On efficiently characterizing solutions of linear diophantine equations and its application to data dependence analysis

In this paper we present severals sets of mathematical tools for characterizing the solutions of linear Diophantine equations. First, a number of methods are given for reducing the complexity of the computations. Thereafter, we introduce different techniques for determining the exact number of solutions of linear Diophantine equations. Finally, we present a method for extracting efficiently the solutions of such equations. For all these methods the main focus has been put on their applicability and efficiency for data dependence analysis