Sign Methods for Counting and Computing Real Roots of Algebraic Systems

Abstract : In this report, we implement the concept of topological degree to isolate and compute all zeros of systems of nonlinear algebraic equations when the only computable information required is the algebraic signs. The basic theorems of Kronecker-Picard theory relate the number of roots to the topological degree. Recent fast methods, which work over fixed precision, are applied to determine the sign of algebraic systems. They are then combined with grid methods in order to estimate the total complexity of computing the topological degree.
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https://hal.inria.fr/inria-00073003
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 11:34:05 AM
Last modification on : Wednesday, October 17, 2018 - 5:02:07 PM
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  • HAL Id : inria-00073003, version 1

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Ioannis Z. Emiris, Bernard Mourrain, Mihail N. Vrahatis. Sign Methods for Counting and Computing Real Roots of Algebraic Systems. RR-3669, INRIA. 1999. ⟨inria-00073003⟩

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