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Decomposition of ordinary differential polynomials

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Abstract

In this paper, we present a complete algorithm to decompose nonlinear differential polynomials in one variable and with coefficients in a computable differential field \({\mathcal K}\) of characteristic zero. The algorithm provides an efficient reduction of the problem to the factorization of LODOs over the same coefficient field. Besides arithmetic operations, the algorithm needs decomposition of algebraic polynomials, factorization of multi-variable polynomials, and solution of algebraic linear equation systems. The algorithm is implemented in Maple for the constant field case. The program can be used to decompose differential polynomials with thousands of terms effectively.

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Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Academia Sinica, Beijing, 100080, China

    Xiao-Shan Gao & Mingbo Zhang

Authors
  1. Xiao-Shan Gao
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  2. Mingbo Zhang
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Correspondence to Xiao-Shan Gao.

Additional information

This article was partially supported by a National Key Basic Research Project of China (NO. G1998030600) and by a USA NSF grant CCR-0201253.

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Gao, XS., Zhang, M. Decomposition of ordinary differential polynomials. AAECC 19, 1–25 (2008). https://doi.org/10.1007/s00200-008-0059-z

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  • DOI: https://doi.org/10.1007/s00200-008-0059-z

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