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
Type de document :
Article dans une revue
Journal of Complexity, Elsevier, 2000, 16 (4), pp.716-750. 〈10.1006/jcom.2000.0563〉
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https://hal.inria.fr/inria-00099275
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 08:52:19
Dernière modification le : vendredi 31 août 2018 - 09:25:57

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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. Journal of Complexity, Elsevier, 2000, 16 (4), pp.716-750. 〈10.1006/jcom.2000.0563〉. 〈inria-00099275〉

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