Optimizations of the subresultant algorithm Original Research Article

The subresultant algorithm is the most universal and used tool to compute the resultant or the greatest common divisor of two polynomials with coefficients in an integral ring (see (A.G. Akritas, Elements of Computer Algebra with Applications, Wiley, New York, 1989, H. Cohen, A Course in Computational Algebraic Number Theory, Ch. 3, Springer, Berlin, 1993, S.R. Czapor, K.O. Geddes, G. Labahn, Algorithms for Computer Algebra, Kluwer Academic Publishers, Dordrecht, 1992.)). Nevertheless, there exists several notable ameliorations of this algorithm (see (L. Ducos, Algorithme de Bareiss, Algorithme des sous-résultants, Theoret. Inform. Appl. 30 (4) (1996) 319–347, T. Lickteig, M.-F. Roy, Cauchy index computation. Manuscrit non publié (à paraître), Novembre 1996.)).