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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346#############################################################################
##
## ModulePresentationsForCAP package
##
## Copyright 2014, Sebastian Gutsche, TU Kaiserslautern
## Sebastian Posur, RWTH Aachen
##
#############################################################################
#######################################
##
## FunctorStandardModule
##
#######################################
BindGlobal( "INSTALL_FUNCTOR_STANDARD_MODULE_METHODS",
function( functor_standard_module, presentations, basis_of_module, decide_zero, as_presentation )
InstallMethod( functor_standard_module,
[ IsHomalgRing ],
function( ring )
local category, functor;
category := presentations( ring );
functor := CapFunctor( Concatenation( "Standard module for ", Name( category ) ), category, category );
AddObjectFunction( functor,
function( object )
local matrix;
matrix := basis_of_module( UnderlyingMatrix( object ) );
return as_presentation( matrix );
end );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local matrix;
matrix := UnderlyingMatrix( morphism );
matrix := decide_zero( matrix, UnderlyingMatrix( new_range ) );
return PresentationMorphism( new_source, matrix, new_range );
end );
return functor;
end );
end );
BindGlobal( "INSTALL_FUNCTOR_STANDARD_MODULE",
function( )
INSTALL_FUNCTOR_STANDARD_MODULE_METHODS( FunctorStandardModuleLeft, LeftPresentations, BasisOfRowModule, DecideZeroRows, AsLeftPresentation );
INSTALL_FUNCTOR_STANDARD_MODULE_METHODS( FunctorStandardModuleRight, RightPresentations, BasisOfColumnModule, DecideZeroColumns, AsRightPresentation );
end );
INSTALL_FUNCTOR_STANDARD_MODULE( );
#######################################
##
## FunctorGetRidOfZeroGenerators
##
#######################################
BindGlobal( "INSTALL_FUNCTOR_GET_RID_OF_ZERO_GENERATORS_METHODS",
function( functor_get_rid_of_zero_generators, presentations, get_rid_of_zero_generators_transformation_triple, as_presentation, parity )
InstallMethod( functor_get_rid_of_zero_generators,
[ IsHomalgRing ],
function( ring )
local category, functor;
category := presentations( ring );
functor := CapFunctor( Concatenation( "Get rid of zero generators for ", Name( category ) ), category, category );
AddObjectFunction( functor,
function( object )
local matrix, triple;
matrix := UnderlyingMatrix( object );
matrix := get_rid_of_zero_generators_transformation_triple( matrix );
return as_presentation( matrix[1] );
end );
if parity = "left" then
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local source_transformation_triple, range_transformation_triple, new_morphism_matrix;
source_transformation_triple := get_rid_of_zero_generators_transformation_triple( UnderlyingMatrix( Source( morphism ) ) );
range_transformation_triple := get_rid_of_zero_generators_transformation_triple( UnderlyingMatrix( Range( morphism ) ) );
new_morphism_matrix := UnderlyingMatrix( morphism );
new_morphism_matrix := source_transformation_triple[ 3 ] * new_morphism_matrix * range_transformation_triple[ 2 ];
return PresentationMorphism( new_source, new_morphism_matrix, new_range );
end );
else
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local source_transformation_triple, range_transformation_triple, new_morphism_matrix;
source_transformation_triple := get_rid_of_zero_generators_transformation_triple( UnderlyingMatrix( Source( morphism ) ) );
range_transformation_triple := get_rid_of_zero_generators_transformation_triple( UnderlyingMatrix( Range( morphism ) ) );
new_morphism_matrix := UnderlyingMatrix( morphism );
new_morphism_matrix := range_transformation_triple[ 2 ] * new_morphism_matrix * source_transformation_triple[ 3 ];
return PresentationMorphism( new_source, new_morphism_matrix, new_range );
end );
fi;
return functor;
end );
end );
BindGlobal( "INSTALL_FUNCTOR_GET_RID_OF_ZERO_GENERATORS",
function( )
INSTALL_FUNCTOR_GET_RID_OF_ZERO_GENERATORS_METHODS(
FunctorGetRidOfZeroGeneratorsLeft, LeftPresentations, NonZeroGeneratorsTransformationTripleLeft, AsLeftPresentation, "left" );
INSTALL_FUNCTOR_GET_RID_OF_ZERO_GENERATORS_METHODS(
FunctorGetRidOfZeroGeneratorsRight, RightPresentations, NonZeroGeneratorsTransformationTripleRight, AsRightPresentation, "right" );
end );
INSTALL_FUNCTOR_GET_RID_OF_ZERO_GENERATORS( );
#######################################
##
## FunctorLessGenerators
##
#######################################
##
InstallMethod( FunctorLessGeneratorsLeft,
[ IsHomalgRing ],
function( ring )
local category, functor;
category := LeftPresentations( ring );
functor := CapFunctor( Concatenation( "Less generators for ", Name( category ) ), category, category );
AddObjectFunction( functor,
function( object )
local new_object;
new_object := LessGeneratorsTransformationTripleLeft( UnderlyingMatrix( object ) )[1];
return AsLeftPresentation( new_object );
end );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local source_transformation_triple, range_transformation_triple, new_morphism_matrix;
source_transformation_triple := LessGeneratorsTransformationTripleLeft( UnderlyingMatrix( Source( morphism ) ) );
range_transformation_triple := LessGeneratorsTransformationTripleLeft( UnderlyingMatrix( Range( morphism ) ) );
new_morphism_matrix := UnderlyingMatrix( morphism );
new_morphism_matrix := source_transformation_triple[ 3 ] * new_morphism_matrix * range_transformation_triple[ 2 ];
return PresentationMorphism( new_source, new_morphism_matrix, new_range );
end );
return functor;
end );
##
InstallMethod( FunctorLessGeneratorsRight,
[ IsHomalgRing ],
function( ring )
local category, functor;
category := RightPresentations( ring );
functor := CapFunctor( Concatenation( "Less generators for ", Name( category ) ), category, category );
AddObjectFunction( functor,
function( object )
local new_object;
new_object := LessGeneratorsTransformationTripleRight( UnderlyingMatrix( object ) )[1];
return AsRightPresentation( new_object );
end );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local source_transformation_triple, range_transformation_triple, new_morphism_matrix;
source_transformation_triple := LessGeneratorsTransformationTripleRight( UnderlyingMatrix( Source( morphism ) ) );
range_transformation_triple := LessGeneratorsTransformationTripleRight( UnderlyingMatrix( Range( morphism ) ) );
new_morphism_matrix := UnderlyingMatrix( morphism );
new_morphism_matrix := range_transformation_triple[ 2 ] * new_morphism_matrix * source_transformation_triple[ 3 ];
return PresentationMorphism( new_source, new_morphism_matrix, new_range );
end );
return functor;
end );
##
InstallMethod( FunctorDualLeft,
[ IsHomalgRing ],
function( ring )
local category, functor;
category := LeftPresentations( ring );
functor := CapFunctor( Concatenation( "Hom( , R ) functor for ", Name( category ) ), category, category );
AddObjectFunction( functor,
function( object )
local mat, N, M, mor;
mat := UnderlyingMatrix( object );
N := FreeLeftPresentation( NrColumns( mat ), ring );
M := FreeLeftPresentation( NrRows( mat ), ring );
mor := PresentationMorphism( N, Involution( mat ), M );
return KernelObject( mor );
end );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local matrix_of_morphism, mor1, mor2, mor, mor3, matrix_of_the_source, matrix_of_the_range;
matrix_of_morphism := UnderlyingMatrix( morphism );
mor2 := PresentationMorphism( FreeLeftPresentation( NrColumns( matrix_of_morphism ), ring )
, Involution( matrix_of_morphism ), FreeLeftPresentation( NrRows( matrix_of_morphism ), ring ) );
matrix_of_the_range := UnderlyingMatrix( Range( morphism ) );
mor1 := KernelEmbedding( PresentationMorphism( FreeLeftPresentation( NrColumns( matrix_of_the_range ), ring )
, Involution( matrix_of_the_range ), FreeLeftPresentation( NrRows( matrix_of_the_range ), ring ) ) );
mor := PreCompose( mor1, mor2 );
matrix_of_the_source := UnderlyingMatrix( Source( morphism ) );
mor3 := PresentationMorphism( FreeLeftPresentation( NrColumns( matrix_of_the_source ), ring )
, Involution( matrix_of_the_source ), FreeLeftPresentation( NrRows( matrix_of_the_source ), ring ) );
return KernelLift( mor3, mor );
end );
return functor;
end );
##
InstallMethod( FunctorDualRight,
[ IsHomalgRing ],
function( ring )
local category, functor;
category := RightPresentations( ring );
functor := CapFunctor( Concatenation( "Hom( , R ) functor for ", Name( category ) ), category, category );
AddObjectFunction( functor,
function( object )
local mat, N, M, mor;
mat := UnderlyingMatrix( object );
N := FreeRightPresentation( NrColumns( mat ), ring );
M := FreeRightPresentation( NrRows( mat ), ring );
mor := PresentationMorphism( M, Involution( mat ), N );
return KernelObject( mor );
end );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
local matrix_of_morphism, mor1, mor2, mor, mor3, matrix_of_the_source, matrix_of_the_range;
matrix_of_morphism := UnderlyingMatrix( morphism );
mor2 := PresentationMorphism( FreeRightPresentation( NrRows( matrix_of_morphism ), ring )
, Involution( matrix_of_morphism ), FreeRightPresentation( NrColumns( matrix_of_morphism ), ring ) );
matrix_of_the_range := UnderlyingMatrix( Range( morphism ) );
mor1 := KernelEmbedding( PresentationMorphism( FreeRightPresentation( NrRows( matrix_of_the_range ), ring )
, Involution( matrix_of_the_range ), FreeRightPresentation( NrColumns( matrix_of_the_range ), ring ) ) );
mor := PreCompose( mor1, mor2 );
matrix_of_the_source := UnderlyingMatrix( Source( morphism ) );
mor3 := PresentationMorphism( FreeRightPresentation( NrRows( matrix_of_the_source ), ring )
, Involution( matrix_of_the_source ), FreeRightPresentation( NrColumns( matrix_of_the_source ), ring ) );
return KernelLift( mor3, mor );
end );
return functor;
end );
##
InstallMethod( FunctorDoubleDualLeft,
[ IsHomalgRing ],
function( ring )
local category, functor, dual_functor;
category := LeftPresentations( ring );
functor := CapFunctor( Concatenation( " Hom( Hom( , R ), R ) functor for ", Name( category ) ), category, category );
dual_functor := FunctorDualLeft( ring );
AddObjectFunction( functor,
function( object )
return ApplyFunctor( dual_functor, ApplyFunctor( dual_functor, object ) );
end );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
return ApplyFunctor( dual_functor, ApplyFunctor( dual_functor, morphism ) );
end );
return functor;
end );
##
InstallMethod( FunctorDoubleDualRight,
[ IsHomalgRing ],
function( ring )
local category, functor, dual_functor;
category := RightPresentations( ring );
functor := CapFunctor( Concatenation( " Hom( Hom( , R ), R ) functor for ", Name( category ) ), category, category );
dual_functor := FunctorDualRight( ring );
AddObjectFunction( functor,
function( object )
return ApplyFunctor( dual_functor, ApplyFunctor( dual_functor, object ) );
end );
AddMorphismFunction( functor,
function( new_source, morphism, new_range )
return ApplyFunctor( dual_functor, ApplyFunctor( dual_functor, morphism ) );
end );
return functor;
end );