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# SPDX-License-Identifier: GPL-2.0-or-later
# homalg: A homological algebra meta-package for computable Abelian categories
#
# Implementations
#
## Implementation stuff for homalg.
####################################
#
# global variables:
#
####################################
# a central place for configuration variables:
InstallValue( HOMALG,
rec(
category := rec(
description := "objects and morphisms of a computable Abelian category",
short_description := "_for_Abelian_categories",
),
color_display := false,
SubobjectQuotient_uses_Intersect := false,
MaximumNumberOfResolutionSteps := 1001,
AssertionLevel_CheckIfTheyLieInTheSameCategory := 0,
SuppressParityInViewObjForCommutativeStructureObjects := false,
)
);
####################################
#
# global functions:
#
####################################
## a global function for logical implications:
InstallGlobalFunction( LogicalImplicationsForTwoHomalgObjects,
function( statement, obj_filter, subobj_filter )
local len, prop_obj, prop_subobj, prop, subobject_getter, len_subobj, rank;
len := Length( statement );
if len < 5 then
Error( "the first argument must be a list of length at least 5\n" );
fi;
prop_obj := statement[1];
prop_subobj := statement[3];
prop := statement[5];
subobject_getter := statement[2];
if Length( prop_obj ) = 1 then
prop_obj := prop_obj[1];
len_subobj := Length( prop_subobj );
if len_subobj = 1 then
InstallImmediateMethod( prop,
obj_filter and prop_obj, 0,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[1], p -> Tester( p )( subobj ) and p( subobj ) ) then
return true;
fi;
TryNextMethod( );
end );
InstallImmediateMethod( prop_obj,
obj_filter and Tester( prop ), 0,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[1], p -> Tester( p )( subobj ) and p( subobj ) ) and
not prop( o ) then
return false;
fi;
TryNextMethod( );
end );
if IsBound( statement[6] ) and IsInt( statement[6] ) then
rank := statement[6];
else
rank := 0;
fi;
InstallMethod( prop,
[ obj_filter ], rank,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[1], p -> Tester( p )( subobj ) and p( subobj ) ) and
prop_obj( o ) then
return true;
fi;
TryNextMethod( );
end );
if IsBound( statement[7] ) and IsInt( statement[7] ) then
InstallMethod( prop_obj,
[ obj_filter ], statement[7],
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[1], p -> Tester( p )( subobj ) and p( subobj ) ) and
not prop( o ) then
return false;
fi;
TryNextMethod( );
end );
fi;
elif len_subobj = 3 then
InstallImmediateMethod( prop,
obj_filter and prop_obj and IsHomalgLeftObjectOrMorphismOfLeftObjects, 0,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[1], p -> Tester( p )( subobj ) and p( subobj ) ) then
return true;
fi;
TryNextMethod( );
end );
InstallImmediateMethod( prop,
obj_filter and prop_obj and IsHomalgRightObjectOrMorphismOfRightObjects, 0,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[2], p -> Tester( p )( subobj ) and p( subobj ) ) then
return true;
fi;
TryNextMethod( );
end );
InstallImmediateMethod( prop_obj,
obj_filter and Tester( prop ) and IsHomalgLeftObjectOrMorphismOfLeftObjects, 0,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[1], p -> Tester( p )( subobj ) and p( subobj ) ) and
not prop( o ) then
return false;
fi;
TryNextMethod( );
end );
InstallImmediateMethod( prop_obj,
obj_filter and Tester( prop ) and IsHomalgRightObjectOrMorphismOfRightObjects, 0,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[2], p -> Tester( p )( subobj ) and p( subobj ) ) and
not prop( o ) then
return false;
fi;
TryNextMethod( );
end );
if IsBound( statement[6] ) and IsInt( statement[6] ) then
rank := statement[6];
else
rank := 0;
fi;
InstallMethod( prop,
[ obj_filter and IsHomalgLeftObjectOrMorphismOfLeftObjects ], rank,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[1], p -> Tester( p )( subobj ) and p( subobj ) ) and
prop_obj( o ) then
return true;
fi;
TryNextMethod( );
end );
InstallMethod( prop,
[ obj_filter and IsHomalgRightObjectOrMorphismOfRightObjects ], 0,
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[2], p -> Tester( p )( subobj ) and p( subobj ) ) and
prop_obj( o ) then
return true;
fi;
TryNextMethod( );
end );
if IsBound( statement[7] ) and IsInt( statement[7] ) then
InstallMethod( prop_obj,
[ obj_filter and IsHomalgLeftObjectOrMorphismOfLeftObjects ], statement[7],
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[1], p -> Tester( p )( subobj ) and p( subobj ) ) and
not prop( o ) then
return false;
fi;
TryNextMethod( );
end );
InstallMethod( prop_obj,
[ obj_filter and IsHomalgRightObjectOrMorphismOfRightObjects ], statement[7],
function( o )
local subobj;
subobj := subobject_getter( o );
if ForAll( prop_subobj[2], p -> Tester( p )( subobj ) and p( subobj ) ) and
not prop( o ) then
return false;
fi;
TryNextMethod( );
end );
fi;
fi;
fi;
end );
##
InstallGlobalFunction( InstallLogicalImplicationsForHomalgObjects,
function( arg )
local nargs, properties, filter, subobj_filter, statement;
nargs := Length( arg );
if nargs < 2 then
Error( "too few arguments\n" );
fi;
properties := arg[1];
filter := arg[2];
if nargs = 2 then
for statement in properties do;
LogicalImplicationsForOneHomalgObject( statement, filter );
od;
elif nargs = 3 then
subobj_filter := arg[3];
for statement in properties do;
LogicalImplicationsForTwoHomalgObjects( statement, filter, subobj_filter );
od;
fi;
end );
## a global function for logical implications of subobjects:
InstallGlobalFunction( LogicalImplicationsForHomalgSubobjects,
function( prop_attr, filter_subobject, test_underlying_object, fetch_underlying_object )
InstallImmediateMethod( prop_attr,
filter_subobject and test_underlying_object, 0,
function( o )
if Tester( prop_attr )( fetch_underlying_object( o ) ) then
return prop_attr( fetch_underlying_object( o ) );
fi;
TryNextMethod( );
end );
InstallMethod( prop_attr,
"for homalg subobjects",
[ filter_subobject ],
function( o )
return prop_attr( fetch_underlying_object( o ) );
end );
end );
## a global function for logical implications of subobjects:
InstallGlobalFunction( InstallLogicalImplicationsForHomalgSubobjects,
function( properties_attributes, filter_subobject, test_underlying_object, fetch_underlying_object )
local s;
for s in properties_attributes do
LogicalImplicationsForHomalgSubobjects( s, filter_subobject, test_underlying_object, fetch_underlying_object );
od;
end );
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