Quelle HomalgFiltration.gi Sprache: unbekannt

# 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 );

Quelle HomalgFiltration.gi Sprache: unbekannt

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