Irreducible Decomposition of Curves

In this paper, we propose a fast semi-numerical algorithm for computing all irreducible branches of a curve in Cτdefined by polynomials with rational coefficients, we also treat the case of a non-reduced curve. Our algorithm does not requiresa prior projection procedure which, in many cases, is difficult to achieve. It relies on a fine analysis of a generic “fat" section of the curve. Our approach could be applied to more general situations, it generalizes our previous study on absolute factorization of polynomials.