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Resultant elimination via implicit equation interpolation

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Abstract

It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Min Tang & Zhengfeng Yang

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Zhenbing Zeng

Authors
  1. Min Tang
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  2. Zhengfeng Yang
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  3. Zhenbing Zeng
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Corresponding author

Correspondence to Min Tang.

Additional information

This research was supported in part by the National Natural Science Foundation of China under Grant Nos. 11471209, 61321064 and 61361136002, the Innovation Program of Shanghai Municipal Education Commission under Grant No. 14ZZ046.

This paper was recommended for publication by Editor ZHANG Yang.

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Tang, M., Yang, Z. & Zeng, Z. Resultant elimination via implicit equation interpolation. J Syst Sci Complex 29, 1411–1435 (2016). https://doi.org/10.1007/s11424-016-4159-8

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  • DOI: https://doi.org/10.1007/s11424-016-4159-8

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