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An Extension of Gröbner Basis Theory to Indexed Polynomials Without Eliminations

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Abstract

In computer algebra, it remains to be challenging to establish general computational theories for determining the equivalence of indexed polynomials. In previous work, the author solved the equivalence determination problem for Riemann tensor polynomials by extending Gröbner basis theory. This paper extends the previous work to more general indexed polynomials that involve no eliminations of indices and functions, by the method of ST-restricted rings. A decomposed form of the Gröbner basis of the defining syzygy set in each ST-restricted ring is provided, and then the canonical form of an indexed polynomial proves to be the normal form with respect to the Gröbner basis in the ST-fundamental restricted ring.

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Authors and Affiliations

  1. Department of Systems Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Jiang Liu

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  1. Jiang Liu
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Correspondence to Jiang Liu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11701370.

This paper was recommended for publication by Editor LI Hongbo.

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Liu, J. An Extension of Gröbner Basis Theory to Indexed Polynomials Without Eliminations. J Syst Sci Complex 33, 1708–1718 (2020). https://doi.org/10.1007/s11424-020-9135-7

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  • DOI: https://doi.org/10.1007/s11424-020-9135-7

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