def _is_valid_homomorphism_(self, codomain, im_gens):
r"""
This gets called implicitly when one constructs a ring homomorphism
from a power series ring.
EXAMPLE::
sage: S = RationalField(); R.<t>=PowerSeriesRing(S)
sage: f = R.hom([0])
sage: f(3)
3
sage: g = R.hom([t^2])
sage: g(-1 + 3/5 * t)
-1 + 3/5*t^2
.. 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.
"""
if im_gens[0] == 0:
return True # this is allowed.
from laurent_series_ring import is_LaurentSeriesRing
if is_PowerSeriesRing(codomain) or is_LaurentSeriesRing(codomain):
return im_gens[0].valuation() > 0
return False
def _is_valid_homomorphism_(self, codomain, im_gens):
r"""
This gets called implicitly when one constructs a ring homomorphism
from a power series ring.
EXAMPLE::
sage: S = RationalField(); R.<t>=PowerSeriesRing(S)
sage: f = R.hom([0])
sage: f(3)
3
sage: g = R.hom([t^2])
sage: g(-1 + 3/5 * t)
-1 + 3/5*t^2
.. 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.
"""
if im_gens[0] == 0:
return True # this is allowed.
from laurent_series_ring import is_LaurentSeriesRing
if is_PowerSeriesRing(codomain) or is_LaurentSeriesRing(codomain):
return im_gens[0].valuation() > 0
return False