On Thursday, April 14, 2016 at 8:28:22 AM UTC-7, Jeroen Demeyer wrote:
>
>
> True, but a polynomial with polynomial coefficients is a very different 
> thing than a multi-variate polynomial. Therefore, it's perfectly fine if 
> they behave differently. 
>

OK. I misremembered. I thought towers of multivariate polynomials behaved 
better than this, but the seem to do exactly the same thing:

sage: R=ZZ['a','x']['b','y']
sage: S=ZZ['b','x']['a','y']
sage: aR=R.base().0
sage: bR=R.0
sage: S(aR^2+bR)
a + b^2

which is a bit worrisome, but at least we don't support anything smart in 
any of these situations.

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