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A Note on Dynamic Gröbner Bases Computation

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Book cover Computer Algebra in Scientific Computing (CASC 2016)

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Abstract

For most applications of Gröbner bases, one needs only a nice Gröbner basis of a given ideal and does not need to specify the monomial ordering. From a nice basis, we mean a basis with small size. For this purpose, Gritzmann and Sturmfels [14] introduced the method of dynamic Gröbner bases computation and also a variant of Buchberger’s algorithm to compute a nice Gröbner basis. Caboara and Perry [6] improved this approach by reducing the size and number of intermediate linear programs. In this paper, we improve the latter approach by proposing an algorithm to compute nicer Gröbner bases. The proposed algorithm has been implemented in Sage and its efficiency is discussed via a set of benchmark polynomials.

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Notes

  1. 1.

    The Sage code of the implementations of our algorithms and examples are available at http://amirhashemi.iut.ac.ir/softwares.

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Acknowledgments

The research of the first author was in part supported by a grant from IPM (No. 94550420). The authors are grateful to anonymous referees for their useful and helpful comments on preliminary version of this paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    Amir Hashemi

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), 19395-5746, Tehran, Iran

    Amir Hashemi

  3. Department of Electrical and Computer Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    Delaram Talaashrafi

Authors
  1. Amir Hashemi
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  2. Delaram Talaashrafi
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Correspondence to Amir Hashemi .

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Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Hashemi, A., Talaashrafi, D. (2016). A Note on Dynamic Gröbner Bases Computation. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2016. Lecture Notes in Computer Science(), vol 9890. Springer, Cham. https://doi.org/10.1007/978-3-319-45641-6_18

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  • DOI: https://doi.org/10.1007/978-3-319-45641-6_18

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