Real Root Isolation of Regular Chains

  • François Boulier
  • Changbo Chen
  • François LemaireEmail author
  • Marc Moreno MazaEmail author
Conference paper


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.


Real Root Algebraic Number Polynomial System Univariate Polynomial Regular Chain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.LIFLUniversité de Lille 1Villeneuve D’Ascq CedexFrance
  2. 2.ORCCAUniversity of Western Ontario (UWO)LondonCanada
  3. 3.Chongqing Key Laboratory of Automated Reasoning and CognitionChongqing Institute of Green and Intelligent Technology, Chinese Academy of SciencesChongqingChina

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