Application of computer mathematics systems for solving problems of contact geometry

Task. The development of research in the field of contact geometry is impossible without the use of computer mathematics systems. Carrying out a computational experiment allows not only obtaining numerical results, analytical expressions, but also highlighting the correct and promising direction in obtaining theoretical results. Purpose of the work: to consider the application of computer mathematics systems to solving problems of contact geometry. Achieving the goals set in the work is carried out on the basis of the integrated use of computer algebra methods, mathematical modeling, the theory of differential geometry and tensor analysis. Findings. In this paper, we present schemes for studying contact Lie groups of arbitrary odd dimension. An algorithm and a set of programs have been developed in the Maxima computer mathematics system for modeling the proof of the existence of Sasakian structures. Practical value. This algorithm can be used to study contact structures on homogeneous spaces. The proposed schemes are of scientific and practical interest for specialists in the field of differential geometry and methods of its applications, as well as for solving the problems of developing quantum computing devices.