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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-3-5,
author = {Amir Hashemi},
title = {Solving linear systems of equations over integers with Gr\"obner bases},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {261-270},
zbl = {1304.13049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-3-5}
}
Amir Hashemi. Solving linear systems of equations over integers with Gröbner bases. Acta Arithmetica, Tome 166 (2014) pp. 261-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-3-5/