Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time

@article{Chze2010ComputationOD,
  title={Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time},
  author={Guillaume Ch{\`e}ze},
  journal={CoRR},
  year={2010},
  volume={abs/1009.2876}
}
In this paper we study planar polynomial differential systems of this form: dX dt = Ẋ = A(X, Y ), dY dt = Ẏ = B(X, Y ), where A, B ∈ Z[X, Y ] and deg A ≤ d, deg B ≤ d, ‖A‖∞ ≤ H and ‖B‖∞ ≤ H. A lot of properties of planar polynomial differential systems are related to irreducible Darboux polynomials of the corresponding derivation: D = A(X, Y )∂X + B(X, Y )∂Y . Darboux polynomials are usually computed with the method of undetermined coefficients. With this method we have to solve a polynomial… CONTINUE READING