def _coerce_impl(self, x):
"""
Check to see if we can coerce ``x`` into a homomorphism with the
correct rings.
EXAMPLES::
sage: H = Hom(ZZ, QQ)
sage: phi = H([1])
sage: H2 = Hom(QQ, QQ)
sage: phi2 = H2(phi); phi2 # indirect doctest
Ring endomorphism of Rational Field
Defn: 1 |--> 1
sage: H(phi2) # indirect doctest
Ring morphism:
From: Integer Ring
To: Rational Field
Defn: 1 |--> 1
"""
if not isinstance(x, morphism.RingHomomorphism):
raise TypeError
if x.parent() is self:
return x
# Case 1: the parent fits
if x.parent() == self:
if isinstance(x, morphism.RingHomomorphism_im_gens):
return morphism.RingHomomorphism_im_gens(self, x.im_gens())
elif isinstance(x, morphism.RingHomomorphism_cover):
return morphism.RingHomomorphism_cover(self)
elif isinstance(x, morphism.RingHomomorphism_from_base):
return morphism.RingHomomorphism_from_base(
self, x.underlying_map())
# Case 2: unique extension via fraction field
try:
if isinstance(x, morphism.RingHomomorphism_im_gens) and x.domain(
).fraction_field().has_coerce_map_from(self.domain()):
return morphism.RingHomomorphism_im_gens(self, x.im_gens())
except StandardError:
pass
# Case 3: the homomorphism can be extended by coercion
try:
return x.extend_codomain(self.codomain()).extend_domain(
self.domain())
except StandardError:
pass
# Last resort, case 4: the homomorphism is induced from the base ring
if self.domain() == self.domain().base() or self.codomain(
) == self.codomain().base():
raise TypeError
try:
x = self.domain().base().Hom(self.codomain().base())(x)
return morphism.RingHomomorphism_from_base(self, x)
except StandardError:
raise TypeError
def __call__(self, im_gens, check=True):
"""
Create a homomorphism.
EXAMPLES::
sage: H = Hom(ZZ, QQ)
sage: H([1])
Ring morphism:
From: Integer Ring
To: Rational Field
Defn: 1 |--> 1
TESTS::
sage: H = Hom(ZZ, QQ)
sage: H == loads(dumps(H))
True
"""
if isinstance(im_gens, (morphism.RingHomomorphism_im_gens,
morphism.RingHomomorphism_cover,
morphism.RingHomomorphism_from_base)):
return self._coerce_impl(im_gens)
try:
return morphism.RingHomomorphism_im_gens(self,
im_gens,
check=check)
except (NotImplementedError, ValueError), err:
try:
return self._coerce_impl(im_gens)
except TypeError:
raise TypeError, "images do not define a valid homomorphism"
def __call__(self, im_gens, check=True):
"""
EXAMPLES::
sage: H = Hom(ZZ, QQ)
sage: phi = H([])
Traceback (most recent call last):
...
TypeError: images do not define a valid homomorphism
TESTS::
sage: H = Hom(ZZ, QQ)
sage: H == loads(dumps(H))
True
"""
if isinstance(im_gens, (morphism.RingHomomorphism_im_gens,
morphism.RingHomomorphism_cover,
morphism.RingHomomorphism_from_base)):
return self._coerce_impl(im_gens)
try:
return morphism.RingHomomorphism_im_gens(self,
im_gens,
check=check)
except (NotImplementedError, ValueError), err:
try:
return self._coerce_impl(im_gens)
except TypeError:
raise TypeError, "images do not define a valid homomorphism"
def _coerce_impl(self, x):
if not isinstance(x, morphism.RingHomomorphism):
raise TypeError
if x.parent() is self:
return x
# Case 1: the parent fits
if x.parent() == self:
if isinstance(x, morphism.RingHomomorphism_im_gens):
return morphism.RingHomomorphism_im_gens(self, x.im_gens())
elif isinstance(x, morphism.RingHomomorphism_cover):
return morphism.RingHomomorphism_cover(self)
elif isinstance(x, morphism.RingHomomorphism_from_base):
return morphism.RingHomomorphism_from_base(
self, x.underlying_map())
# Case 2: unique extension via fraction field
try:
if isinstance(x, morphism.RingHomomorphism_im_gens) and x.domain(
).fraction_field().has_coerce_map_from(self.domain()):
return morphism.RingHomomorphism_im_gens(self, x.im_gens())
except:
pass
# Case 3: the homomorphism can be extended by coercion
try:
return x.extend_codomain(self.codomain()).extend_domain(
self.domain())
except:
pass
# Last resort, case 4: the homomorphism is induced from the base ring
if self.domain() == self.domain().base() or self.codomain(
) == self.codomain().base():
raise TypeError
try:
x = self.domain().base().Hom(self.codomain().base())(x)
return morphism.RingHomomorphism_from_base(self, x)
except:
raise TypeError