Hi Nathann!

On Nov 26, 2:06 pm, Nathann Cohen <nathann.co...@gmail.com> wrote:
> I could cache the results... But I still do not understand why just
> evaluating x^999999 takes so much time !

I guess this is a limitation of Singular.

In Singular, exponents are restricted to 32767. Usually, multivariate
polynomial rings in Sage are based on libSingular, and I guess it has
the same limitation. Compare 
http://www.singular.uni-kl.de/Manual/latest/sing_343.htm#SEC384

So, if you have a larger exponent, Sage has to fall back to a
different (and probably much slower) implementation.

However, if I understood correctly, you have a *uni*variate polynomial
ring, right? So, probably you can disregard what I just said, since
univariate polynomial rings are different from multivariate (based on
ntl? not sure...) . Perhaps there are similar limitations?

Cheers,
Simon

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