On the intrinsic complexity of point finding in real singular hypersurfaces

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

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2009-12, 9

MSC 2000

14Q10 Surfaces, hypersurfaces

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.