On the intrinsic complexity of point finding in real singular hypersurfaces

Authors:
Bernd Bank;Marc Giusti;Joos Heintz;Luis Miguel Pardo
Affiliations:
Humboldt-Universität zu Berlin, Institut für Mathematik, D-10099 Berlin, Germany;CNRS, École Polytechnique, Laboratoire LIX, F-91228 Palaiseau Cedex, France;Departamento de Computación, Universidad de Buenos Aires and CONICET, Ciudad Univ., Pab. I, 1428 Ciudad Autónoma de Buenos Aires, Argentina and Departamento de Matemáticas, Estad ...;Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain
Venue:
Information Processing Letters
Year:
2009

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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.