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Computing 38, 369-=-372 (1987) Computing 9 by Springer-Verlag1987

Summary: Computing 38, 369-=-372 (1987) Computing
9 by Springer-Verlag1987
A Simple Proof of the Validity of the Reduced prs Algorithm
A. G. Akritas, Lawrence, Kansas
Received November 11, 1986; revised February 23, 1987
Abstract -- Zusammenfassung
A Simple Proof of the Validity of the Reduced prs Algorithm. Given two univariate polynomials with
integer coefficients, it has been rediscovered [2] that the reduced polynomial remainder sequence (prs)
algorithm can be used mainly to compute over the integers the members of a normal prs, keeping under
control the coefficient growth and avoiding greatest common divisor (gcd) computations of the coefficients.
The validity proof of this algorithm as presented in the current literature [2] is very involved and has
obscured simple divisibility properties. In this note, we present Sylvester's theorem of 1853 [4] which
makes these simple divisibility properties clear for normal prs's. The proof presented here is a
modification of Sylvester's original proof.
AMS Subject Classifications: 68A15, 68-03.
Key words: Polynomial greatest common divisor, polynomial remainder sequence, Sylvester's theorem
Ein einfacher Beweis der Giiitigkeit des reduzierten Polynom-Rest-Sequenz-Algorithmus. Ftir zwei
gegebene Polynome in einer Variablen und mit ganzzahligen Koeff'Lzienten wurde wiederentdeckt [2],
dab der reduzierte prs-Algorithmus haupts~chlich verwendet werden kann, um die Elemente einer


Source: Akritas, Alkiviadis G. - Department of Computer and Communication Engineering, University of Thessaly


Collections: Computer Technologies and Information Sciences