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Comprehensive Involutive Systems

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Computer Algebra in Scientific Computing (CASC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7442))

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Abstract

In this paper we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Gröbner system in theory of Gröbner bases. Given a parametric ideal, the space of parameters is decomposed into a finite set of cells. Each cell yields the corresponding involutive basis of the ideal for the values of parameters in that cell. Using the Gerdt–Blinkov algorithm described in [6] for computing involutive bases and also the Montes DisPGB algorithm for computing comprehensive Gröbner systems [13], we present an algorithm for construction of comprehensive involutive systems. The proposed algorithm has been implemented in Maple, and we provide an illustrative example showing the step-by-step construction of comprehensive involutive system by our algorithm.

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Author information

Authors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980, Dubna, Russia

    Vladimir Gerdt

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

    Amir Hashemi

Authors
  1. Vladimir Gerdt
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  2. Amir Hashemi
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

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

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2012 Springer-Verlag Berlin Heidelberg

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Gerdt, V., Hashemi, A. (2012). Comprehensive Involutive Systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_9

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  • DOI: https://doi.org/10.1007/978-3-642-32973-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32972-2

  • Online ISBN: 978-3-642-32973-9

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