Diophantine approximation of linear forms over an algebraic number field

This paper gives an algorithm for generating all the solutions in integers x0, x1…, xn of the inequalitywhere 1, α1, …,αn are numbers, linearly independent over the rationals, in a real algebraic number field of degree n + 1 ≥ 3 and c is any sufficiently large positive constant. It is well known [2, p. 79] that if c is small enough, then (1) has no integer solutions with x1…, xn not all zero.