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Solving Parametric Polynomial Systems by RealComprehensiveTriangularize

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Mathematical Software – ICMS 2014 (ICMS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8592))

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Abstract

In the authors’ previous work, the concept of comprehensive triangular decomposition of parametric semi-algebraic systems (RCTD for short) was introduced. For a given parametric semi-algebraic system, say S, an RCTD partitions the parametric space into disjoint semi-algebraic sets, above each of which the real solutions of S are described by a finite family of triangular systems. Such a decomposition permits to easily count the number of distinct real solutions depending on different parameter values as well as to conveniently describe the real solutions as continuous functions of the parameters. In this paper, we present the implementation of RCTD in the RegularChains library, namely the RealComprehensiveTriangularize command. The use of RCTD is illustrated by the stability analysis of several biological systems.

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Author information

Authors and Affiliations

  1. Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, China

    Changbo Chen

  2. ORCCA, University of Western Ontario, Canada

    Marc Moreno Maza

Authors
  1. Changbo Chen
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  2. Marc Moreno Maza
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Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, 27695, Raleigh, NC, USA

    Hoon Hong

  2. Courant Institute, Dept. of Computer Science, New York Institute, 251 Mercer Street, 10012, New York, NY, USA

    Chee Yap

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Chen, C., Maza, M.M. (2014). Solving Parametric Polynomial Systems by RealComprehensiveTriangularize . In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_76

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  • DOI: https://doi.org/10.1007/978-3-662-44199-2_76

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

  • Online ISBN: 978-3-662-44199-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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