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We provide an irreducibility test in the ring K[[x]][y] whose complexity isquasi-linear with respect to the valuation of the discriminant, assuming theinput polynomial F square-free and K a perfect field of characteristic zero orgreater than deg(F). The algorithm uses the theory of approximate roots and maybe seen as a generalization of Abhyankhar's irreducibility criterion to thecase of non algebraically closed residue fields. More generally, we show thatwe can test within the same complexity if a polynomial is pseudo-irreducible, alarger class of polynomials containing irreducible ones. If $F$ ispseudo-irreducible, the algorithm computes also the valuation of thediscriminant and the equisingularity types of the germs of plane curve definedby F along the fiber x=0.

Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]