In this report the problems of orbital and spin nonlinear calculations
are discussed. The introduction of the special P and D-functions allo
ws us to formalize the determination of the orbital and spin Lie opera
tors and to apply the systems of the analytical calculations to find t
hem. An increase in the accuracy of numerical calculations can be achi
eved through the usage of these functions instead of the standard math
-library functions cos, sin and etc.