Help with algorithm to find rational roots of a bivariate equation?
- To: mathgroup at smc.vnet.net
- Subject: [mg105080] Help with algorithm to find rational roots of a bivariate equation?
- From: TPiezas <tpiezas at gmail.com>
- Date: Fri, 20 Nov 2009 06:39:05 -0500 (EST)
Hello all, Does anyone know an efficient algorithm using Mathematica that can find _rational_ roots of a non-homogenous eqn in two variables with deg > 4? For ex, you want to find rational {x,y} such that, F(x,y) = x^n + (P_1)x^(n-1) + (P_2)x^(n-2) + .... = 0 where the P_i are polynomials in y. I _always_ come across this situation in the course of experimental mathematics, and it would be great if Mathematica had a built-in feature that solves _bivariate_ eqns in the rationals. Right now, I have a 22-deg eqn in x with coefficients in y. I know three non- trivial rational pairs {x,y} such that F(x,y) = 0, but I want to know if there are others. If there are, a certain family of identities would have more members. Any help will be appreciated. - Titus
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