def _is_valid_homomorphism_(self, codomain, im_gens):
## NOTE: There are no ring homomorphisms from the ring of
## all formal power series to most rings, e.g, the p-adic
## field, since you can always (mathematically!) construct
## some power series that doesn't converge.
## Note that 0 is not a *ring* homomorphism.
from power_series_ring import is_PowerSeriesRing
if is_PowerSeriesRing(codomain) or is_LaurentSeriesRing(codomain):
return im_gens[0].valuation() > 0
return False
def _is_valid_homomorphism_(self, codomain, im_gens):
## NOTE: There are no ring homomorphisms from the ring of
## all formal power series to most rings, e.g, the p-adic
## field, since you can always (mathematically!) construct
## some power series that doesn't converge.
## Note that 0 is not a *ring* homomorphism.
from power_series_ring import is_PowerSeriesRing
if is_PowerSeriesRing(codomain) or is_LaurentSeriesRing(codomain):
return im_gens[0].valuation() > 0
return False
def _is_valid_homomorphism_(self, codomain, im_gens):
"""
EXAMPLES::
sage: R.<x> = LaurentSeriesRing(GF(17))
sage: S.<y> = LaurentSeriesRing(GF(19))
sage: R.hom([y], S) # indirect doctest
Traceback (most recent call last):
...
TypeError: images do not define a valid homomorphism
sage: f = R.hom(x+x^3,R)
sage: f(x^2)
x^2 + 2*x^4 + x^6
"""
## NOTE: There are no ring homomorphisms from the ring of
## all formal power series to most rings, e.g, the p-adic
## field, since you can always (mathematically!) construct
## some power series that doesn't converge.
## Note that 0 is not a *ring* homomorphism.
from power_series_ring import is_PowerSeriesRing
if is_PowerSeriesRing(codomain) or is_LaurentSeriesRing(codomain):
return im_gens[0].valuation() > 0 and codomain.has_coerce_map_from(self.base_ring())
return False
def _is_valid_homomorphism_(self, codomain, im_gens):
"""
EXAMPLES::
sage: R.<x> = LaurentSeriesRing(GF(17))
sage: S.<y> = LaurentSeriesRing(GF(19))
sage: R.hom([y], S) # indirect doctest
Traceback (most recent call last):
...
TypeError: images do not define a valid homomorphism
sage: f = R.hom(x+x^3,R)
sage: f(x^2)
x^2 + 2*x^4 + x^6
"""
## NOTE: There are no ring homomorphisms from the ring of
## all formal power series to most rings, e.g, the p-adic
## field, since you can always (mathematically!) construct
## some power series that doesn't converge.
## Note that 0 is not a *ring* homomorphism.
from power_series_ring import is_PowerSeriesRing
if is_PowerSeriesRing(codomain) or is_LaurentSeriesRing(codomain):
return im_gens[0].valuation() > 0 and codomain.has_coerce_map_from(self.base_ring())
return False
