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

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

  • 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.

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