Solving linear systems of equations over integers with Gröbner bases
Volume 163 / 2014
Acta Arithmetica 163 (2014), 261-270
MSC: Primary 13P10; Secondary 11D04.
DOI: 10.4064/aa163-3-5
Abstract
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.
