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Factoring larger multivariate polynomials

Published: 01 November 1976 Publication History

Abstract

An improved algorithm for factoring multivariate polynomials over the integers has been developed. For larger polynomials, it is generally faster and requires less storage than the original algorithm as described by Wang and Rothschild [2]. The new algorithm has improved strategy to deal with the known problems of the original algorithm. namely, the leading coefficient problem, the bad-zero problem and the combinatorial search for true factors. It features a linearly convergent variable-by-variable p-adic construction procedure for parallel lifting of all factors at once. This procedure is very efficient and it relies on i) distributing the factors of the leading coefficient correctly, and ii) solving the equation αf+βg = h, with multivariate f, g and h, efficiently. Details of these and other aspects of this algorithm together with its generalization to factoring over algebraic number fields will be forthcoming. Obviously, the EZ-GCD algorithm [1] can be similarly improved if its lifting procedure is replaced.

References

[1]
J. Moses and D. Y. Y. Yun. "The EZ GCD Algorithm," Proc. 1973 ACM National Conference, Atlanta, Ga., pp. 159--166, August 1973.
[2]
P. S. Wang and L. Rothschild, "Factoring Multivariate Polynomials Over the Integers," Mathematics of Computation, Vol. 29, No. 131, Julg 1975.

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cover image ACM SIGSAM Bulletin
ACM SIGSAM Bulletin  Volume 10, Issue 4
November 1976
43 pages
ISSN:0163-5824
DOI:10.1145/1088222
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 November 1976
Published in SIGSAM Volume 10, Issue 4

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