I have the following:
sage: R.<a,b> = QQ[]
sage: K = FractionField(R)
sage: S.<x,y> = K[]
I then create an ideal, J, in S. I'd like to take various
specializations of the base. That is I have a homomorphism which maps
a and b to specific values in Q, and I'd like to form the ideal in a
bivariate polynomial ring QQ[] which is the specialization of this
ideal. I almost had it by first using J.subs({a:value,b:value}) but
that doesn't change the base, and Sage complains when I try to do a
change_ring on the specialized version of J since the base field is
still K and not QQ. It would be nice if change_ring could be
supplemented by allowing a morphism instead of a ring. If that were
specified then the source should be the original ring and the new
ideal (or other things that have a change_ring method) would be
obtained by applying that morphism. In some sense that's what's done
now, but the morphism used is the implicit coercion.
Victor
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