The van Hoeij Algorithm for Factoring Polynomials

Abstract

In this survey we report about a new algorithm for factoring polynomials due to Mark van Hoeij. The main idea is that the combinatorial problem which occurs in the Zassenhaus algorithm is reduced to a very special knapsack problem. In case of rational polynomials this knapsack problem can be very efficiently solved by the LLL algorithm. This gives a polynomial time algorithm which also works very well in practice.

Métodos numérico-simbólicos para calcular soluciones liouvillianas de ecuaciones diferenciales lineales

“…The LLL authors construct a suitable lattice in [LLL82,§2] for the algorithm given in [LLL82,§3]. For a survey on factorization methods depending on lattice reduction, see [Klü10]; also [Nov08, Ch. 1].…”