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11319 Cannot create homomorphism from prime residue field to finite field johanbosman robertwb "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. = 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." defect closed major sage-4.8 coercion fixed residue fields, finite fields, hom, sd35 sage-4.8.alpha6 Johan Bosman Kiran Kedlaya, Michiel Kosters N/A