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Journal Articles Journal of Complexity Year : 2000

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

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.

Dates and versions

inria-00099275 , version 1 (26-09-2006)

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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, 2000, 16 (4), pp.716-750. ⟨10.1006/jcom.2000.0563⟩. ⟨inria-00099275⟩
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