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On factor left prime factorization problems for multivariate polynomial matrices

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Abstract

This paper is concerned with factor left prime factorization problems for multivariate polynomial matrices without full row rank. We propose a necessary and sufficient condition for the existence of factor left prime factorizations of a class of multivariate polynomial matrices, and then design an algorithm to compute all factor left prime factorizations if they exist. We implement the algorithm on the computer algebra system Maple, and two examples are given to illustrate the effectiveness of the algorithm. The results presented in this paper are also true for the existence of factor right prime factorizations of multivariate polynomial matrices without full column rank.

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Authors and Affiliations

  1. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China

    Dong Lu

  2. School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Dong Lu

  3. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Dingkang Wang

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Dingkang Wang

  5. School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China

    Fanghui Xiao

Authors
  1. Dong Lu
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  2. Dingkang Wang
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  3. Fanghui Xiao
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Correspondence to Fanghui Xiao.

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This research was supported by the National Natural Science Foundation of China under Grant No. 12001030, the CAS Key Project QYZDJ-SSW-SYS022 and the National Key Research and Development Project 2020YFA0712300.

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Lu, D., Wang, D. & Xiao, F. On factor left prime factorization problems for multivariate polynomial matrices. Multidim Syst Sign Process 32, 975–992 (2021). https://doi.org/10.1007/s11045-021-00768-x

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  • DOI: https://doi.org/10.1007/s11045-021-00768-x

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