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

Mostafa Khorramizadeh


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.


Hermite normal form, free module, linear diophantine system

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