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Science China Mathematics

, Volume 57, Issue 10, pp 2123–2142 | Cite as

Sparse bivariate polynomial factorization

  • WenYuan Wu
  • JingWei Chen
  • Yong Feng
Articles

Abstract

Motivated by Sasaki’s work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynomial over the rational number field. Another feature of the factorization algorithm presented in this article is a new recombination method, which can solve the extraneous factor problem before lifting based on numerical linear algebra. Both theoretical analysis and experimental data show that the algorithm is efficient, especially for sparse bivariate polynomials.

Keywords

polynomial factorization sparse polynomial generalized Hensel lifting 

MSC(2010)

12Y05 68W30 11Y16 12D05 13P05 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent TechnologyChinese Academy of SciencesChongqingChina

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