Bipolar varieties and real solving of a singular polynomial equation

• Bernd Bank ^[1] ; Marc Giusti ^[4] ; Joos Heintz ^[2] ; Luis Miguel Pardo ^[3]
  1. [1] Humboldt University of Berlin

     Humboldt University of Berlin

     Berlin, Stadt, Alemania

     
  2. [2] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
  3. [3] Universidad de Cantabria

     Universidad de Cantabria

     Santander, España

     
  4. [4] CNRS

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• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 2, Nº. 1, 2010, págs. 65-77
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.