A note on abnormal polynomial remainder sequences

Authors:
S. C. Johnson
Affiliations:
Bell Laboratories, Murray Hill, New Jersey
Venue:
ACM SIGSAM Bulletin
Year:
1975

Citing 3
Cited 0

Subresultants and Reduced Polynomial Remainder Sequences

Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors

Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants

Journal of the ACM (JACM)

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Abstract

Polynomial Remainder Sequences (PRS) have been used in the computation of greatest common divisors of polynomials for many years. We call a polynomial division abnormal if the degree of the remainder is strictly less than the degree of the divisor minus one; an abnormal PRS is one with at least one abnormal division. An abnormal polynomial division in general implies a nontrivial greatest common divisor among the coefficients of the remainder; this can lead to inefficiencies in the later computations in the PRS.These results suggest that the "classical" PRS methods may have not exploited all of the algebraic structure available in the problem.