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Optimal algorithm for algebraic factoring

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Abstract

This paper presents an optimized method for factoring multivariate polynomials over algebraic extension fields defined by an irreducible ascending set. The basic idea is to convert multivariate polynomials to univariate polynomials and algebraic extension fields to algebraic number fields by suitable integer substitutions. Then factorize the univariate polynomials over the algebraic number fields. Finally, construct multivariate factors of the original polynomial by Hensel lemma and TRUEFACTOR test. Some examples with timing are included.

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Authors and Affiliations

  1. Institute of System Science, The Chinese Academy of Sciences, 100080, Beijing

    Zhi Lihong

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  1. Zhi Lihong
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Correspondence to Zhi Lihong.

Additional information

This paper is partially supported by the Climbing Project Foundation of China.

Zhi Lihong received her B.Sc. degree in pure mathematics in 1991 from Peking University, and her Ph.D. degree from Institute of Systems Science, The Chinese Academy of Sciences, in 1996. Her research interests include geomtric reasoning, computer algebra and analysis, and computer-aided geometry design.

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Zhi, L. Optimal algorithm for algebraic factoring. J. of Comput. Sci. & Technol. 12, 1–9 (1997). https://doi.org/10.1007/BF02943139

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  • DOI: https://doi.org/10.1007/BF02943139

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