On the Resolution of F(x,y)=G(x,y)

Let F(x,y), G(x,y) ε [x, y] be polynomials of degree n and m, respectively. Assume, that F is homogeneous and n - m ≥ 3. We give a fast algorithm for the resolution of the inequality F(x, y) ≤ G(x, y) in x, yε , max (x ,y) < C. We illustrate the method by solving x5 - xy4 - y5 ≤ 200 (x2 + y2), max (x,y ≤ 10500.