def _coerce_map_from_(self, S):
"""
The rings that canonically coerce to the MPFR complex field are:
- This MPFR complex field, or any other of higher precision
- Anything that canonically coerces to the mpfr real field
with this prec
EXAMPLES::
sage: ComplexField(200)(1) + RealField(90)(1) # indirect doctest
2.0000000000000000000000000
sage: parent(ComplexField(200)(1) + RealField(90)(1)) # indirect doctest
Complex Field with 90 bits of precision
sage: CC.0 + RLF(1/3) # indirect doctest
0.333333333333333 + 1.00000000000000*I
sage: ComplexField(20).has_coerce_map_from(CDF)
True
sage: ComplexField(200).has_coerce_map_from(CDF)
False
"""
RR = self._real_field()
if RR.has_coerce_map_from(S):
return complex_number.RRtoCC(RR, self) * RR._internal_coerce_map_from(S)
if is_ComplexField(S) and S._prec >= self._prec:
return self._generic_convert_map(S)
late_import()
if S in [AA, QQbar, CLF, RLF] or (S == CDF and self._prec <= 53):
return self._generic_convert_map(S)
return self._coerce_map_via([CLF], S)
def __init__(self, prec=53):
"""
TESTS::
sage: C = ComplexField(200)
sage: C.category()
Category of fields
sage: TestSuite(C).run()
"""
self._prec = int(prec)
from sage.categories.fields import Fields
ParentWithGens.__init__(self, self._real_field(), ('I',), False, category = Fields())
# self._populate_coercion_lists_()
self._populate_coercion_lists_(coerce_list=[complex_number.RRtoCC(self._real_field(), self)])
def __init__(self, prec=53):
"""
Initialize ``self``.
TESTS::
sage: C = ComplexField(200)
sage: C.category()
Join of Category of fields and Category of complete metric spaces
sage: TestSuite(C).run()
"""
self._prec = int(prec)
from sage.categories.fields import Fields
ParentWithGens.__init__(self, self._real_field(), ('I',), False, category=Fields().Metric().Complete())
# self._populate_coercion_lists_()
self._populate_coercion_lists_(coerce_list=[complex_number.RRtoCC(self._real_field(), self)])