On May 21, 2010, at 11:35 PM, Simon King wrote:

On 22 Mai, 00:12, Robert Bradshaw <[email protected]>
wrote:
Try working a multivariate ring rather than a tower of univariate
rings, e.g. ...

... which suggests the question why Sage does not automatically
transform a tower of polynomial rings into a single ring -- for
efficiency, and in order to avoid weird constructions such as
 sage: QQ['t']['t']['t']
 Univariate Polynomial Ring in t over Univariate Polynomial Ring in t
over Univariate Polynomial Ring in t over Rational Field

There is a difference, for example list(f) and degree(f) have different meanings if f is a Univariate ring with a polynomial basering. Also, I can safely do

sage: P.<x> = R['x']

Of course we could possibility do this transformation under the hood, and then remember where things came from.

- Robert

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