Real Algebraic Numbers

[Gereon Kremer <gkremer@stanford.edu>]

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