and HasRankOfObject( target ) then
if RankOfObject( target ) = 0 then
SetRankOfObject( ker, RankOfObject( source ) );
fi;
fi;
if HasIsModuleOfGlobalSectionsTruncatedAtCertainDegree( Source( psi ) ) and
IsInt( IsModuleOfGlobalSectionsTruncatedAtCertainDegree( Source( psi ) ) ) and
HasIsModuleOfGlobalSectionsTruncatedAtCertainDegree( Range( psi ) ) and
IsInt( IsModuleOfGlobalSectionsTruncatedAtCertainDegree( Range( psi ) ) ) and
IsModuleOfGlobalSectionsTruncatedAtCertainDegree( Source( psi ) ) = IsModuleOfGlobalSectionsTruncatedAtCertainDegree( Range( psi ) ) then
SetIsModuleOfGlobalSectionsTruncatedAtCertainDegree( UnderlyingObject( ker ), IsModuleOfGlobalSectionsTruncatedAtCertainDegree( Source( psi ) ) );
fi;
return ker;
end );
##
InstallMethod( IsAutomorphism,
"for homalg graded module maps",
[ IsMapOfGradedModulesRep ],
function( phi )
return IsAutomorphism( UnderlyingMorphismMutable( phi ) ) and IsHomalgGradedSelfMap( phi );
end );
##
InstallMethod( AdditiveInverse,
"for homalg graded maps",
[ IsMapOfGradedModulesRep ],
function( phi )
local psi;
psi := GradedMap( -UnderlyingMorphismMutable( phi ), Source( phi ), Range( phi ) );
SetPropertiesOfAdditiveInverse( psi, phi );
return psi;
end );
##
InstallMethod( CastelnuovoMumfordRegularity,
"for homalg graded maps",
[ IsMapOfGradedModulesRep ],
function( phi )
return Maximum( CastelnuovoMumfordRegularity( Source( phi ) ), CastelnuovoMumfordRegularity( Range( phi ) ) );
end );
##
InstallMethod( MaximalIdealAsLeftMorphism,
"for homalg graded rings",
[ IsHomalgGradedRingRep ],
function( S )
local F,result;
F := FreeLeftModuleWithDegrees( WeightsOfIndeterminates( S ), S );
result := GradedMap( MaximalIdealAsColumnMatrix( S ), F, 1 * S );
Assert( 4, IsMorphism( result ) );
SetIsMorphism( result, true );
return result;
end );
##
InstallMethod( MaximalIdealAsRightMorphism,
"for homalg graded rings",
[ IsHomalgGradedRingRep ],
function( S )
local F,result;
F := FreeRightModuleWithDegrees( WeightsOfIndeterminates( S ), S );
result := GradedMap( MaximalIdealAsRowMatrix( S ), F, S * 1 );
Assert( 4, IsMorphism( result ) );
SetIsMorphism( result, true );
return result;
end );
##
InstallMethod( IsMorphism,
"for homalg graded maps",
[ IsMapOfGradedModulesRep ],
function( phi )
local degs, degt, deg, mat, i, j, nonzero;
if not IsMorphism( UnderlyingMorphismMutable( phi ) ) then
return false;
fi;
deg := DegreesOfEntries( MatrixOfMap( phi ) );
degs := DegreesOfGenerators( Source( phi ) );
degt := DegreesOfGenerators( Range( phi ) );
# deg := List( deg, i -> List( i, HomalgElementToInteger ) );
# degs := List( degs, HomalgElementToInteger );
# degt := List( degt, HomalgElementToInteger );
mat := MatrixOfMap( phi );
for i in [ 1 .. Length( degs ) ] do
for j in [ 1 .. Length( degt ) ] do
if IsHomalgLeftObjectOrMorphismOfLeftObjects( phi ) then
if not ( degs[i] = deg[i][j] + degt[j] ) then
if not IsBound( nonzero ) then
nonzero := IndicatorMatrixOfNonZeroEntries( mat );
fi;
if nonzero[i][j] <> 0 then
return false;
fi;
fi;
else
if not ( degs[i] = deg[j][i] + degt[j] ) then
if not IsBound( nonzero ) then
nonzero := IndicatorMatrixOfNonZeroEntries( mat );
fi;
if nonzero[j][i] <> 0 then
return false;
fi;
fi;
fi;
od;
od;
return true;
end );
[ Dauer der Verarbeitung: 0.34 Sekunden
(vorverarbeitet)
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