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)
