Polynomial equation solving by lifting procedures for ramified fibers

  • Authors:

  • A. Bompadre;G. Matera;R. Wachenchauzer;A. Waissbein

  • Affiliations:

  • MIT Operations Research Center, Cambridge, MA and Departamento de Matemáticas, Facultad de Ciencias y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428) Buen ...;Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, Campus Universitario, José M. Gutiérrez 1150 (1613), Los Polvorines, Pcia. de Buenos Aires, Argentina and Membe ...;Departamento de Computación, Facultad de Ingeniería, Universidad de Buenos Aires, Av. Paseo Colón 850 (1063) Buenos Aires, Argentina;Departamento de Matemáticas, Facultad de Ciencias y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428) Buenos Aires, Argentina

  • Venue:
  • Theoretical Computer Science - Algebraic and numerical algorithm
  • Year:
  • 2004

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Abstract

Let be given a parametric polynomial equation system which represents a generically unramified family of zero-dimensional algebraic varieties. We exhibit an efficient algorithm which computes a complete description of the solution set of an arbitrary parameter instance from a complete description of the infinitesimal structure of a particular ramified parameter instance of our family. This generalizes in the case of space curves previous methods of Heintz et al. and Schost, which require the given parameter instance to be unramified. We illustrate our method solving particular polynomial equation systems by deformation techniques.