Section: New Results
Efficient algorithms for rational first integrals
We presented in [14] fast algorithms for
computing rational first integrals with bounded degree of a planar
polynomial vector field. Our approach is inspired by an idea of
Ferragut and Giacomini. We improve upon their work by proving that
rational first integrals can be computed via systems of
linear equations instead of systems of quadratic
equations. This leads to a probabilistic algorithm with arithmetic
complexity