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Gröbner bases in difference-differential modules and difference-differential dimension polynomials

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Abstract

In this paper we extend the theory of Gröbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural filtration. We present and verify algorithms for constructing these Gröbner bases counterparts. To this aim we introduce the concept of “generalized term order” on ℕm×ℤn and on difference-differential modules. Using Gröbner bases on difference-differential modules we present a direct and algorithmic approach to computing the difference-differential dimension polynomials of a difference-differential module and of a system of linear partial difference-differential equations.

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Authors and Affiliations

  1. Department of Mathematics and LMIB, Beihang University, and KLMM, Beijing, 100083, China

    Meng Zhou

  2. RISC-Linz, J. Kepler University Linz, A-4040, Linz, Austria

    Winkler Franz

Authors
  1. Meng Zhou
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  2. Winkler Franz
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Corresponding author

Correspondence to Meng Zhou.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 60473019) and the KLMM (Grant No. 0705)

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Zhou, M., Franz, W. Gröbner bases in difference-differential modules and difference-differential dimension polynomials. Sci. China Ser. A-Math. 51, 1732–1752 (2008). https://doi.org/10.1007/s11425-008-0081-4

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  • DOI: https://doi.org/10.1007/s11425-008-0081-4

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