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Decomposing Polynomial Sets Simultaneously into Gröbner Bases and Normal Triangular Sets

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Abstract

In this paper we focus on the algorithms and their implementations for decomposing an arbitrary polynomial set simultaneously into pairs of lexicographic Gröbner bases and normal triangular sets with inherent connections in between and associated zero relationship with the polynomial set. In particular, a method by temporarily changing the variable orderings to handle the failure of the variable ordering assumption is proposed to ensure splitting needed for characteristic decomposition. Experimental results of our implementations for (strong) characteristic decomposition with comparisons with available implementations of triangular decomposition are also reported.

This work was partially supported by the National Natural Science Foundation of China (NSFC 11401018).

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Notes

  1. 1.

    http://www.lifl.fr/~lemaire/BCLM09/BCLM09-systems.txt.

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Acknowledgements

The authors would like to thank the reviewers for their detailed comments which have led to effective improvements on this paper.

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Authors and Affiliations

  1. LMIB–SKLSDE–School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China

    Rina Dong & Chenqi Mou

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  1. Rina Dong
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  2. Chenqi Mou
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Correspondence to Chenqi Mou .

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Editors and Affiliations

  1. Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Dong, R., Mou, C. (2017). Decomposing Polynomial Sets Simultaneously into Gröbner Bases and Normal Triangular Sets. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2017. Lecture Notes in Computer Science(), vol 10490. Springer, Cham. https://doi.org/10.1007/978-3-319-66320-3_7

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  • DOI: https://doi.org/10.1007/978-3-319-66320-3_7

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-66320-3

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