A geometric-numeric algorithm for absolute factorization of multivariate polynomials

  • Authors:

  • Robert M. Corless;André Galligo;Ilias S. Kotsireas;Stephen M. Watt

  • Affiliations:

  • University of Western Ontario, London ON, N6A 5B7 Canada;Université de Nice-Sophia Antipolis, Nice 06108 Cedex 2, France;University of Western Ontario, London ON, N6A 5B7 Canada and Wilfrid Laurier University, Waterloo ON, N2L 3C5 Canada and Wilfrid Laurier University, Waterloo ON, N2L 3C5 Canada;University of Western Ontario, London ON, N6A 5B7 Canada

  • Venue:
  • Proceedings of the 2002 international symposium on Symbolic and algebraic computation
  • Year:
  • 2002

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Abstract

In this paper, we propose a new semi-numerical algorithmic method for factoring multivariate polynomials absolutely. It is based on algebraic and geometric properties after reduction to the bivariate case in a generic system of coordinates. The method combines 4 tools: zero-sum relations at triplets of points, partial information on monodromy action, Newton interpolation on a structured grid, and a homotopy method. The algorithm relies on a probabilistic approach and uses numerical computations to propose a candidate factorization (with probability almost one) which is later validated.