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International Workshop on Computer Algebra in Scientific Computing

CASC 2016: Computer Algebra in Scientific Computing pp 58–72Cite as

Improved Computation of Involutive Bases

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9890))

Abstract

In this paper, we describe improved algorithms to compute Janet and Pommaret bases. To this end, based on the method proposed by Möller et al. [20], we present a more efficient variant of Gerdt’s algorithm (than the algorithm presented in [16]) to compute minimal involutive bases. Furthermore, by using an involutive version of the Hilbert driven technique along with the new variant of Gerdt’s algorithm, we modify the algorithm given in [23] to compute a linear change of coordinates for a given homogeneous ideal so that the new ideal (after performing this change) possesses a finite Pommaret basis. All the proposed algorithms have been implemented in Maple and their efficiency is discussed via a set of benchmark polynomials.

A. Hashemi—The research of the second author was in part supported by a grant from IPM (No. 94550420).

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Notes

  1. 1.

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

  2. 2.

    See http://invo.jinr.ru.

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Authors and Affiliations

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

    Bentolhoda Binaei & Amir Hashemi

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

    Amir Hashemi

  3. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Werner M. Seiler

Authors
  1. Bentolhoda Binaei
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  2. Amir Hashemi
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  3. Werner M. Seiler
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Corresponding author

Correspondence to Amir Hashemi .

Editor information

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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Binaei, B., Hashemi, A., Seiler, W.M. (2016). Improved Computation of Involutive Bases. 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_5

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  • DOI: https://doi.org/10.1007/978-3-319-45641-6_5

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