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On Characteristic Decomposition and Quasi-characteristic Decomposition

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Computer Algebra in Scientific Computing (CASC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11661))

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Abstract

In this paper, the concepts of quasi-characteristic pair and quasi-characteristic decomposition are introduced. The former is a pair \((\mathcal {G}, \mathcal {C})\) of a reduced lexicographic Gröbner basis \(\mathcal {G}\) and the W-characteristic set \(\mathcal {C}\) which is regular and extracted from \(\mathcal {G}\); the latter is the decomposition of a polynomial set into finitely many quasi-characteristic pairs with associated zero relations. We show that the quasi-characteristic decomposition of any polynomial set can be obtained algorithmically regardless of the variable ordering condition. A new algorithm is presented for computing characteristic decomposition when the variable ordering condition is always satisfied, otherwise it degenerates to compute the quasi one. Some properties of quasi-characteristic pairs and decomposition are proved, and examples are given to illustrate the algorithm.

This work was partially supported by the National Natural Science Foundation of China (NSFC 11771034) and the Fundamental Research Funds for the Central Universities in China (YWF-19-BJ-J-324).

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Notes

  1. 1.

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

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Acknowledgments

The authors would like to thank the anonymous reviewers for their detailed and helpful comments on an earlier version of this paper.

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Authors and Affiliations

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

    Rina Dong & Chenqi Mou

  2. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China

    Chenqi Mou

Authors
  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. Coventry University, Coventry, UK

    Matthew England

  2. University of Kassel, Kassel, Germany

    Wolfram Koepf

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. University of Kassel, Kassel, Germany

    Werner M. Seiler

  5. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Dong, R., Mou, C. (2019). On Characteristic Decomposition and Quasi-characteristic Decomposition. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-26831-2_9

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