On Thursday, April 14, 2016 at 1:52:37 AM UTC-7, Jeroen Demeyer wrote:
>
> I like it exactly the way it is. If you explicitly ask for a polynomial 
> over a polynomial, this is the expected answer. 
>
 
It is at odds with the behaviour for multivariate polynomials, though.

The other surprising part is that one ends up in the situation where both 
ZZ['a'] and ZZ['a']['b'] have a conversion into ZZ['b']['a'], but the 
second conversion map does not extend the first one:

sage: R=ZZ['a']['b']
sage: S=ZZ['b']['a']
sage: aR=R.base().0
sage: bR=R.0
sage: aS=S.0
sage: bS=S.base().0
sage: S(aR)
a
sage: S(bR)
a
sage: S(aR+bR-bR)
b

That's a horrible trap.

(luckily, coercion doesn't use these maps. Then this behaviour would really 
be a bug)

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