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A criterion for the similarity of length-two elements in a noncommutative PID

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Abstract

This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B 1 A 1 and B 2 A 2 are similar, where A 1,A 2,B 1,B 2 are first-order differential (difference) operators. The main step in the algorithm is to find a rational solution of a parametric differential (difference) Risch’s equation, which has been well-studied in symbolic integration (summation).

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Authors and Affiliations

  1. Key Laboratory of Mathematics and Mechanization, Academy of Mathematics and Systems Science, Beijing, 100190, China

    Ziming Li & Huaifu Wang

Authors
  1. Ziming Li
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  2. Huaifu Wang
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Correspondence to Ziming Li.

Additional information

This research is supported by a 973 key project under Grant No. 2004CB318000 and the National Natural Science Foundation under Grant No. 76596100.

This paper was recommended for publication by Editor Xiao-Shan GAO.

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Li, Z., Wang, H. A criterion for the similarity of length-two elements in a noncommutative PID. J Syst Sci Complex 24, 580–592 (2011). https://doi.org/10.1007/s11424-011-8392-x

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  • DOI: https://doi.org/10.1007/s11424-011-8392-x

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