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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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