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Journal of Systems Science and Complexity

, Volume 28, Issue 1, pp 243–260 | Cite as

Exact bivariate polynomial factorization over ℚ by approximation of roots

  • Yong Feng
  • Wenyuan Wu
  • Jingzhong Zhang
  • Jingwei Chen
Article

Abstract

Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not support symbolic computation directly. Hence, it leads to difficulties in applying factorization in engineering fields. In this paper, the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients. The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library. In addition, the numerical computation part often only requires double precision and is easily parallelizable.

Keywords

Factorization of multivariate polynomials interpolation methods minimal polynomial numerical continuation 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Yong Feng
    • 1
  • Wenyuan Wu
    • 1
  • Jingzhong Zhang
    • 1
  • Jingwei Chen
    • 1
  1. 1.Chongqing Key Lab of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology (CIGIT)Chinese Academy of SciencesChongqingChina

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