def JacobiD1NNFourierExpansionModule(K, m, weak_forms = False) :
r"""
INPUT:
- `m` -- The index of the associated Jacobi forms.
- `weak_forms` -- If True the weak condition
`r^2 \le 4 m n`n will be imposed on the
indices.
"""
R = EquivariantMonoidPowerSeriesModule(
JacobiFormD1NNIndices(m, weak_forms = weak_forms),
TrivialCharacterMonoid("L^1_2(ZZ)", ZZ),
TrivialRepresentation("L^1_2(ZZ)", K) )
if K is ZZ :
R._set_multiply_function( lambda k, d1,d2, ch1,ch2, res : mult_coeff_int(k, d1, d2, ch1, ch2, res, m)
if not weak_forms
else lambda k, d1,d2, ch1,ch2, res : mult_coeff_int_weak(k, d1, d2, ch1, ch2, res, m) )
else :
R._set_multiply_function( lambda k, d1,d2, ch1,ch2, res : mult_coeff_generic(k, d1, d2, ch1, ch2, res, m)
if not weak_forms
else lambda k, d1,d2, ch1,ch2, res : mult_coeff_generic_weak(k, d1, d2, ch1, ch2, res, m) )
return R
def SiegelModularFormG2FourierExpansionRing(K, with_character=False):
if with_character:
raise NotImplementedError
#R = EquivariantMonoidPowerSeriesRing(
# SiegelModularFormG2Indices_discriminant_xreduce(),
# GL2CharacterMonoid(K),
# TrivialRepresentation("GL(2,ZZ)", K) )
# Characters in GL2CharacterMonoid should accept (det, sgn)
#R._set_reduction_function(sreduce_GL)
#if K is ZZ :
# R._set_multiply_function(mult_coeff_int_character)
#else :
# R._set_multiply_function(mult_coeff_generic_character)
else:
R = EquivariantMonoidPowerSeriesRing(
SiegelModularFormG2Indices_discriminant_xreduce(),
TrivialCharacterMonoid("GL(2,ZZ)", ZZ),
TrivialRepresentation("GL(2,ZZ)", K))
R._set_reduction_function(reduce_GL)
if K is ZZ:
R._set_multiply_function(mult_coeff_int_without_character)
else:
R._set_multiply_function(mult_coeff_generic_without_character)
return R
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 SiegelModularFormG4FourierExpansionRing(K, genus):
R = EquivariantMonoidPowerSeriesRing(
SiegelModularFormG4Indices_diagonal_lll(genus),
TrivialCharacterMonoid("GL(%s,ZZ)" % (genus, ), ZZ),
TrivialRepresentation("GL(%s,ZZ)" % (genus, ), K))
return R
def TestExpansionAmbient(A):
"""
TESTS::
sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
sage: ea = TestExpansionAmbient(QQ)
"""
return EquivariantMonoidPowerSeriesRing(NNMonoid(),
TrivialCharacterMonoid("1", ZZ),
TrivialRepresentation("1", A))
def TestExpansionAmbient_vv(A):
"""
TESTS::
sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
sage: ea = TestExpansionAmbient_vv(QQ)
"""
return EquivariantMonoidPowerSeriesModule(
NNMonoid(), TrivialCharacterMonoid("1", ZZ),
TrivialRepresentation(
"1", FreeModule(A, ModularFormTestType_vectorvalued.rank)))
def JacobiFormD1FourierExpansionModule(K, k, L, weak_forms=False):
r"""
INPUT:
- `L` -- The index of the associated Jacobi forms.
- ``weak_forms`` -- If ``False`` the condition `|L| L^{-1} r**2 <= 4 |L| n`
will be imposed.
"""
indices = JacobiFormD1Indices(L, weak_forms=weak_forms)
return EquivariantMonoidPowerSeriesModule(
indices,
JacobiFormD1FourierExpansionCharacterMonoid(L.matrix().nrows()),
TrivialRepresentation(indices.group(), K))
def ParamodularFormD2FourierExpansionRing(K, level) :
R = EquivariantMonoidPowerSeriesRing(
ParamodularFormD2Indices_discriminant(level),
TrivialCharacterMonoid("GL(2,ZZ)_0 (%s)" % (level,), ZZ),
TrivialRepresentation("GL(2,ZZ)_0 (%s)" % (level,), K) )
# R._set_reduction_function(reduce_GL)
# if K is ZZ :
# R._set_multiply_function(mult_coeff_int)
# else :
# R._set_multiply_function(mult_coeff_generic)
return R
def JacobiFormD1NNFourierExpansionModule(K, m, weak_forms=False):
r"""
INPUT:
- `m` -- The index of the associated Jacobi forms.
- `weak_forms` -- If True the weak condition
`r^2 \le 4 m n`n will be imposed on the
indices.
"""
R = EquivariantMonoidPowerSeriesModule(
JacobiFormD1NNIndices(m, weak_forms=weak_forms),
JacobiFormD1FourierExpansionCharacterMonoid(),
TrivialRepresentation("\Gamma^J_{1, M\infty}", K))
return R