def _coerce_map_from_(self, P):
"""
Return a coercion map from `P` to ``self``, or True, or None.
The following rings admit a coercion map to the Laurent series
ring `A((t))`:
- any ring that admits a coercion map to `A` (including `A`
itself);
- any Laurent series ring, power series ring or polynomial
ring in the variable `t` over a ring admitting a coercion
map to `A`.
EXAMPLES::
sage: S.<t> = LaurentSeriesRing(ZZ)
sage: S.has_coerce_map_from(ZZ)
True
sage: S.has_coerce_map_from(PolynomialRing(ZZ, 't'))
True
sage: S.has_coerce_map_from(LaurentPolynomialRing(ZZ, 't'))
True
sage: S.has_coerce_map_from(PowerSeriesRing(ZZ, 't'))
True
sage: S.has_coerce_map_from(S)
True
sage: S.has_coerce_map_from(QQ)
False
sage: S.has_coerce_map_from(PolynomialRing(QQ, 't'))
False
sage: S.has_coerce_map_from(LaurentPolynomialRing(QQ, 't'))
False
sage: S.has_coerce_map_from(PowerSeriesRing(QQ, 't'))
False
sage: S.has_coerce_map_from(LaurentSeriesRing(QQ, 't'))
False
sage: R.<t> = LaurentSeriesRing(QQ['x'])
sage: R.has_coerce_map_from(QQ[['t']])
True
sage: R.has_coerce_map_from(QQ['t'])
True
sage: R.has_coerce_map_from(ZZ['x']['t'])
True
sage: R.has_coerce_map_from(ZZ['t']['x'])
False
sage: R.has_coerce_map_from(ZZ['x'])
True
"""
A = self.base_ring()
from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
from sage.rings.power_series_ring import is_PowerSeriesRing
from sage.rings.polynomial.laurent_polynomial_ring import is_LaurentPolynomialRing
if ((is_LaurentSeriesRing(P) or is_LaurentPolynomialRing(P)
or is_PowerSeriesRing(P) or is_PolynomialRing(P))
and P.variable_name() == self.variable_name()
and A.has_coerce_map_from(P.base_ring())):
return True
def _coerce_map_from_(self, P):
"""
Return a coercion map from `P` to ``self``, or True, or None.
The following rings admit a coercion map to the Laurent series
ring `A((t))`:
- any ring that admits a coercion map to `A` (including `A`
itself);
- any Laurent series ring, power series ring or polynomial
ring in the variable `t` over a ring admitting a coercion
map to `A`.
EXAMPLES::
sage: S.<t> = LaurentSeriesRing(ZZ)
sage: S.has_coerce_map_from(ZZ)
True
sage: S.has_coerce_map_from(PolynomialRing(ZZ, 't'))
True
sage: S.has_coerce_map_from(LaurentPolynomialRing(ZZ, 't'))
True
sage: S.has_coerce_map_from(PowerSeriesRing(ZZ, 't'))
True
sage: S.has_coerce_map_from(S)
True
sage: S.has_coerce_map_from(QQ)
False
sage: S.has_coerce_map_from(PolynomialRing(QQ, 't'))
False
sage: S.has_coerce_map_from(LaurentPolynomialRing(QQ, 't'))
False
sage: S.has_coerce_map_from(PowerSeriesRing(QQ, 't'))
False
sage: S.has_coerce_map_from(LaurentSeriesRing(QQ, 't'))
False
sage: R.<t> = LaurentSeriesRing(QQ['x'])
sage: R.has_coerce_map_from(QQ[['t']])
True
sage: R.has_coerce_map_from(QQ['t'])
True
sage: R.has_coerce_map_from(ZZ['x']['t'])
True
sage: R.has_coerce_map_from(ZZ['t']['x'])
False
sage: R.has_coerce_map_from(ZZ['x'])
True
"""
A = self.base_ring()
if A is P:
return True
f = A.coerce_map_from(P)
if f is not None:
return self.coerce_map_from(A) * f
from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
from sage.rings.power_series_ring import is_PowerSeriesRing
from sage.rings.polynomial.laurent_polynomial_ring import is_LaurentPolynomialRing
if ((is_LaurentSeriesRing(P) or
is_LaurentPolynomialRing(P) or
is_PowerSeriesRing(P) or
is_PolynomialRing(P))
and P.variable_name() == self.variable_name()
and A.has_coerce_map_from(P.base_ring())):
return True