Solving Rank One Perturbed Linear Diophantine Systems Using the Hermite Normal Form
Abstract
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.
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.
Keywords
Hermite normal form, free module, linear diophantine system
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