real polynomial equation solving intrinsic complexity singularities polar copolar and bipolar variety degree of variety Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity Bernd Bank Bank Bernd Marc Giusti Giusti Marc Joos Heintz Heintz Joos Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2012, 23

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.


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