Algorithms for Solving Linear Constraints Over the Ring Of Integers

The author proposes algorithms for constructing a prebasis and the basis of the set of solutions to systems of linear constraints in the form of equalities and inequalities in the domains of integers, which are based on combined coefficients of constraints. The article considers the algorithm for constructing the prebasis and basis of systems of linear equations and algorithms for constructing the fundamental system of solutions to systems of linear homogeneous and linear inhomogeneous inequalities.