The complexity of factoring univariatepolynomials over the rationals: tutorial abstract

Abstract

This tutorial will explain the algorithm behind the currently fastest implementations for univariate factorization over the rationals. The complexity will be analyzed; it turns out that modifications were needed in order to prove a polynomial time complexity while preserving the best practical performance. The complexity analysis leads to two results: (1) it shows that the practical performance on common inputs can be improved without harming the worst case performance, and (2) it leads to an improved complexity, not only for factoring, but for LLL reduction as well.