|
# SPDX-License-Identifier: GPL-2.0-or-later
# GradedModules: A homalg based package for the Abelian category of finitely presented graded modules over computable graded rings
#
# Implementations
#
## implementation stuff for degrees of sets of generators.
####################################
#
# representations:
#
####################################
# a new representation for the GAP-category IsSetsOfGenerators:
DeclareRepresentation( "IsSetOfDegreesOfGeneratorsRep",
IsSetOfDegreesOfGenerators,
[ "ListOfPositionsOfKnownDegrees" ] );
####################################
#
# families and types:
#
####################################
# a new family:
BindGlobal( "TheFamilyOfHomalgSetOfDegreesOfGenerators",
NewFamily( "TheFamilyOfHomalgSetOfDegreesOfGenerators" ) );
# a new type:
BindGlobal( "TheTypeHomalgSetOfDegreesOfGenerators",
NewType( TheFamilyOfHomalgSetOfDegreesOfGenerators,
IsSetOfDegreesOfGeneratorsRep ) );
####################################
#
# methods for operations:
#
####################################
##
InstallMethod( AddDegreesOfGenerators,
"for a set of degrees of generators",
[ IsSetOfDegreesOfGeneratorsRep, IsInt, IsList ],
function( gens, pos, degrees )
gens!.(pos) := degrees;
Add( gens!.ListOfPositionsOfKnownDegreesOfGenerators, pos );
end );
##
InstallMethod( GetDegreesOfGenerators,
"for a set of degrees of generators",
[ IsSetOfDegreesOfGeneratorsRep, IsPosInt ],
function( gens, pos )
if IsBound( gens!.(pos) ) then
return gens!.(pos);
else
return fail;
fi;
end );
##
InstallMethod( ListOfPositionsOfKnownDegreesOfGenerators,
"for a set of degrees of generators",
[ IsSetOfDegreesOfGeneratorsRep ],
function( gens )
return gens!.ListOfPositionsOfKnownDegreesOfGenerators;
end );
####################################
#
# constructor functions and methods:
#
####################################
##
InstallMethod( CreateSetOfDegreesOfGenerators,
"for list of degrees",
[ IsList ],
function( degrees )
return CreateSetOfDegreesOfGenerators( degrees, 1 );
end );
##
InstallMethod( CreateSetOfDegreesOfGenerators,
"for list of degrees and a position",
[ IsList, IsInt ],
function( degrees, pos )
local generators;
generators := rec(
ListOfPositionsOfKnownDegreesOfGenerators := [ pos ]
);
generators!.(pos) := degrees;
## Objectify:
Objectify( TheTypeHomalgSetOfDegreesOfGenerators, generators );
return generators;
end );
##
InstallMethod( DegreesOfGenerators,
"for homalg graded modules",
[ IsGradedModuleRep, IsPosInt ],
function( M, pos )
local degrees, l_deg, l_rel, T;
degrees := GetDegreesOfGenerators( SetOfDegreesOfGenerators( M ), pos );
if degrees = fail then
l_deg := ListOfPositionsOfKnownDegreesOfGenerators( SetOfDegreesOfGenerators( M ) );
l_rel := ListOfPositionsOfKnownSetsOfRelations( M );
if not pos in l_rel then
return fail;
fi;
#use a heuristic here to find a smaller/better/faster-to-compute transition matrix?
if IsHomalgLeftObjectOrMorphismOfLeftObjects( M ) then
T := TransitionMatrix( M, pos, l_deg[1] );
degrees := NonTrivialDegreePerRow( T, DegreesOfGenerators( M, l_deg[1] ) );
else
T := TransitionMatrix( M, l_deg[1], pos );
degrees := NonTrivialDegreePerColumn( T, DegreesOfGenerators( M, l_deg[1] ) );
fi;
AddDegreesOfGenerators( SetOfDegreesOfGenerators( M ), pos, degrees );
fi;
return degrees;
end );
##
InstallMethod( DegreesOfGenerators,
"for homalg graded modules",
[ IsGradedModuleRep ],
function( M )
return DegreesOfGenerators( M, PositionOfTheDefaultPresentation( UnderlyingModule( M ) ) );
end );
##
InstallMethod( DegreesOfGenerators,
"for homalg graded modules",
[ IsGradedModuleRep and IsZero ],
function( M )
if NrGenerators( M ) > 0 then
TryNextMethod( );
fi;
return [ ];
end );
InstallMethod( DegreesOfGenerators,
"for homalg graded modules",
[ IsGradedSubmoduleRep ],
function( M )
return DegreesOfGenerators( Source( MorphismHavingSubobjectAsItsImage( M ) ) );
end );
####################################
#
# View, Print, and Display methods:
#
####################################
InstallMethod( ViewObj,
"for set of degrees of generators",
[ IsSetOfDegreesOfGeneratorsRep ],
function( o )
local l;
l := Length( o!.ListOfPositionsOfKnownDegreesOfGenerators );
Print( "<A set containing " );
if l = 1 then
Print( "a single list " );
else
Print( l, " lists " );
fi;
Print( "of degrees of generators of a graded homalg module>" );
end );
##
InstallMethod( Display,
"for set of degrees of generators",
[ IsSetOfDegreesOfGeneratorsRep ], ## since we don't use the filter IsHomalgLeftObjectOrMorphismOfLeftObjects we need to set the ranks high
function( o )
ViewObj( o );
end );
[ Verzeichnis aufwärts0.43unsichere Verbindung
Übersetzung europäischer Sprachen durch Browser
]
|
