An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic. II

We suggest algorithms for factoring polynomials in the rings of multivariables formal power series over the ground field of zero–characteristic and over an algebraic closure of this ground field. Also we construct algorithms for factoring monic polynomials in one variable over these formal power series rings. We give explicit estimates for the complexity of suggested algorithms. These results are important for local investigation of algebraic varieties from the algorithmic point of view.