Re: precision of result when adding t_REAL with lots of cancellation

[Jeroen Demeyer <jdemeyer@cage.ugent.be>]

On 2014-09-14 23:27, Bill Allombert wrote:
> On Mon, Aug 18, 2014 at 10:52:57PM +0200, Jeroen Demeyer wrote:
> > Let me add that having a nfpolsturm() function would also be useful.
>
> What would this function do ?
Given a polynomial f over a number field, give a vector with the number 
of real roots of phi(f), where phi ranges over the real embeddings.

For Denis Simon's script, we only need the number of roots on the real 
line, but you could also have a version with endpoints, where the 
endpoints are also number field elements.

Importantly, since both the input and output will be exact, this should 
be done in a way which does not depend on the realprecision.

Cheers,
Jeroen.