On the New Face of Kovacic’s Algorithm

Manuel Bronstein ETH Zentrum Wissenschaftliches Rechnen, IFW D.25.1 CH - 8092 Zürich, Switzerland Email: bronstein@inf.ethz.ch

Recent progress on Kovacic’s algorithm has radically changed the way in which equations of the form y” + p(x) y’ + q(x) y = 0 are solved symbolically. In this talk we describe the rational algorithm of Ulmer and Weil for completely reducible second order equations, then discuss its efficient stand-alone implementation in the bernina system, and finally outline new rational heuristics for the non-completely reducible case.