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

We show how we can obtain the general solution of rankone perturbed linear diophantine systems (a + uvt )x = b using onlyinformation from the application of the hermite normal form algorithmto the corresponding linear diophantine system ax = b. the empiricalresults show that use of the proposed algorithm may result in savingconsiderable computing time.