If getting numerical roots is sufficient, then you might want to check
out the optional phcpack package. I am working on a more full-
featured interface for sage-2.11 that classifies roots of
multivariable polynomial systems.
Phcpack is be able to compute roots for systems where Groebner bases
are much too difficult to compute.
-M. Hampton
On Mar 25, 5:29 am, "David Joyner" <[EMAIL PROTECTED]> wrote:
> It might work if you try coercing f = B[0] first into
>
> R2.<x,y> = PolynomialRing(CC, 2, 'xy')
>
> then applying factor or whatever to R2(f). I haven't tried it with your
> problem but that general idea has worked for me in similar situations.
>
> On Tue, Mar 25, 2008 at 5:18 AM, continuum121 <[EMAIL PROTECTED]> wrote:
>
> > Hi!
>
> > I have a problem. Here is its formulation. I work in some polynomial
> > ring - lets say
> > R,(x,y) = PolynomialRing(QQ, 2, 'xy', order='lex').objgens()
> > and consider ideal in R
> > I = ideal(x+y^3-2,y+x^3-2)
> > then I calculate grobner basis for ideal I
> > B = I.groebner_basis(); B
> > B[0] is univariate polynomial. Here the real problem begins. I would
> > like to get real roots of polynomial B[0]. I can do B[0].factor() but
> > it gives only part of information us factorization is over Q[x,y].
> > More intuitive way for me is to treat it symbolicly. I want to write
> > solve(B[0] == 0, x) but it doesn't work us function solve() needs
> > symbolic object and gets boolean expression.
>
> > The question is: how to find real roots for polynomial object either
> > symbolicly (more desired) or numericly?
>
> > The only solution I have figured out is as follow. I write
> > x,y=var('x,y') and then declare f = ... (here I copy paste B[0]) but
> > it's not the way I want do this.
>
> > Does anyone know how to solve it?
>
> > Best regards
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