def canonical_parameters(group, base_ring, k, ep):
r"""
Return a canonical version of the parameters.
EXAMPLES::
sage: canonical_parameters(5, ZZ, 20/3, int(1))
(Hecke triangle group for n = 5, Integer Ring, 20/3, 1)
"""
if (group == infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
n = group.n()
k = QQ(k)
if (ep == None):
ep = (-1)**(k*ZZ(n-2)/ZZ(2))
ep = ZZ(ep)
num = (k-(1-ep)*n/(n-2))*(n-2)/4
try:
num = ZZ(num)
except TypeError:
raise Exception("Invalid resp. non-occuring weight!")
return (group, base_ring, k, ep)
def __classcall__(cls, group = HeckeTriangleGroup(3), prec=ZZ(10)):
r"""
Return a (cached) instance with canonical parameters.
.. NOTE:
For each choice of group and precision the constructor is
cached (only) once. Further calculations with different
base rings and possibly numerical parameters are based on
the same cached instance.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.series_constructor import MFSeriesConstructor
sage: MFSeriesConstructor() == MFSeriesConstructor(3, 10)
True
sage: MFSeriesConstructor(group=4).hecke_n()
4
sage: MFSeriesConstructor(group=5, prec=12).prec()
12
"""
if (group==infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
prec=ZZ(prec)
# We don't need this assumption the precision may in principle also be negative.
# if (prec<1):
# raise Exception("prec must be an Integer >=1")
return super(MFSeriesConstructor,cls).__classcall__(cls, group, prec)
def canonical_parameters(group, base_ring, red_hom, n=None):
r"""
Return a canonical version of the parameters.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.graded_ring import canonical_parameters
sage: canonical_parameters(4, ZZ, 1)
(Hecke triangle group for n = 4, Integer Ring, True, 4)
sage: canonical_parameters(infinity, RR, 0)
(Hecke triangle group for n = +Infinity, Real Field with 53 bits of precision, False, +Infinity)
"""
if not (n is None):
group = n
if (group == infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
red_hom = bool(red_hom)
n = group.n()
return (group, base_ring, red_hom, n)
def canonical_parameters(group, base_ring, red_hom, n=None):
r"""
Return a canonical version of the parameters.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.graded_ring import canonical_parameters
sage: canonical_parameters(4, ZZ, 1)
(Hecke triangle group for n = 4, Integer Ring, True, 4)
sage: canonical_parameters(infinity, RR, 0)
(Hecke triangle group for n = +Infinity, Real Field with 53 bits of precision, False, +Infinity)
"""
if not (n is None):
group = n
if (group == infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
red_hom = bool(red_hom)
n = group.n()
return (group, base_ring, red_hom, n)
def __classcall__(cls, group=HeckeTriangleGroup(3), prec=ZZ(10)):
r"""
Return a (cached) instance with canonical parameters.
.. NOTE:
For each choice of group and precision the constructor is
cached (only) once. Further calculations with different
base rings and possibly numerical parameters are based on
the same cached instance.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.series_constructor import MFSeriesConstructor
sage: MFSeriesConstructor() == MFSeriesConstructor(3, 10)
True
sage: MFSeriesConstructor(group=4).hecke_n()
4
sage: MFSeriesConstructor(group=5, prec=12).prec()
12
"""
if (group == infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
prec = ZZ(prec)
# We don't need this assumption the precision may in principle also be negative.
# if (prec<1):
# raise Exception("prec must be an Integer >=1")
return super(MFSeriesConstructor, cls).__classcall__(cls, group, prec)
def canonical_parameters(group, base_ring, k, ep, n=None):
r"""
Return a canonical version of the parameters.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.space import canonical_parameters
sage: canonical_parameters(5, ZZ, 20/3, int(1))
(Hecke triangle group for n = 5, Integer Ring, 20/3, 1, 5)
sage: canonical_parameters(infinity, ZZ, 2, int(-1))
(Hecke triangle group for n = +Infinity, Integer Ring, 2, -1, +Infinity)
"""
if not (n is None):
group = n
if (group == infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
n = group.n()
k = QQ(k)
if (ep == None):
if (n == infinity):
ep = (-1)**(k/ZZ(2))
elif (ZZ(2).divides(n)):
ep = (-1)**(k*ZZ(n-2)/ZZ(4))
else:
ep = (-1)**(k*ZZ(n-2)/ZZ(2))
ep = ZZ(ep)
if (n == infinity):
num = (k-(1-ep)) / ZZ(4)
else:
num = (k-(1-ep)*n/(n-2)) * (n-2) / ZZ(4)
try:
num = ZZ(num)
except TypeError:
pass
#raise ValueError("Invalid or non-occuring weight k={}, ep={}!".format(k,ep))
return (group, base_ring, k, ep, n)
def __classcall__(cls, group = HeckeTriangleGroup(3), base_ring = ZZ, prec=ZZ(10), fix_d=False, set_d=None, d_num_prec=ZZ(53)):
r"""
Return a (cached) instance with canonical parameters.
In particular in case ``fix_d = True`` or if ``set_d`` is
set then the ``base_ring`` is replaced by the common parent
of ``base_ring`` and the parent of ``set_d`` (resp. the
numerical value of ``d`` in case ``fix_d=True``).
EXAMPLES::
sage: MFSeriesConstructor() == MFSeriesConstructor(3, ZZ, 10, False, None, 53)
True
sage: MFSeriesConstructor(base_ring = CC, set_d=CC(1)) == MFSeriesConstructor(set_d=CC(1))
True
sage: MFSeriesConstructor(group=4, fix_d=True).base_ring() == QQ
True
sage: MFSeriesConstructor(group=5, fix_d=True).base_ring() == RR
True
"""
if (group==infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
prec=ZZ(prec)
#if (prec<1):
# raise Exception("prec must be an Integer >=1")
fix_d = bool(fix_d)
if (fix_d):
n = group.n()
d = group.dvalue()
if (group.is_arithmetic()):
d_num_prec = None
set_d = 1/base_ring(1/d)
else:
d_num_prec = ZZ(d_num_prec)
set_d = group.dvalue().n(d_num_prec)
else:
d_num_prec = None
if (set_d is not None):
base_ring=(base_ring(1)*set_d).parent()
#elif (not base_ring.is_exact()):
# raise NotImplementedError
return super(MFSeriesConstructor,cls).__classcall__(cls, group, base_ring, prec, fix_d, set_d, d_num_prec)
def canonical_parameters(group, base_ring, red_hom):
r"""
Return a canonical version of the parameters.
EXAMPLES::
sage: canonical_parameters(4, ZZ, 1)
(Hecke triangle group for n = 4, Integer Ring, True)
"""
if (group == infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
red_hom = bool(red_hom)
return (group, base_ring, red_hom)
def __classcall__(cls, group = HeckeTriangleGroup(3), base_ring = ZZ, k=QQ(0), ep=None, n=None):
r"""
Return a (cached) instance with canonical parameters.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.space import (canonical_parameters, ZeroForm)
sage: (group, base_ring, k, ep, n) = canonical_parameters(6, CC, 3, -1)
sage: ZeroForm(6, CC, 3, -1) == ZeroForm(group, base_ring, k, ep, n)
True
"""
(group, base_ring, k, ep, n) = canonical_parameters(group, base_ring, k, ep, n)
return super(FormsSpace_abstract,cls).__classcall__(cls, group=group, base_ring=base_ring, k=k, ep=ep, n=n)
def __classcall__(cls, group = HeckeTriangleGroup(3), base_ring = ZZ, k=QQ(0), ep=None, n=None):
r"""
Return a (cached) instance with canonical parameters.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.space import (canonical_parameters, QuasiMeromorphicModularForms)
sage: (group, base_ring, k, ep, n) = canonical_parameters(5, ZZ, 20/3, int(1))
sage: QuasiMeromorphicModularForms(5, ZZ, 20/3, int(1)) == QuasiMeromorphicModularForms(group, base_ring, k, ep, n)
True
"""
(group, base_ring, k, ep, n) = canonical_parameters(group, base_ring, k, ep, n)
return super(FormsSpace_abstract,cls).__classcall__(cls, group=group, base_ring=base_ring, k=k, ep=ep, n=n)
def canonical_parameters(group, base_ring, k, ep, n=None):
r"""
Return a canonical version of the parameters.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.space import canonical_parameters
sage: canonical_parameters(5, ZZ, 20/3, int(1))
(Hecke triangle group for n = 5, Integer Ring, 20/3, 1, 5)
sage: canonical_parameters(infinity, ZZ, 2, int(-1))
(Hecke triangle group for n = +Infinity, Integer Ring, 2, -1, +Infinity)
"""
if not (n is None):
group = n
if (group == infinity):
group = HeckeTriangleGroup(infinity)
else:
try:
group = HeckeTriangleGroup(ZZ(group))
except TypeError:
group = HeckeTriangleGroup(group.n())
n = group.n()
k = QQ(k)
if (ep == None):
if (n == infinity):
ep = (-1)**(k/ZZ(2))
elif (ZZ(2).divides(n)):
ep = (-1)**(k*ZZ(n-2)/ZZ(4))
else:
ep = (-1)**(k*ZZ(n-2)/ZZ(2))
ep = ZZ(ep)
if (n == infinity):
num = (k-(1-ep)) / ZZ(4)
else:
num = (k-(1-ep)*n/(n-2)) * (n-2) / ZZ(4)
try:
num = ZZ(num)
except TypeError:
raise ValueError("Invalid or non-occuring weight k={}, ep={}!".format(k,ep))
return (group, base_ring, k, ep, n)
def __classcall__(cls,
group=HeckeTriangleGroup(3),
base_ring=ZZ,
red_hom=False,
n=None):
r"""
Return a (cached) instance with canonical parameters.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.graded_ring import ModularFormsRing
sage: ModularFormsRing(3, ZZ, 0) == ModularFormsRing()
True
"""
(group, base_ring, red_hom,
n) = canonical_parameters(group, base_ring, red_hom, n)
return super(FormsRing_abstract,
cls).__classcall__(cls,
group=group,
base_ring=base_ring,
red_hom=red_hom,
n=n)