Factoring polynomials over global fields I

Factoring Polynomials over Global Fields

We prove polynomial time complexity for a now widely used factorization algorithm for polynomials over the rationals. Our approach also yields polynomial time complexity results for bivariate polynomials over a finite field.

Factoring Polynomials over Local Fields

Factoring Polynomials over Number Fields

The purpose of these notes is to give a substantially self-contained introduction to the factorization of polynomials over number fields. In particular, we present Zassenhaus’ algorithm and a factoring algorithm using lattice reduction, which were, respectively, the best in practice and in theory, before 2002. We give references for the van Hoeij-Novocin algorithm, currently the best both in pr...

Factoring Polynomials over Local Fields

Factoring Dickson polynomials over finite fields

We derive the factorizations of the Dickson polynomials Dn(X, a) and En(X, a), and of the bivariate Dickson polynomials Dn(X, a) − Dn(Y, a), over any finite field. Our proofs are significantly shorter and more elementary than those previously known.