Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity

Bernd Bank , Marc Giusti , Joos Heintz

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2012, 23

MSC 2000

68W30 Symbolic computation and algebraic computation

14P05 Real algebraic sets

14B05 Singularities

14B07 Deformations of singularities

68W10 Parallel algorithms

Abstract
This survey covers a decade and a half of joint work with L. Lehmann, G. M. Mbakop, and L. M. Pardo. We address the problem of finding a smooth algebraic sample point for each connected component of a real algebraic variety, being only interested in components which are generically smooth locally complete intersections. The complexity of our algorithms is essentially polynomial in the degree of suitably defined generalized polar varieties and is therefore intrinsic to the problem under consideration.