real polynomial equation solving singularities semi-numerical algorithm Variétés bipolaires et résolution d’une équation polynomiale réelle Bernd Bank Bank Bernd Marc Giusti Giusti Marc Joos Heintz Heintz Joos Luis Miguel Pardo Pardo Luis Miguel Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2009-6, 8p

Variétés bipolaires et résolution d’une équation polynomiale réelle

Bernd Bank , Marc Giusti , Joos Heintz , Luis Miguel Pardo

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2009-6, 8p

MSC 2000

14P05 Real algebraic sets
14B05 Singularities
68W30 Symbolic computation and algebraic computation

Abstract
In previous work we designed an efficient procedure that finds an algebraic sample point for each connected component of a smooth real complete intersection variety. This procedure exploits geometric properties of generic polar varieties and its complexity is intrinsic with respect to the problem. In the present paper we introduce a natural construction that allows to tackle the case of a non–smooth real hypersurface by means of a reduction to a smooth complete intersection.


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