Abstract Algebraic Approach to the Formation of Computational Environments for Solving Problems in Object Formulations

A method for solving mathematical and applied problems in object formulations is proposed. The method is based on the representation of the subject environment and the initial conditions of the problem in terms of abstract algebras and coding of the obtained formulations by means of the object-oriented programming language Java. The key point is to form a computational environment whose dynamics is controlled by functional and predicate components of the object content of the problem, while the actions of the controlling program are reduced to the transfer of messages and control from object to object. The solution is obtained as a result of self-transformation of the problem statement into a system representation adequate to it. The opportunity of application of the method to the solution of algebraic problems, the conditions of which are set in matrix form and in the form of systems of equations is considered, first of all, to determine the structural and group characteristics. #COMESYSO1120.