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Computing PUR of Zero-Dimensional Ideals of Breadth at Most One

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Abstract

In this paper, for a zero-dimensional polynomial ideal I, the authors prove that k[x1, x2, ⋯, xn]/I is cyclic if and only if the breadth of I is 0 or 1. Furthermore, the authors present a new algorithm to compute polynomial univariate representation (PUR) of such an ideal.

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Author information

Authors and Affiliations

  1. School of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun, 130012, China

    Jian Pan & Shugong Zhang

  2. College of Science, Northeast Electric Power University, Jilin, 132012, China

    Baoxin Shang

  3. School of Science, Changchun University of Science and Technology, Changchun, 130022, China

    Zhe Li

Authors
  1. Jian Pan
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  2. Baoxin Shang
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  3. Zhe Li
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  4. Shugong Zhang
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Corresponding author

Correspondence to Shugong Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11671169.

This paper was recommended for publication by Editor FENG Ruyong.

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Pan, J., Shang, B., Li, Z. et al. Computing PUR of Zero-Dimensional Ideals of Breadth at Most One. J Syst Sci Complex 34, 2396–2409 (2021). https://doi.org/10.1007/s11424-021-9330-1

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  • DOI: https://doi.org/10.1007/s11424-021-9330-1

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