Re: Polynomial Roots - how to interpret realprecision?

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

* Gordon Royle [2004-07-05 13:01]:
> I want to use "polroots" to calculate the roots of a large number of 
> *integer* polynomials.
> 
> The documentation indicates that the precision is kept in the variable 
> realprecision.... and then it says
> 
> ".. it is guaranteed to converge and to give the roots to the required 
> precision"
> 
> Now, does this mean that the roots that are output are guaranteed 
> correct to that number of places?

Yes.

> From my (admittedly limited)  understanding of the sensitivity of roots
> of polynomials, I was under  the impression that this would require some
> intermediate calculations  to be performed to a greater precision ...  is
> this so?

This is so.

A posteriori error estimates are made, and the computation is restarted
( with appropriate precision ) if the estimates do not guarantee the
requested precision was obtained.

See also

  http://www.math.u-psud.fr/~belabas/pari/doc/faq.html#root

    Karim.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dep. de Mathematiques, Bat. 425   Fax: (+33) (0)1 69 15 60 19
Universite Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://pari.math.u-bordeaux.fr/  [PARI/GP]