Ziele Untersuchung
mit Columbo Integrität von
Datenbanken Interaktion und
Portierbarkeit Ergonomie der
Schnittstellen

Angebot Produkte Projekt Beratung

Mittel Analytik Modellierung Sprachen Algebra Logik Hardware Denken Kreativität

Zusammenhänge Gesellschaft Wirtschaft Branche Firma


products/sources/formale Sprachen/GAP/pkg/modulepresentationsforcap/gap/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 22.8.2025 mit Größe 3 kB

Quelle Tools.gi Sprache: unbekannt

# SPDX-License-Identifier: GPL-2.0-or-later
# ModulePresentationsForCAP: Category R-pres for CAP
#
# Implementations
#

BindGlobal( "INSTALL_GET_RID_OF_ZERO_GENERATORS_TRANSFORMATION_TRIPLE_METHOD",

  function( get_rid_of_zero_generators_transformation_triple,
          nr_generators, basis_of_module, decide_zero, nonzero_generators, certain_generators, certain_relations )

    InstallMethod( get_rid_of_zero_generators_transformation_triple,
            "for a homalg matrix",
            [ IsHomalgMatrix ],

      function( matrix )
        local ng, id, nz, T, TI;

        ng := nr_generators( matrix );

        id := HomalgIdentityMatrix( ng, HomalgRing( matrix ) );

        nz := nonzero_generators( decide_zero( id, basis_of_module( matrix ) ) );

        if Length( nz ) = ng then
            return [ matrix, id, id ];
        fi;

        matrix := certain_generators( matrix, nz );
        matrix := certain_relations( matrix, nonzero_generators( matrix ) );

        T := certain_generators( id, nz );
        TI := certain_relations( id, nz );

        return [ matrix, T, TI ];

    end );

end );

BindGlobal( "INSTALL_GET_RID_OF_ZERO_GENERATORS_TRANSFORMATION_TRIPLE",

  function( )

    INSTALL_GET_RID_OF_ZERO_GENERATORS_TRANSFORMATION_TRIPLE_METHOD(
            NonZeroGeneratorsTransformationTripleLeft,
            NrColumns,           # nr_generators
            BasisOfRowModule,    # basis_of_module
            DecideZeroRows,      # decide_zero
            NonZeroRows,         # nonzero_generators
            CertainColumns,      # certain_generators
            CertainRows          # certain_relations
            );

    INSTALL_GET_RID_OF_ZERO_GENERATORS_TRANSFORMATION_TRIPLE_METHOD(
            NonZeroGeneratorsTransformationTripleRight,
            NrRows,              # nr_generators
            BasisOfColumnModule, # basis_of_module
            DecideZeroColumns,   # decide_zero
            NonZeroColumns,      # nonzero_generators
            CertainRows,         # certain_generators
            CertainColumns       # certain_relations
            );

end );

##
#= comment for Julia
INSTALL_GET_RID_OF_ZERO_GENERATORS_TRANSFORMATION_TRIPLE( );
# =#

##
InstallMethod( LessGeneratorsTransformationTripleLeft,
               [ IsHomalgMatrix ],

  function( matrix )
    local R, transformation, transformation_inverse, smaller_matrix;

    R := HomalgRing( matrix );

    transformation := HomalgVoidMatrix( R );

    transformation_inverse := HomalgVoidMatrix( R );

    smaller_matrix := SimplerEquivalentMatrix( matrix, transformation, transformation_inverse, "", "" );

    return [ smaller_matrix, transformation, transformation_inverse ];

end );

##
InstallMethod( LessGeneratorsTransformationTripleRight,
               [ IsHomalgMatrix ],

  function( matrix )
    local R, transformation, transformation_inverse, smaller_matrix;

    R := HomalgRing( matrix );

    transformation := HomalgVoidMatrix( R );

    transformation_inverse := HomalgVoidMatrix( R );

    smaller_matrix := SimplerEquivalentMatrix( matrix, transformation, transformation_inverse, "", "", "" );

    return [ smaller_matrix, transformation, transformation_inverse ];

end );