Solving Norm Form Equations over Number Fields

Let K be a number field and L a finite extension of K of degree l. Let w(1) = 1, w(2), ... , w(l) be K-linearly independent integers of L and k an integer of K. We denote by N-L/K the norm from L to K. In this paper we give an algorithm for the computation of algebraic integers, x(1), ... , x(l) is an element of K satisfying the equation N-L/K (w(1)x(1) + ... + x(l)w(l)) = k.