S. C. Johnson
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.
- Brown, W. S., "On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors", J.A.C.M. 18 (1971) p.p. 478--504. Google Scholar
Digital Library
- Brown, W. S., and Traub, J. F., "On Euclid's Algorithm and the Theory of Subresultants", J.A.C.M., 18 (1971) p.p. 505--514. Google ScholarDigital Library
- Collins, G. E., "Subresultants and Reduced Polynomial Remainder Sequences", J.A.C.M., 19 (1967) p.p. 128--142. Google ScholarDigital Library
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