论文信息 - Newton's iteration and the sparse Hensel algorithm (Extended Abstract)

Newton's iteration and the sparse Hensel algorithm (Extended Abstract)

This paper presents an organization of the p-adic lifting (or Hensel) algorithm that differs from the organization previously presented by Zassenhaus [Zas69] and currently used in algebraic manipulation circles [Mos73, Yun74, Wan75, Mus75]. Our organization is somewhat more general than the earlier one and admits the improvements that yielded the “sparse modular” algorithm [Zip79] more easily than the Zassenhaus algorithm. From a pedagogical point of view, the relationship between Newton's iteration and the p-adic algorithms is clearer in our formulation than with the Zassenhaus algorithm.

Richard Zippel

[1] Paul S. Wang,et al. Factoring multivariate polynomials over the integers , 1973, SIGS.

[2] Paul S. Wang,et al. New Algorithms for Polynomial Square-Free Decomposition Over the Integers , 1979, SIAM J. Comput..

[3] Paul S. Wang. An improved multivariate polynomial factoring algorithm , 1978 .

[4] David Y. Y. Yun,et al. The EZ GCD algorithm , 1973, ACM Annual Conference.

[5] E. Berlekamp. Factoring polynomials over large finite fields* , 1970, SYMSAC '71.

[6] Richard Zippel,et al. Probabilistic algorithms for sparse polynomials , 1979, EUROSAM.

[7] H. Zassenhaus. On Hensel factorization, I , 1969 .

[8] E. Berlekamp. Factoring polynomials over large finite fields* , 1971, SYMSAC '71.

[9] David Y. Y. Yun,et al. The Hensel Lemma in Algebraic Manipulation , 1973, Outstanding Dissertations in the Computer Sciences.

[10] David R. Musser,et al. Multivariate Polynomial Factorization , 1975, JACM.