Re: Real Algebraic Numbers

[John Cremona <john.cremona@gmail.com>]

You might want to check out Sage's AA: see
http://doc.sagemath.org/html/en/reference/number_fields/sage/rings/qqbar.html
: as well as QQbar (all algebraic numbers) there is AA (real algebraic
numbers).  I don't know how well it would handle multivariate
polynomials.

John

On Thu, 21 May 2020 at 01:17, Gereon Kremer <gkremer@stanford.edu> wrote:
>
> Hi all,
>
> I'm trying to use PARI for computations with real algebraic numbers,
> ultimately aiming for a CAD implementation. In particular, I'd need the
> following operations:
>
> 1) Multivariate resultants. Does the resultant() method from 8.10.1 work
> on multivariate polynomials (in a main variable)?
>
> 2) Isolate real roots from a univariate polynomial. I got realroots() to
> work, however I'm not sure whether there is a built-in that directly
> couples the numeric approximation with the defining polynomial to form a
> number type. I guess number fields go in this direction to some degree,
> is this the way to go?
>
> 3) Isolate real roots from a multivariate polynomial and a real
> algebraic assignment (for all but one variable from the polynomial).
>
> Can anyone give me some hints how to do this with PARI? (or,
> alternatively, tell me that I should not use PARI for that and maybe
> even suggest an alternative...)
>
> Thanks!
> Gereon
>
>
>
>