Bill Allombert on Mon, 02 Feb 2009 17:42:46 +0100 |
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Re: System of two polynomial equations |
On Mon, Feb 02, 2009 at 04:18:48PM +0100, ewan.Delanoy@math.unicaen.fr wrote: > > > Hello all, > > if F and G are two polynomials in two variables x > and y, the system {F(x,y)=0,G(x,y)=0}, is usually > equivalent to a system of the form {P(x)=0,y=Q(x)}, where > P and Q are univariate polynomials. Could you provide an example and a more definite statement ? Obviously this imply that there are no pair of solution of the form {(x0,y0),(x0,y1)} with y0!=y1 because y0=Q(x0)=y1. > P can be easily computed with GP: it's essentially equal to > polresultant(F(x,y),G(x,y),y). > What about Q ? I can't think of a GP function that deals with > this in a simple way. I suggest you factorize P over K and then factorize G over (K[x]/P). In case where K=Q, you can use nffactor to factorize Q. In case where K=C, you can use polroots. Cheers, Bill.