Algorithms for Constructing Minimal Generating Set of Solutions for Systems of Linear Equations

The authors consider optimization transformations of the algorithm for constructing minimal generating sets of solutions of systems of linear homogeneous equations (SLHE) over the set of natural numbers. The paper describes the features of such SLHEs, substantiates optimization transformations, and presents examples of the algorithm before and after optimization transformations. It illustrates the applying the algorithm with examples of the analysis of Petri net properties and the construction of a basic solution set in the fields of complex, real, and rational numbers and over finite fields.