On Wednesday, April 22, 2015 at 11:02:52 AM UTC-7, vdelecroix wrote:

> Definitely! A side effect of the current behavior 
>
> sage: p = ZZ['x'](range(5)) 
> sage: f = sum(i*x**i for i in range(5)) 
> sage: str(p) == str(f) 
> True 
> sage: p == f 
> (((4*x + 3)*x + 2)*x + 1)*x == 4*x^4 + 3*x^3 + 2*x^2 + x 
>

which is true and is not essentially different from

sage: f == f
4*x^4 + 3*x^3 + 2*x^2 + x == 4*x^4 + 3*x^3 + 2*x^2 + x

so I'm not so sure this would really change if just changing the evaluation 
scheme of polynomials at symbolic input would change that in a significant 
way.

Naturally, for multivariate polynomials, which are usually sparsely 
represented, this issue doesn't arise:

sage: ZZ['x','y'](f)(x,0)
4*x^4 + 3*x^3 + 2*x^2 + x


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