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# SPDX-License-Identifier: GPL-2.0-or-later
# Modules: A homalg based package for the Abelian category of finitely presented modules over computable rings
#
# Implementations
#
## Implementation stuff for a filtration.
####################################
#
# methods for operations:
#
####################################
##
InstallMethod( HomalgRing,
"for filtration of homalg objects",
[ IsFiltrationOfFinitelyPresentedObjectRep ],
function( filt )
return HomalgRing( LowestDegreeMorphism( filt ) );
end );
##
InstallMethod( MatrixOfFiltration,
"for filtrations of homalg modules",
[ IsFiltrationOfFinitelyPresentedObjectRep, IsInt ],
function( filt, p_min )
local stack;
stack := List( Filtered( DegreesOfFiltration( filt ), p -> p >= p_min ) , d -> CertainMorphism( filt, d ) );
stack := Iterated( stack, CoproductMorphism );
return MatrixOfMap( stack );
end );
##
InstallMethod( MatrixOfFiltration,
"for filtrations of homalg modules",
[ IsFiltrationOfFinitelyPresentedObjectRep ],
function( filt )
return MatrixOfFiltration( filt, LowestDegree( filt ) );
end );
##
InstallMethod( BasisOfModule,
"for homalg filtrations",
[ IsHomalgFiltration ],
function( filt )
List( ObjectsOfFiltration( filt ), BasisOfModule );
BasisOfModule( UnderlyingObject( filt ) );
return filt;
end );
##
InstallMethod( DecideZero,
"for homalg filtrations",
[ IsHomalgFiltration ],
function( filt )
List( MorphismsOfFiltration( filt ), DecideZero );
return filt;
end );
##
InstallMethod( OnLessGenerators,
"for homalg filtrations",
[ IsHomalgFiltration ],
function( filt )
List( ObjectsOfFiltration( filt ), OnLessGenerators );
OnLessGenerators( UnderlyingObject( filt ) );
return filt;
end );
##
InstallMethod( ByASmallerPresentation,
"for homalg filtrations",
[ IsHomalgFiltration ],
function( filt )
List( ObjectsOfFiltration( filt ), ByASmallerPresentation );
ByASmallerPresentation( UnderlyingObject( filt ) );
DecideZero( filt );
return filt;
end );
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