Jeroen Demeyer on Mon, 15 Sep 2014 08:31:38 +0200

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

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.