A fast algorithm for polynomial factorization over \(\mathbb Q_p\) (Q1396437)

The authors consider the problem of factoring monic, square-free polynomials with \(p\)-adic coefficients. Based on the Round Four algorithm of H. Zassenhaus and on a criterion stating that a monic, square-free polynomial in \({\mathbb Z}_p[X]\) is reducible over \({\mathbb Q}_p[x]\) if and only if a certain condition involving a resultant in \({\mathbb Z}_p[X]\) is satisfied, the authors present a method to factorize such polynomials into irreducible factors. They present numerical experiments to show that their method is considerably faster than the classical Round Four maximal order algorithm.