Polynomial remainder sequence and approximate GCD

Authors:
Tateaki Sasaki;Mutsuko Sasaki
Affiliations:
-;-
Venue:
ACM SIGSAM Bulletin
Year:
1997

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Abstract

Let P1 and P2 be polynomials, univariate or multivariate, and let (P1, P2, P3,…, Pi,…) be a polynomial remainder sequence. Let Ai and Bi (i = 3, 4,…) be polynomials such that AiP1 + BiP2 = Pi, deg(Ai) < deg(P2) - deg(Pi), deg(Bi) < deg(P1) - deg(Pi), where the degree is for the main variable. We derive relations such as CiP1 = -Bi+1Pi + BiPi+1 and CiP2 = Ai+1Pi - AiPi+1, where Ci is independent of the main variable. Using these relations, we discuss approximate common divisors calculated by polynomial remainder sequence.