A note on subresultants and the Lazard/Rioboo/Trager formula in rational function integration (Q1360963)

The well-known algorithm of D. Lazard, R. Rioboo and B. M. Trager for computing the logarithmic part of the integral of a rational function is based upon a formula connecting the logarithmic part and certain subresultants [\textit{D. Lazard} and \textit{R. Rioboo}, J. Symb. Comput. 9, 113-115 (1990; Zbl 0723.68053)]. In this paper the author shows that this formula may lead to wrong results if interpreted incorrectly. He gives the correct interpretation and indicates how the algorithm is to be altered correspondingly. \textit{M. Bronstein}'s book ``Symbolic integration vol. 1'' (Springer 1996; Zbl 0880.12005) presents a corrected version -- as described in this paper -- of the Lazard-Rioboo-Trager algorithm.