Real Root Isolation of Regular Chains

François Boulier (), Changbo Chen (), François Lemaire () and Marc Moreno Maza ()
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François Boulier: Université de Lille 1, LIFL
Changbo Chen: University of Western Ontario (UWO), ORCCA
François Lemaire: Université de Lille 1, LIFL
Marc Moreno Maza: University of Western Ontario (UWO), ORCCA

A chapter in Computer Mathematics, 2014, pp 33-48 from Springer

Abstract: 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.

Keywords: Real Root; Algebraic Number; Polynomial System; Univariate Polynomial; Regular Chain (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-43799-5_4

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DOI: 10.1007/978-3-662-43799-5_4

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