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 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 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 SiegelModularFormG2VVFourierExpansionRing(K):
R = EquivariantMonoidPowerSeriesRing(
SiegelModularFormG2Indices_discriminant_xreduce(),
TrivialCharacterMonoid("GL(2,ZZ)", ZZ),
SiegelModularFormG2VVRepresentation(K))
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 SiegelModularFormG4FourierExpansionRing(K, genus):
R = EquivariantMonoidPowerSeriesRing(
SiegelModularFormG4Indices_diagonal_lll(genus),
TrivialCharacterMonoid("GL(%s,ZZ)" % (genus, ), ZZ),
TrivialRepresentation("GL(%s,ZZ)" % (genus, ), K))
return R
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