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On the Complexity of Computing the Topology of Real Algebraic Space Curves

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Abstract

This paper presents an algorithm to compute the topology of an algebraic space curve. This is a modified version of the previous algorithm. Furthermore, the authors also analyse the bit complexity of the algorithm, which is \(\widetilde{\cal O}\left( {{N^{20}}} \right)\), where N = max{d, τ}, d and τ are the degree bound and the bit size bound of the coefficients of the defining polynomials of the algebraic space curve. To our knowledge, this is the best bound among the existing work. It gains the existing results at least N2. Meanwhile, the paper contains some contents of the conference papers (CASC 2014 and SNC 2014).

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, 437100, China

    Kai Jin

  2. Key Lab of Mathematics Mechanization Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Jinsan Cheng

Authors
  1. Kai Jin
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  2. Jinsan Cheng
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Corresponding author

Correspondence to Kai Jin.

Additional information

This research was supported by Hubei Provincial Natural Science Foundation of China under Grant No.2020CFB479, the Research and Development Funds of Hubei University of Science and Technology under Grant No. BK202024, and the National Natural Science Foundation of China under Grant No. 11471327.

This paper was recommended for publication by Editor LI Hongbo.

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Jin, K., Cheng, J. On the Complexity of Computing the Topology of Real Algebraic Space Curves. J Syst Sci Complex 34, 809–826 (2021). https://doi.org/10.1007/s11424-020-9164-2

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  • DOI: https://doi.org/10.1007/s11424-020-9164-2

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