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Real Root Isolation of Regular Chains

In: Computer Mathematics

Author

Listed:
  • François Boulier

    (Université de Lille 1, LIFL)

  • Changbo Chen

    (University of Western Ontario (UWO), ORCCA
    Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing Key Laboratory of Automated Reasoning and Cognition)

  • François Lemaire

    (Université de Lille 1, LIFL)

  • Marc Moreno Maza

    (University of Western Ontario (UWO), ORCCA)

Abstract

We present an algorithm RealRootIsolate for isolating the real roots of a polynomial system given by a zerodimensional squarefree regular chain. The output of the algorithm is guaranteed in the sense that all real roots are obtained and are described by boxes of arbitrary precision. Real roots are encoded with a hybrid representation, combining a symbolic object, namely a regular chain and a numerical approximation given by intervals. Our algorithm is a generalization, for regular chains, of the algorithm proposed by Collins and Akritas. We have implemented RealRootIsolate as a command of the module SemiAlgebraicSetTools of the RegularChains library in Maple. Benchmarks are reported.

Suggested Citation

  • François Boulier & Changbo Chen & François Lemaire & Marc Moreno Maza, 2014. "Real Root Isolation of Regular Chains," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 33-48, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_4
    DOI: 10.1007/978-3-662-43799-5_4
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