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Название: A Geometric-Numeric Algorithm for Absolute Factorization of Multivariate Polynomials
Авторы: Corless R.M., Galligo A., Kotsires L.S.
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.