|
# 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 );
[ Dauer der Verarbeitung: 0.31 Sekunden
(vorverarbeitet)
]
|
