Hello,
It seems like quotient_ring doesn't have '__call__'. Does it a bug or a
> feature?
>
> sage: K = GF(2^8,'a')
> sage: P = PolynomialRing(K,'x')
> sage: Q = P.quotient_ring(P("x^256+x"),'y')
> sage: f = Q.random_element()
> sage: f.subs(y=K.random_element()) # random
> (a^7 + a^6 + a^3 + a)*y^255 + (a^7 + a^4)*y^254 ...
> sage: Q
> Univariate Quotient Polynomial Ring in y over Finite Field in a of size 2^
> 8 with modulus x^256 + x
>
> I expect that the output will be in K.
>
It would in principle not be hard to implement the functionality you are
asking for, but I would recommend a solution like the following:
sage: K = GF(2^8, 'a')
sage: P.<x> = PolynomialRing(K)
sage: Q.<y> = P.quotient_ring(x^256 - x)
sage: a = K.random_element()
sage: ev_a = Q.hom([a]) # homomorphism "evaluation in a": Q -> K
sage: f = Q.random_element()
sage: b = ev_a(f)
sage: b # random
a^7 + a^5 + a^3 + a^2 + a + 1
sage: b.parent() is K
True
In this way, the fact that ev_a is well-defined is checked during its
construction, so it doesn't have to be checked when doing the actual
evaluation.
Peter
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