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Comprehensive Involutive Systems

  • Vladimir Gerdt
  • Amir Hashemi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7442)

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.

Keywords

Symbolic Computation Polynomial Ideal Parametric Ideal Parametric Polynomial Involutive Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vladimir Gerdt
    • 1
  • Amir Hashemi
    • 2
  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia
  2. 2.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

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