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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, 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.
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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

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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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