def __init__(self, O, C, R):
r"""
INPUT:
- `O` -- An action of a group `G` on a monoid as implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.NNMonoid`.
- `C` -- A monoid of charcters `G -> K` for a ring `K`. As implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.CharacterMonoid_class`.
- `R` -- A representation of `G` on some `K`-algebra or module `A`.
As implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.TrivialRepresentation`.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesSymmetrisationModuleFunctor
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import NNMonoid, TrivialRepresentation, TrivialCharacterMonoid
sage: F = MonoidPowerSeriesSymmetrisationModuleFunctor(NNMonoid(), TrivialCharacterMonoid("1", ZZ), TrivialRepresentation("1", FreeModule(ZZ, 1)))
"""
if O.group() != C.group():
raise ValueError, "The action on S and the characters must have the same group"
if R.base_ring() != C.codomain():
if C.codomain().has_coerce_map_from(R.base_ring()):
pass
elif R.base_ring().has_coerce_map_from(C.codomain()):
pass
else:
raise ValueError, "character codomain and representation base ring must be coercible"
self.__O = O
self.__C = C
self.__R = R
ConstructionFunctor.__init__(self, CommutativeAdditiveGroups(),
CommutativeAdditiveGroups())
def __init__(self, O, C, R) :
r"""
INPUT:
- `O` -- An action of a group `G` on a monoid as implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.NNMonoid`.
- `C` -- A monoid of charcters `G -> K` for a ring `K`. As implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.CharacterMonoid_class`.
- `R` -- A representation of `G` on some `K`-algebra or module `A`.
As implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.TrivialRepresentation`.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesSymmetrisationModuleFunctor
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import NNMonoid, TrivialRepresentation, TrivialCharacterMonoid
sage: F = MonoidPowerSeriesSymmetrisationModuleFunctor(NNMonoid(), TrivialCharacterMonoid("1", ZZ), TrivialRepresentation("1", FreeModule(ZZ, 1)))
"""
if O.group() != C.group() :
raise ValueError, "The action on S and the characters must have the same group"
if R.base_ring() != C.codomain() :
if C.codomain().has_coerce_map_from(R.base_ring()) :
pass
elif R.base_ring().has_coerce_map_from(C.codomain()) :
pass
else :
raise ValueError, "character codomain and representation base ring must be coercible"
self.__O = O
self.__C = C
self.__R = R
ConstructionFunctor.__init__(self, CommutativeAdditiveGroups(), CommutativeAdditiveGroups())
def __init__(self, O, C, R) :
r"""
INPUT:
- `O` -- An action of a group `G` on a monoid as implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.NNMonoid`.
- `C` -- A monoid of charcters `G -> K` for a ring `K`. As implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.CharacterMonoid_class`.
- `R` -- A representation of `G` on some `K`-algebra or module `A`.
As implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.TrivialRepresentation`.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import EquivariantMonoidPowerSeriesRingFunctor
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import NNMonoid, TrivialRepresentation, TrivialCharacterMonoid
sage: F = EquivariantMonoidPowerSeriesRingFunctor(NNMonoid(), TrivialCharacterMonoid("1", ZZ), TrivialRepresentation("1", ZZ))
"""
if O.group() != C.group() :
raise ValueError( "The action on S and the characters must have the same group" )
if R.base_ring() != C.codomain() :
# if C.codomain().has_coerce_map_from(R.base_ring()) :
# pass
# el
if R.base_ring().has_coerce_map_from(C.codomain()) :
pass
else :
raise ValueError( "character codomain and representation base ring must be coercible" )
if not O.is_monoid_action() :
raise ValueError( "monoid structure must be compatible with group action" )
self.__O = O
self.__C = C
self.__R = R
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, O, C, R):
r"""
INPUT:
- `O` -- An action of a group `G` on a monoid as implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.NNMonoid`.
- `C` -- A monoid of charcters `G -> K` for a ring `K`. As implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.CharacterMonoid_class`.
- `R` -- A representation of `G` on some `K`-algebra or module `A`.
As implemented in :class:`~fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basismonoids.TrivialRepresentation`.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import EquivariantMonoidPowerSeriesRingFunctor
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import NNMonoid, TrivialRepresentation, TrivialCharacterMonoid
sage: F = EquivariantMonoidPowerSeriesRingFunctor(NNMonoid(), TrivialCharacterMonoid("1", ZZ), TrivialRepresentation("1", ZZ))
"""
if O.group() != C.group():
raise ValueError(
"The action on S and the characters must have the same group")
if R.base_ring() != C.codomain():
# if C.codomain().has_coerce_map_from(R.base_ring()) :
# pass
# el
if R.base_ring().has_coerce_map_from(C.codomain()):
pass
else:
raise ValueError(
"character codomain and representation base ring must be coercible"
)
if not O.is_monoid_action():
raise ValueError(
"monoid structure must be compatible with group action")
self.__O = O
self.__C = C
self.__R = R
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, base):
"""
Initialize ``self``.
EXAMPLES::
sage: from sage.algebras.tensor_algebra import TensorAlgebraFunctor
sage: F = TensorAlgebraFunctor(Rings())
sage: TestSuite(F).run()
"""
ConstructionFunctor.__init__(self, Modules(base), Algebras(base))
def __init__(self, base):
"""
Initialize ``self``.
EXAMPLES::
sage: from sage.algebras.tensor_algebra import TensorAlgebraFunctor
sage: F = TensorAlgebraFunctor(Rings())
sage: TestSuite(F).run()
"""
ConstructionFunctor.__init__(self, Modules(base), Algebras(base))
def __init__(self, field):
"""
TESTS::
sage: from sage.rings.function_field.differential import DifferentialsSpaceFunctor
sage: K.<x> = FunctionField(QQ)
sage: DifferentialsSpaceFunctor(K)(K)
Space of differentials of Rational function field in x over Rational Field
"""
ConstructionFunctor.__init__(self, FunctionFields(),
DifferentialsSpaces(field))
def __init__(self, S) :
r"""
INPUT:
- `S` -- A monoid as in :class:`~from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids.NNMonoid`
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesRingFunctor
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import NNMonoid
sage: F = MonoidPowerSeriesRingFunctor(NNMonoid(False))
"""
self.__S = S
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, S):
r"""
INPUT:
- `S` -- A monoid as in :class:`~from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids.NNMonoid`
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesRingFunctor
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import NNMonoid
sage: F = MonoidPowerSeriesRingFunctor(NNMonoid(False))
"""
self.__S = S
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, group):
r"""
See :class:`GroupAlgebraFunctor` for full documentation.
EXAMPLES::
sage: from sage.categories.algebra_functor import GroupAlgebraFunctor
sage: GroupAlgebra(SU(2, GF(4, 'a')), IntegerModRing(12)).category()
Category of finite group algebras over Ring of integers modulo 12
"""
self.__group = group
from sage.categories.rings import Rings
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, group) :
r"""
See :class:`GroupAlgebraFunctor` for full documentation.
EXAMPLES::
sage: from sage.algebras.group_algebra_new import GroupAlgebraFunctor
sage: GroupAlgebra(SU(2, GF(4, 'a')), IntegerModRing(12)).category()
Category of hopf algebras with basis over Ring of integers modulo 12
"""
self.__group = group
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, B, S) :
r"""
INPUT:
- `B` -- A ring.
- `S` -- A monoid as in :class:`~from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids.NNMonoid`
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesModuleFunctor
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import NNMonoid
sage: F = MonoidPowerSeriesModuleFunctor(ZZ, NNMonoid(False))
"""
self.__S = S
ConstructionFunctor.__init__(self, Modules(B), CommutativeAdditiveGroups())
def __init__(self, relations):
"""
Initialization of ``self``.
TESTS::
sage: from sage.modules.module_functors import QuotientModuleFunctor
sage: B = (2/3)*ZZ^2
sage: F = QuotientModuleFunctor(B)
sage: TestSuite(F).run()
"""
R = relations.category().base_ring()
ConstructionFunctor.__init__(self, Modules(R), Modules(R))
self._relations = relations
def __init__(self, B, S) :
r"""
INPUT:
- `B` -- A ring.
- `S` -- A monoid as in :class:`~from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids.NNMonoid`
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesModuleFunctor
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import NNMonoid
sage: F = MonoidPowerSeriesModuleFunctor(ZZ, NNMonoid(False))
"""
self.__S = S
ConstructionFunctor.__init__(self, Modules(B), CommutativeAdditiveGroups())
def __init__(self, relations):
"""
Initialization of ``self``.
TESTS::
sage: from sage.modules.module_functors import QuotientModuleFunctor
sage: B = (2/3)*ZZ^2
sage: F = QuotientModuleFunctor(B)
sage: TestSuite(F).run()
"""
R = relations.category().base_ring()
ConstructionFunctor.__init__(self, Modules(R), Modules(R))
self._relations = relations
def __init__(self, arguments):
"""
A functor which produces a CallableSymbolicExpressionRing from
the SymbolicRing.
EXAMPLES::
sage: from sage.symbolic.callable import CallableSymbolicExpressionFunctor
sage: x,y = var('x,y')
sage: f = CallableSymbolicExpressionFunctor((x,y)); f
CallableSymbolicExpressionFunctor(x, y)
sage: f(SR)
Callable function ring with arguments (x, y)
sage: loads(dumps(f))
CallableSymbolicExpressionFunctor(x, y)
"""
self._arguments = arguments
from sage.categories.all import Rings
self.rank = 3
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, arguments):
"""
A functor which produces a CallableSymbolicExpressionRing from
the SymbolicRing.
EXAMPLES::
sage: from sage.symbolic.callable import CallableSymbolicExpressionFunctor
sage: x,y = var('x,y')
sage: f = CallableSymbolicExpressionFunctor((x,y)); f
CallableSymbolicExpressionFunctor(x, y)
sage: f(SR)
Callable function ring with arguments (x, y)
sage: loads(dumps(f))
CallableSymbolicExpressionFunctor(x, y)
"""
self._arguments = arguments
from sage.categories.all import Rings
self.rank = 3
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, type, precision):
"""
A functor constructing a ring or module of modular forms.
INPUT:
- ``type`` -- A type of modular forms.
- ``precision`` -- A precision.
NOTE:
This does not respect keyword and has to be extended as soon as subclasses of
ModularFormsAmbient_abstract demand for it.
TESTS::
sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_functor import *
sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: F = ModularFormsFunctor( ModularFormTestType_scalar(), NNFilter(5) )
"""
self.__type = type
self.__precision = precision
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__(self, type, precision) :
"""
A functor constructing a ring or module of modular forms.
INPUT:
- ``type`` -- A type of modular forms.
- ``precision`` -- A precision.
NOTE:
This does not respect keyword and has to be extended as soon as subclasses of
ModularFormsAmbient_abstract demand for it.
TESTS::
sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_functor import *
sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: F = ModularFormsFunctor( ModularFormTestType_scalar(), NNFilter(5) )
"""
self.__type = type
self.__precision = precision
ConstructionFunctor.__init__(self, Rings(), Rings())
def __init__( self, base_ring_generators, generators,
relations, grading, all_relations = True, reduce_before_evaluating = True ) :
r"""
INPUT:
- ``base_ring_generators`` -- A sequence of (equivariant) monoid power series with
coefficient domain the base ring of the coefficient
domain of the generators or ``None``.
- ``generators`` -- A sequence of (equivariant) monoid power series; The generators
of the ambient over the ring generated by the base ring
generators.
- ``relations`` -- An ideal in a polynomial ring with ``len(base_ring_generators) + len(generators)``
variables.
- ``grading`` -- A grading deriving from :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_grading`;
A grading for the polynomial ring of the relations.
- ``all_relations`` -- A boolean (default: ``True``); If ``True`` the relations given
for the polynomial ring are all relations that the Fourier
expansion have.
- ``reduce_before_evaluating`` -- A boolean (default: ``True``); If ``True`` any monomial
will be Groebner reduced before the Fourier expansion
is calculated.
NOTE:
The grading must respect the relations of the generators.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_element import *
sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_grading import DegreeGrading
sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_functor import *
sage: mps = MonoidPowerSeriesRing(QQ, NNMonoid(False))
sage: funct = GradedExpansionFunctor(Sequence([MonoidPowerSeries(mps, {1: 1}, mps.monoid().filter(4))]), Sequence([MonoidPowerSeries(mps, {1: 1, 2: 3}, mps.monoid().filter(4))]), PolynomialRing(QQ, ['a', 'b']).ideal(0), DegreeGrading((1,2)))
"""
if grading.ngens() != relations.ring().ngens() :
raise ValueError( "Grading must have the same number of variables as the relations' polynomial ring." )
self.__relations = relations
self.__grading = grading
self.__all_relations = all_relations
self.__reduce_before_evaluating = reduce_before_evaluating
self.__gen_expansions = Sequence(generators)
if base_ring_generators is None :
self.__base_gen_expansions = Sequence([], universe = self.__gen_expansions.universe().base_ring())
else :
self.__base_gen_expansions = Sequence(base_ring_generators)
if len(self.__base_gen_expansions) == 0 :
scalar_ring = self.__gen_expansions.universe().base_ring()
if self.__gen_expansions.universe().coefficient_domain() != self.__gen_expansions.universe().base_ring() :
scalar_ring = self.__gen_expansions.universe().base_ring().base_ring()
else :
scalar_ring = self.__gen_expansions.universe().base_ring()
else :
scalar_ring = self.__base_gen_expansions.universe().base_ring()
if not relations.base_ring().has_coerce_map_from(scalar_ring) :
raise ValueError( "The generators must be defined over the base ring of relations" )
if not isinstance(self.__gen_expansions.universe(), Algebra) and \
not isinstance(self.__gen_expansions.universe(), Module) :
raise TypeError( "The generators' universe must be an algebra or a module" )
ConstructionFunctor.__init__( self, Rings(), Rings() )
def __init__(self,
base_ring_generators,
generators,
relations,
grading,
all_relations=True,
reduce_before_evaluating=True):
r"""
INPUT:
- ``base_ring_generators`` -- A sequence of (equivariant) monoid power series with
coefficient domain the base ring of the coefficient
domain of the generators or ``None``.
- ``generators`` -- A sequence of (equivariant) monoid power series; The generators
of the ambient over the ring generated by the base ring
generators.
- ``relations`` -- An ideal in a polynomial ring with ``len(base_ring_generators) + len(generators)``
variables.
- ``grading`` -- A grading deriving from :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_grading`;
A grading for the polynomial ring of the relations.
- ``all_relations`` -- A boolean (default: ``True``); If ``True`` the relations given
for the polynomial ring are all relations that the Fourier
expansion have.
- ``reduce_before_evaluating`` -- A boolean (default: ``True``); If ``True`` any monomial
will be Groebner reduced before the Fourier expansion
is calculated.
NOTE:
The grading must respect the relations of the generators.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_element import *
sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_grading import DegreeGrading
sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_functor import *
sage: mps = MonoidPowerSeriesRing(QQ, NNMonoid(False))
sage: funct = GradedExpansionFunctor(Sequence([MonoidPowerSeries(mps, {1: 1}, mps.monoid().filter(4))]), Sequence([MonoidPowerSeries(mps, {1: 1, 2: 3}, mps.monoid().filter(4))]), PolynomialRing(QQ, ['a', 'b']).ideal(0), DegreeGrading((1,2)))
"""
if grading.ngens() != relations.ring().ngens():
raise ValueError(
"Grading must have the same number of variables as the relations' polynomial ring."
)
self.__relations = relations
self.__grading = grading
self.__all_relations = all_relations
self.__reduce_before_evaluating = reduce_before_evaluating
self.__gen_expansions = Sequence(generators)
if base_ring_generators is None:
self.__base_gen_expansions = Sequence(
[], universe=self.__gen_expansions.universe().base_ring())
else:
self.__base_gen_expansions = Sequence(base_ring_generators)
if len(self.__base_gen_expansions) == 0:
scalar_ring = self.__gen_expansions.universe().base_ring()
if self.__gen_expansions.universe().coefficient_domain(
) != self.__gen_expansions.universe().base_ring():
scalar_ring = self.__gen_expansions.universe().base_ring(
).base_ring()
else:
scalar_ring = self.__gen_expansions.universe().base_ring()
else:
scalar_ring = self.__base_gen_expansions.universe().base_ring()
if not relations.base_ring().has_coerce_map_from(scalar_ring):
raise ValueError(
"The generators must be defined over the base ring of relations"
)
if not isinstance(self.__gen_expansions.universe(), Algebra) and \
not isinstance(self.__gen_expansions.universe(), Module) :
raise TypeError(
"The generators' universe must be an algebra or a module")
ConstructionFunctor.__init__(self, Rings(), Rings())
