Computing isolated roots of sparse polynomial systems in affine space

  • Authors:

  • María Isabel Herrero;Gabriela Jeronimo;Juan Sabia

  • Affiliations:

  • Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, (1428) Buenos Aires, Argentina;Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, (1428) Buenos Aires, Argentina;Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, (1428) Buenos Aires, Argentina and Departamento de Ciencias Ex ...

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

We present a symbolic probabilistic algorithm to compute the isolated roots in C^n of sparse polynomial equation systems. As some already known numerical algorithms solving this task, our procedure is based on polyhedral deformations and homotopies, but it amounts to solving a smaller number of square systems of equations and in fewer variables. The output of the algorithm is a geometric resolution of a finite set of points including the isolated roots of the system. The complexity is polynomial in the size of the combinatorial structure of the system supports up to a pre-processing yielding the mixed cells in a subdivision of the family of these supports.