  A constructive version of Newton-Puiseux theorem for computing the Puiseux
expansions of algebraic curves is presented. The proof is based on a classical
proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base
field need not be algebraically closed and a factorization algorithm of
polynomials over the base field is not needed. The extensions obtained are a
type of regular algebras over the base field and the expansions are given as
formal power series over these algebras.
