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

Fabrice Rouillier; Marie-Françoise Roy; Mohab Safey El Din

doi:10.1006/jcom.2000.0563

Journal articles

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

Fabrice Rouillier ^{1, 2} Marie-Françoise Roy Mohab Safey El Din ^{2, 1}

1 SPACES - Solving problems through algebraic computation and efficient software

INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications

2 CALFOR - Calcul formel

LIP6 - Laboratoire d'Informatique de Paris 6

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.

Mots-clés : infinitésimaux solutions réelles hypersurfaces real solutions hypersurfaces infinitesimals

Document type :

Journal articles

Domain :

Computer Science [cs] / Other [cs.OH]

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https://hal.inria.fr/inria-00099275
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Submitted on : Tuesday, September 26, 2006 - 8:52:19 AM
Last modification on : Friday, February 4, 2022 - 4:17:43 AM

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

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

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