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, HumboldtUniversität zu Berlin (ISSN 08630976), 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, HumboldtUniversität zu Berlin (ISSN 08630976), 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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