A quasi-linear irreducibility test in K[[x]][y] - Poteaux, Adrien; Weimann, Martin (Computational complexity, 2022)
We provide an irreducibility test in the ring K [ [ x ] ] [ y ] whose complexity is quasi-linear with respect to the discriminant valuation, assuming the input polynomial F is square-free and K is a perfect field of characteristic not dividing deg ( F ) . The algorithm uses the theory of approximate roots and may be seen as a generalisation of Abhyankar's irreducibility criterion to the case of non-algebraically closed residue fields.