Polynomial irreducibility testing through Minkowski summand computation

In this paper, we address the problem of deciding absolute irreducibility of multivariate polynomials. Our work has been motivated by a recent work due to Gao et. al. [1, 2, 3] where they have considered the problem for bivariate polynomials by studying the integral decomposability of polygons in the sense of Minkowski sum. We have generalized their result to polynomials containing arbitrary number of variables by reducing the problem of Minkowski decomposability of an integer (lattice) polytope to an integer linear program. We also present experimental results of computation of Minkowski decomposition using this integer program.