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International Congress on Mathematical Software

ICMS 2018: Mathematical Software – ICMS 2018 pp 191–199Cite as

Universal Gröbner Basis for Parametric Polynomial Ideals

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10931))

Abstract

In this paper, we introduce the concept of universal Gröbner basis for a parametric polynomial ideal. In this direction, we present a new algorithm, called UGS, which takes as input a finite set of parametric polynomials and outputs a universal Gröbner system for the ideal generated by input polynomials, by decomposing the space of parameters into a finite set of parametric cells and for each cell associating a finite set of parametric polynomials which is a universal Gröbner basis for the ideal corresponding to that cell. Indeed, for each values of parameters satisfying a condition set, the corresponding polynomial set forms a universal Gröbner basis for the ideal. Our method relies on the parametric variant of the Gröbner basis conversion and also on the PGBMain algorithm due to Kapur et al. to compute parametric Gröbner bases. The proposed UGS algorithm has been implemented in Maple-Sage and its performance is investigated through an example.

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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

    Mahdi Dehghani Darmian

  3. Department of Computer Engineering, Sharif University of Technology, 11365-8639, Tehran, Iran

    Marzieh Barkhordar

Authors
  1. Amir Hashemi
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  2. Mahdi Dehghani Darmian
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  3. Marzieh Barkhordar
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Corresponding author

Correspondence to Mahdi Dehghani Darmian .

Editor information

Editors and Affiliations

  1. University of Bath, Bath, United Kingdom

    James H. Davenport

  2. Johannes Kepler University, Linz, Austria

    Manuel Kauers

  3. University of Waterloo, Waterloo, Ontario, Canada

    George Labahn

  4. Czech Technical University in Prague, Prague 6, Czech Republic

    Josef Urban

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Hashemi, A., Darmian, M.D., Barkhordar, M. (2018). Universal Gröbner Basis for Parametric Polynomial Ideals. In: Davenport, J., Kauers, M., Labahn, G., Urban, J. (eds) Mathematical Software – ICMS 2018. ICMS 2018. Lecture Notes in Computer Science(), vol 10931. Springer, Cham. https://doi.org/10.1007/978-3-319-96418-8_23

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  • DOI: https://doi.org/10.1007/978-3-319-96418-8_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96417-1

  • Online ISBN: 978-3-319-96418-8

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