Solving Rank One Perturbed Linear Diophantine Systems Using the Hermite Normal Form

We show how we can obtain the general solution of rank one perturbed linear Diophantine systems (A + uvT )x = b using only information from the application of the Hermite normal form algorithm to the corresponding linear Diophantine system Ax = b. The empirical results show that use of the proposed algorithm may result in saving considerable computing time.