11.4 Space of homomorphisms between two rings

Module: sage.rings.homset

Module-level Functions

RingHomset( R, S)

is_RingHomset( H)

Class: RingHomset_generic

class RingHomset_generic
RingHomset_generic( self, R, S)

Functions: natural_map

Special Functions: __call__,$  $ _repr_

__call__( self, im_gens, [check=True])

sage: H = Hom(Z,Q)
sage: phi = H([])
Traceback (most recent call last):
...
TypeError: images (=[]) do not define a valid homomorphism

Class: RingHomset_quo_ring

class RingHomset_quo_ring
Space of ring homomorphism where the domain is a (formal) quotient ring.

sage: R, (x,y) = PolynomialRing(Q, 2, 'xy').objgens()
sage: S, (a,b) = (R/(x^2 + y^2)).objgens('ab')
sage: phi = S.hom([b,a]); phi
Ring endomorphism of Quotient of Polynomial Ring in x, y over Rational
Field by the ideal (y^2 + x^2)
  Defn: a |--> b
        b |--> a
sage: phi(a)
b
sage: phi(b)
a

Special Functions: __call__

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