We describe through an algebraic and geometrical study, a new method for solving systems of linear diophantine equations. This approach yields an algorithm which is intrinsically parallel. In addition to the algorithm, we give a geometrical interpretation of the satisfiability of an homogeneous system, as well as upper bounds on height and length of all minimal solutions of such a system. We also show how our results apply to inhomogeneous systems yielding necessary conditions for satisfiability and upper bounds on the minimal solutions.
CITATION STYLE
Domenjoud, E. (1991). Solving systems of linear diophantine equations: An algebraic approach. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 520 LNCS, pp. 141–150). Springer Verlag. https://doi.org/10.1007/3-540-54345-7_57
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