ИСТИНА

It is well known that the most interesting properties of ODEs system are mainly defined by the lowest no vanished orders of the normal form. Unfortunately, such an order can be very high. We study integrability of the degenerated 5 parametric planar ODEs system by the normal form method where the resonant normal form is calculated by the NORT program. We have found six first integrals of motion of the system at different sets of the parameters. But the last step of the study demands a calculation of the corresponding normal form till the $27^{th}$ order. I.e. it needs to calculate the truncated power series in two small variables and 4 no small parameters until the $27^{th}$ order. This problem has been solved. In the report, we discuss the internal representation of series in the STANDARD LISP program NORT and give estimations for a calculation of the problem by a straight method and with the usage of lazy calculations.