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Solving linear systems of equations over integers with Gröbner bases

Amir Hashemi (2014)

Acta Arithmetica

We introduce a novel application of Gröbner bases to solve (non-homogeneous) systems of integer linear equations over integers. For this purpose, we present a new algorithm which ascertains whether a linear system of equations has an integer solution or not; in the affirmative case, the general integer solution of the system is determined.

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