John Cremona on Thu, 21 May 2020 10:24:55 +0200

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Re: Real Algebraic Numbers

You might want to check out Sage's AA: see
: as well as QQbar (all algebraic numbers) there is AA (real algebraic
numbers).  I don't know how well it would handle multivariate


On Thu, 21 May 2020 at 01:17, Gereon Kremer <> 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