A new method for computing polynomial greates common divisors and polynomial remainder sequences

Summary A new method is presented for the computation of a greatest common divisor (gcd) of two polynomials, along with their polynomial remainder sequence (prs). This method is based on our generalization of a theorem by Van Vleck 12] and uniformly treats both normal and abnormal prs's, making use of Bareiss's 3] integer-preserving transformation algorithm for Gaussian elimination. Moreover, for the polynomials of the prs's, this method provides the smallest coefficients that can be expected without coefficient ged computations (as in Bareiss 3]) and it clearly demonstrates the divisibility properties; hence, it combines the best of both the reduced and the subresultant prs algorithms.This paper is affectionately dedicated to the memory of my father