Irreducibility testing over local fields

The purpose of this paper is to describe a method to determine whether a bivariate polynomial with rational coefficients is irreducible when regarded as an element in , the ring of polynomials with coefficients from the field of Laurent series in with rational coefficients. This is achieved by computing certain associated Puiseux expansions, and as a result, a polynomial-time complexity bound for the number of bit operations required to perform this irreducibility test is computed.