Fast Modular Algorithms for Squarefree Factorization and Hermite Integration

Abstract

We present new modular algorithms for the squarefree factorization of a primitive polynomial in ℤ[x] and for computing the rational part of the integral of a rational function in ℚ(x). We analyze both algorithms with respect to classical and fast arithmetic and argue that the latter variants are – up to logarithmic factors – asymptotically optimal. Even for classical arithmetic, the integration algorithm is faster than previously known methods.