✦ LIBER ✦

Multi-Modular Approach to Polynomial-Time Factorization of Bivariate Integral Polynomials

✍ Scribed by Kazuhiro Yokoyama; Masayuki Noro; Taku Takeshima

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 685 KB
Volume: 17
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1994.1034

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✦ Synopsis

Efficient algorithms to factorize bivariate integral polynomials are discussed. As a key technique to provide the most efficient algorithms in theory, an approach, named multimodular approach, is proposed and its implication is discussed intensively. The approach uses combined information from several modular factorizations of different types. Although essentially the same idea was already proposed by Chistov & Grigoryev in 1982, the concept is presented independently in detail but in a more intelligible form. Effectiveness of the multi-modular approach is proved by affording two new algorithms superior to any other existing algorithms.

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The objective of this paper is twofold. First, we describe a method to solve large systems of polynomial equations using modular arithmetics. Then, we apply the approach to the study of the problem of linearizability for a quadratic system of ordinary differential equations.