Module: sage.rings.homset
Space of homomorphisms between two rings.
Module-level Functions
R, S) |
H) |
Class: RingHomset_generic
self, R, S) |
Functions: has_coerce_map_from,
natural_map
self, x) |
The default for coercion maps between ring homomorphism spaces is very restrictive (until more implementation work is done).
Special Functions: __call__,
__init__,
_coerce_impl,
_repr_
self, im_gens, [check=True]) |
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
Class: RingHomset_quo_ring
sage: R.<x,y> = PolynomialRing(QQ, 2) sage: S.<a,b> = R.quotient(x^2 + y^2) sage: phi = S.hom([b,a]); phi Ring endomorphism of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2) Defn: a |--> b b |--> a sage: phi(a) b sage: phi(b) a
TESTS: We test pickling of a homset from a quotient.
sage: R.<x,y> = PolynomialRing(QQ, 2) sage: S.<a,b> = R.quotient(x^2 + y^2) sage: H = S.Hom(R) sage: H == loads(dumps(H)) True
We test pickling of actual homomorphisms in a quotient:
sage: phi = S.hom([b,a]) sage: phi == loads(dumps(phi)) True
Special Functions: __call__,
_coerce_impl
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