Determining The Double Freeness Of Arrangements By Computer

The purpose of this thesis is to study the double freeness of hyperplane arrangements. An algorithm for computing the basis of double free hyperplane arrangments is given.This paper consists of two parts. The first part is about hyperplane arrangements and free hyperplane arrangements. The second part is about how to compute a basis of the logarithmic derivation module of a double free arrangement. An algorithm for calculating the basis of logarithmic derivations for double free hyperplane arrangements is given. This algorithm can determine if an arrangement is double free or not. Some examples of linear arrangements are given.