|Bill Allombert on Thu, 21 May 2020 12:09:46 +0200|
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|Re: Real Algebraic Numbers|
On Wed, May 20, 2020 at 10:41:06PM +0200, 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)? In principle yes, in practice it depends on the number of variables. > 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? Yes. > 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...) I would say it depends on the number of variables you need. PARI/GP is good for one or two variables but is not suited for large number of variables. On the other hand it can handle large algebraic degrees. Cheers, Bill.