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Exact bivariate polynomial factorization over ℚ by approximation of roots

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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.

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Authors and Affiliations

  1. Chongqing Key Lab of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology (CIGIT), Chinese Academy of Sciences, Chongqing, 400714, China

    Yong Feng, Wenyuan Wu, Jingzhong Zhang & Jingwei Chen

Authors
  1. Yong Feng
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  2. Wenyuan Wu
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  3. Jingzhong Zhang
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  4. Jingwei Chen
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Corresponding author

Correspondence to Wenyuan Wu.

Additional information

This work was partly supported by the National Natural Science Foundation of China under Grant Nos. 91118001 and 11170153, the National Key Basic Research Project of China under Grant No. 2011CB302400, and Chongqing Science and Technology Commission Project under Grant No. cstc2013jjys40001.

This paper was recommended for publication by Editor ZHI Lihong.

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Feng, Y., Wu, W., Zhang, J. et al. Exact bivariate polynomial factorization over ℚ by approximation of roots. J Syst Sci Complex 28, 243–260 (2015). https://doi.org/10.1007/s11424-014-2170-5

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  • DOI: https://doi.org/10.1007/s11424-014-2170-5

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