A Fast Algorithm for Polynomial Factorization over Q

We present an algorithm that returns a proper factor of a polynomial Φ(x) over the p-adic integers Zp (if Φ(x) is reducible over Qp) or returns a power basis of the ring of integers of Qp[x]/Φ(x)Qp[x] (if Φ(x) is irreducible over Qp). Our algorithm is based on the Round Four maximal order algorithm. Experimental results show that the new algorithm is considerably faster than the Round Four algorithm.