Cannot create homomorphism from prime residue field to finite field #11319
Description
Consider K = QQ(sqrt(337)). The prime 5 is inert in K and the prime 13 splits. We'll start with 13 to see what goes wrong:
sage: K.<w> = QuadraticField(337)
sage: pp = K.ideal(13).factor()[0][0]
sage: RF13 = K.residue_field(pp)
sage: RF13.gens()
(1,)
sage: RF13.hom([GF(13)(1)])
...
TypeError: images do not define a valid homomorphism
However, for residue fields that aren't prime fields it does work:
sage: RF5 = K.residue_field(5)
sage: F25 = GF(25, names='a', modulus=RF5.polynomial())
sage: RF5.hom([F25.0])
Ring morphism:
From: Residue field in wbar of Fractional ideal (5)
To: Finite Field in a of size 5^2
Defn: wbar |--> a
Btw, this is in sage 4.6.2. on Mac OS 10.6.7.
Component: coercion
Keywords: residue fields, finite fields, hom, sd35
Author: Johan Bosman
Reviewer: Kiran Kedlaya, Michiel Kosters
Merged: sage-4.8.alpha6
Issue created by migration from https://trac.sagemath.org/ticket/11319