A new method for computing polynomial greatest common divisors and polynomial remainder sequences (Q1822238)

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 (1899) and uniformly treats both normal and abnormal prs's, making use of Bareiss's (1968) 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 gcd computations (as in Bareiss) and it clearly demonstrates the divisibility properties; hence, it combines the best of both the reduced and the subresultant prs algorithms.