Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 714102, 7 pages
http://dx.doi.org/10.5402/2011/714102
Research Article

Polynomial GCD Derived through Monic Polynomial Subtractions

Allwave Corporation, 3860 Del Amo Boulevard, No. 404, Torrance, CA 90503, USA

Received 10 March 2011; Accepted 19 April 2011

Academic Editors: E. Kita and F. Lebon

Copyright © 2011 Feng Cheng Chang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A simple and efficient algorithm for finding the GCD of a pair of univariate polynomials is derived. The process requires only successive subtraction of two monic polynomials. Amazingly, this approach gives the desired GCD for a pair of test polynomials of very high degree, such as ( 𝑥 + 1 ) 1 0 0 0 and its derivative.