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products/sources/formale Sprachen/GAP/pkg/cap/gap/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 22.8.2025 mit Größe 5 kB

Quelle PrintingFunctions.gi Sprache: unbekannt

# SPDX-License-Identifier: GPL-2.0-or-later
# CAP: Categories, Algorithms, Programming
#
# Implementations
#
InstallGlobalFunction( InfoStringOfInstalledOperationsOfCategory,

  function( category )
    local result, MaximalPropertiesWithRegardToImplication, list_of_potential_categorical_properties, list_of_mathematical_properties,
          list_of_potential_algorithmic_properties, list_of_algorithmic_and_not_yet_algorithmic_properties,
          list_of_algorithmic_properties, list_of_maximal_algorithmic_properties,
          list_of_not_yet_algorithmic_properties, list_of_maximal_not_yet_algorithmic_properties,
          property,
          list_of_mathematical_properties_not_implied_by_algorithmic_or_not_yet_algorithmic_properties, list_of_maximal_mathematical_properties_not_implied_by_algorithmic_or_not_yet_algorithmic_properties;

    if not IsCapCategory( category ) then
        Error( "first argument must be a category" );
        return;
    fi;

    result := String( Length( ListPrimitivelyInstalledOperationsOfCategory( category ) ) );
    result := Concatenation( result, " primitive operations were used to derive " );
    result := Concatenation( result, String( Length( ListInstalledOperationsOfCategory( category ) ) ) );
    result := Concatenation( result, " operations for this category" );

    MaximalPropertiesWithRegardToImplication := function ( list_of_properties )

        return MaximalObjects( list_of_properties, { p1, p2 } -> IsSpecializationOfFilter( ValueGlobal( p1 ), ValueGlobal( p2 ) ) );

    end;

    list_of_potential_categorical_properties := Set( Filtered( Concatenation( CAP_INTERNAL_CATEGORICAL_PROPERTIES_LIST ), x -> x <> fail ) );

    list_of_mathematical_properties := ListKnownCategoricalProperties( category );

    list_of_potential_algorithmic_properties := SortedList( RecNames( CAP_INTERNAL_CONSTRUCTIVE_CATEGORIES_RECORD ) );

    # check that all potential algorithmic properties except "IsCapCategory" are potential categorical properties
    Assert( 0, Difference( list_of_potential_algorithmic_properties, list_of_potential_categorical_properties ) = [ "IsCapCategory" ] );

    list_of_algorithmic_and_not_yet_algorithmic_properties := Intersection( list_of_mathematical_properties, list_of_potential_algorithmic_properties );

    list_of_algorithmic_properties := Filtered( list_of_algorithmic_and_not_yet_algorithmic_properties, p -> IsEmpty( MissingOperationsForConstructivenessOfCategory( category, p ) ) );

    list_of_maximal_algorithmic_properties := MaximalPropertiesWithRegardToImplication( list_of_algorithmic_properties );

    StableSortBy( list_of_maximal_algorithmic_properties, p -> Length( ListOfDefiningOperations( p ) ) );

    if not IsEmpty( list_of_maximal_algorithmic_properties ) then

        result := Concatenation( result, " which algorithmically" );

        for property in list_of_maximal_algorithmic_properties do

            result := Concatenation( result, "\n* " );
            result := Concatenation( result, property );

        od;
    fi;

    list_of_not_yet_algorithmic_properties := Difference( list_of_algorithmic_and_not_yet_algorithmic_properties, list_of_algorithmic_properties );

    list_of_maximal_not_yet_algorithmic_properties := MaximalPropertiesWithRegardToImplication( list_of_not_yet_algorithmic_properties );

    StableSortBy( list_of_maximal_not_yet_algorithmic_properties, p -> Length( ListOfDefiningOperations( p ) ) );

    if not IsEmpty( list_of_maximal_not_yet_algorithmic_properties ) then

        if IsEmpty( list_of_maximal_algorithmic_properties ) then
            result := Concatenation( result, " which" );
        else
            result := Concatenation( result, "\nand" );
        fi;

        result := Concatenation( result, " not yet algorithmically" );

        for property in list_of_maximal_not_yet_algorithmic_properties do
            result := Concatenation( result, "\n* " );
            result := Concatenation( result, property );
        od;

    fi;

    ## Finally, capture the remaining mathematical properties influencing the derivation mechanism:
    list_of_mathematical_properties_not_implied_by_algorithmic_or_not_yet_algorithmic_properties :=
      Filtered( list_of_mathematical_properties, pm -> not ForAny( list_of_algorithmic_and_not_yet_algorithmic_properties, pa -> IsSpecializationOfFilter( ValueGlobal( pm ), ValueGlobal( pa ) ) ) );

    list_of_maximal_mathematical_properties_not_implied_by_algorithmic_or_not_yet_algorithmic_properties :=
      MaximalPropertiesWithRegardToImplication( list_of_mathematical_properties_not_implied_by_algorithmic_or_not_yet_algorithmic_properties );

    if not IsEmpty( list_of_maximal_mathematical_properties_not_implied_by_algorithmic_or_not_yet_algorithmic_properties ) then

        if IsEmpty( list_of_maximal_algorithmic_properties ) and IsEmpty( list_of_maximal_not_yet_algorithmic_properties ) then
            result := Concatenation( result, " which" );
        else
            result := Concatenation( result, "\nand furthermore" );
        fi;
        result := Concatenation( result, " mathematically" );

        for property in list_of_maximal_mathematical_properties_not_implied_by_algorithmic_or_not_yet_algorithmic_properties do
            result := Concatenation( result, "\n* " );
            result := Concatenation( result, property );
        od;

    fi;

    return result;

end );

InstallGlobalFunction( InfoOfInstalledOperationsOfCategory,

  function( category )

    Display( InfoStringOfInstalledOperationsOfCategory( category ) );

end );