def __call__(self, im_gens, check=True):
"""
Create a homomorphism.
EXAMPLES::
sage: R.<x,y> = PolynomialRing(QQ, 2)
sage: S.<a,b> = R.quotient(x^2 + y^2)
sage: H = S.Hom(R)
sage: phi = H([b,a]); phi
Ring morphism:
From: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
To: Multivariate Polynomial Ring in x, y over Rational Field
Defn: a |--> b
b |--> a
"""
if isinstance(im_gens, morphism.RingHomomorphism_from_quotient):
return morphism.RingHomomorphism_from_quotient(
self, im_gens._phi())
try:
pi = self.domain().cover()
phi = pi.domain().hom(im_gens, check=check)
return morphism.RingHomomorphism_from_quotient(self, phi)
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):
if isinstance(im_gens, morphism.RingHomomorphism_from_quotient):
return morphism.RingHomomorphism_from_quotient(
self, im_gens._phi())
try:
pi = self.domain().cover()
phi = pi.domain().hom(im_gens, check=check)
return morphism.RingHomomorphism_from_quotient(self, phi)
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_from_quotient):
raise TypeError
if x.parent() is self:
return x
if x.parent() == self:
return morphism.RingHomomorphism_from_quotient(self, x._phi())
raise TypeError
def _coerce_impl(self, x):
"""
Check to see if we can coerce ``x`` into a homomorphism with the
correct rings.
EXAMPLES::
sage: R.<x,y> = PolynomialRing(QQ, 2)
sage: S.<a,b> = R.quotient(x^2 + y^2)
sage: H = S.Hom(R)
sage: phi = H([b,a])
sage: R2.<x,y> = PolynomialRing(ZZ, 2)
sage: H2 = Hom(R2, S)
sage: H2(phi) # indirect doctest
Composite map:
From: Multivariate Polynomial Ring in x, y over Integer Ring
To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
Defn: Conversion map:
From: Multivariate Polynomial Ring in x, y over Integer Ring
To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
then
Composite map:
From: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
Defn: Ring morphism:
From: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
To: Multivariate Polynomial Ring in x, y over Rational Field
Defn: a |--> b
b |--> a
then
Conversion map:
From: Multivariate Polynomial Ring in x, y over Rational Field
To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
"""
if not isinstance(x, morphism.RingHomomorphism_from_quotient):
raise TypeError
if x.parent() is self:
return x
if x.parent() == self:
return morphism.RingHomomorphism_from_quotient(self, x._phi())
raise TypeError
