Resumen de Bipolar varieties and real solving of a singular polynomial equation

Bernd Bank, Marc Giusti, Joos Heintz, Luis Miguel Pardo Vasallo

• We introduce the concept of a bipolar variety of a real algebraic hypersurface.

  This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the connected components of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of the given hypersurface and in this sense intrinsic.