def __init__(self, O, C, R) :
"""
INPUT:
- `O` -- A monoid with an action of a group; As implemented in
:class:~`fourier_expansion_framework.monoidpowerseries.NNMonoid`.
- `C` -- A monoid of characters; As implemented in ::class:~`fourier_expansion_framework.monoidpowerseries.CharacterMonoid_class`.
- `R` -- A representation on a module; As implemented
in :class:~`fourier_expansion_framework.monoidpowerseries.TrivialRepresentation`.
EXAMPLES::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import EquivariantMonoidPowerSeriesModule
sage: emps = EquivariantMonoidPowerSeriesModule_generic(NNMonoid(True), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", FreeModule(QQ, 2))) # indirect doctest
"""
# If the representation O respects the monoid structure of S
# the base ring should be the associated power series ring.
if O.is_monoid_action() :
Module.__init__(self, EquivariantMonoidPowerSeriesRing(O,C,TrivialRepresentation(R.group(), R.base_ring())))
else :
Module.__init__(self, R.codomain())
EquivariantMonoidPowerSeriesAmbient_abstract.__init__(self, O, C, R)
self.__coeff_gens = \
[self._element_class( self,
dict([( C.one_element(), dict([(self.monoid().zero_element(), a)]) )]),
self.monoid().filter_all() )
for a in self.coefficient_domain().gens()]
def __init__(self, O, C, R) :
r"""
INPUT:
- `O` -- A monoid with an action of a group; As implemented in
:class:~`fourier_expansion_framework.monoidpowerseries.NNMonoid`.
- `C` -- A monoid of characters; As implemented in ::class:~`fourier_expansion_framework.monoidpowerseries.CharacterMonoid_class`.
- `R` -- A representation on a module; As implemented
in :class:~`fourier_expansion_framework.monoidpowerseries.TrivialRepresentation`.
EXAMPLES::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import EquivariantMonoidPowerSeriesModule_generic
sage: emps = EquivariantMonoidPowerSeriesModule_generic(NNMonoid(True), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", FreeModule(QQ, 2))) # indirect doctest
sage: emps = EquivariantMonoidPowerSeriesModule_generic(NNMonoid(True), TrivialCharacterMonoid("1", ZZ), TrivialRepresentation("1", FreeModule(ZZ, 2))) # indirect doctest
sage: emps.base_ring()
Ring of equivariant monoid power series over NN
sage: (1 / 2) * emps.0
Equivariant monoid power series in Module of equivariant monoid power series over NN
"""
# If the representation O respects the monoid structure of S
# the base ring should be the associated power series ring.
if O.is_monoid_action() :
Module.__init__(self, EquivariantMonoidPowerSeriesRing(O,C,TrivialRepresentation(R.group(), R.base_ring())))
else :
Module.__init__(self, R.codomain())
EquivariantMonoidPowerSeriesAmbient_abstract.__init__(self, O, C, R)
self.__coeff_gens = \
[self._element_class( self,
dict([( C.one_element(), dict([(self.monoid().zero_element(), a)]) )]),
self.monoid().filter_all() )
for a in self.coefficient_domain().gens()]
def __init__(self, O, C, R):
r"""
INPUT:
- `O` -- A monoid with an action of a group; As implemented in
:class:~`fourier_expansion_framework.monoidpowerseries.NNMonoid`.
- `C` -- A monoid of characters; As implemented in ::class:~`fourier_expansion_framework.monoidpowerseries.CharacterMonoid_class`.
- `R` -- A representation on an algebra; As implemented
in :class:~`fourier_expansion_framework.monoidpowerseries.TrivialRepresentation`.
EXAMPLES::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import EquivariantMonoidPowerSeriesRing_generic
sage: emps = EquivariantMonoidPowerSeriesRing_generic(NNMonoid(True), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", QQ)) # indirect doctest
sage: emps = EquivariantMonoidPowerSeriesRing_generic(NNMonoid(True), TrivialCharacterMonoid("1", ZZ), TrivialRepresentation("1", ZZ)) # indirect doctest
sage: emps.base_ring()
Integer Ring
sage: (1 / 2) * emps.0
Equivariant monoid power series in Ring of equivariant monoid power series over NN
"""
Algebra.__init__(self, R.base_ring())
EquivariantMonoidPowerSeriesAmbient_abstract.__init__(self, O, C, R)
self.__monoid_gens = \
[self._element_class(self,
dict([( C.one_element(), dict([(s, self.coefficient_domain().one_element())]) )]),
self.monoid().filter_all() )
for s in self.action().gens()]
self.__character_gens = \
[self._element_class(self,
dict([( c, dict([(self.monoid().zero_element(), self.coefficient_domain().one_element())]) )]),
self.monoid().filter_all() )
for c in C.gens()]
self.__coefficient_gens = \
[self._element_class(self,
dict([( C.one_element(), dict([(self.monoid().zero_element(), g)]))]),
self.monoid().filter_all() )
for g in self.coefficient_domain().gens()]
from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesBaseRingInjection
self._populate_coercion_lists_(
coerce_list=[
MonoidPowerSeriesBaseRingInjection(R.codomain(), self)
],
convert_list=([O.monoid()]
if isinstance(O.monoid(), Parent) else []))
def __init__(self, O, C, R) :
r"""
INPUT:
- `O` -- A monoid with an action of a group; As implemented in
:class:~`fourier_expansion_framework.monoidpowerseries.NNMonoid`.
- `C` -- A monoid of characters; As implemented in ::class:~`fourier_expansion_framework.monoidpowerseries.CharacterMonoid_class`.
- `R` -- A representation on an algebra; As implemented
in :class:~`fourier_expansion_framework.monoidpowerseries.TrivialRepresentation`.
EXAMPLES::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import EquivariantMonoidPowerSeriesRing_generic
sage: emps = EquivariantMonoidPowerSeriesRing_generic(NNMonoid(True), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", QQ)) # indirect doctest
sage: emps = EquivariantMonoidPowerSeriesRing_generic(NNMonoid(True), TrivialCharacterMonoid("1", ZZ), TrivialRepresentation("1", ZZ)) # indirect doctest
sage: emps.base_ring()
Integer Ring
sage: (1 / 2) * emps.0
Equivariant monoid power series in Ring of equivariant monoid power series over NN
"""
Algebra.__init__(self, R.base_ring())
EquivariantMonoidPowerSeriesAmbient_abstract.__init__(self, O, C, R)
self.__monoid_gens = \
[self._element_class(self,
dict([( C.one_element(), dict([(s, self.coefficient_domain().one_element())]) )]),
self.monoid().filter_all() )
for s in self.action().gens()]
self.__character_gens = \
[self._element_class(self,
dict([( c, dict([(self.monoid().zero_element(), self.coefficient_domain().one_element())]) )]),
self.monoid().filter_all() )
for c in C.gens()]
self.__coefficient_gens = \
[self._element_class(self,
dict([( C.one_element(), dict([(self.monoid().zero_element(), g)]))]),
self.monoid().filter_all() )
for g in self.coefficient_domain().gens()]
from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesBaseRingInjection
self._populate_coercion_lists_(
coerce_list = [MonoidPowerSeriesBaseRingInjection(R.codomain(), self)] ,
convert_list = ([O.monoid()] if isinstance(O.monoid(), Parent) else []) )
