On the geometry of polar varieties

The aim of this paper is a comprehensive presentation of the geometrical tools which are necessary to prove the correctness of several up to date algorithms with intrinsic complexity bounds for the problem of real root finding in (mainly) smooth real algebraic varieties given by reduced regular sequences of polynomial equations (see [4, 5, 6, 7], [30] and [31]). The results exposed in this paper form also the geometrical main ingredients for the computational treatment of singular hypersurfaces (see [8]). In particular, we show the non

• Type: Journal
• Year: 2010
• Where: AAECC
• Authors: Bernd Bank, Marc Giusti, Joos Heintz, Mohab Safey El Din, Éric Schost
• Keywords: AAECC 2010, Algorithms, Generic Polar Varieties, Polar Varieties, Real Algebraic Varieties