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Finding at least one point in each connected component of a real algebraic set defined by a single equation

Fabrice Rouillier 1 Marie-Françoise Roy Mohab Safey El Din
1 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Deciding efficiently the emptiness of a real algebraic set defined by a single equation is a fundamental problem of computational real algebraic geometry. We propose an algorithm for this test. We find, when the algebraic set is non empty, at least one point on each semi-algebraically connected component. The problem is reduced to deciding the existence of real critical points of the distance function and computing them.
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https://hal.inria.fr/inria-00107845
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Thursday, October 19, 2006 - 9:11:41 AM
Last modification on : Friday, February 4, 2022 - 3:30:52 AM
Long-term archiving on: : Friday, November 25, 2016 - 12:38:04 PM

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  • HAL Id : inria-00107845, version 1

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Fabrice Rouillier, Marie-Françoise Roy, Mohab Safey El Din. Finding at least one point in each connected component of a real algebraic set defined by a single equation. [Intern report] A00-R-017 || rouillier00a, 2000, 42 p. ⟨inria-00107845⟩

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