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

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Jeroen Demeyer [2014-09-15 08:31]:
> 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.

The basic version is now available in 'master' (over the real line), as
nfpolsturm, with an interface analogous to nfeltsign and nfeltembed
(i.e. an argument allows to select the embedding; all real embeddings by
default).

Cheers,

    K.B.

P.S. It is easy to add endpoints but I don't see any applications and it
would complicate the code. If there is a real use case, I'll add it.
The interface would be slightly awkward, though:
  nfpolsturm(nf, T, {embeddings}, {[a,b]})
...

--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
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