On computation of the ordinary Hilbert series for Sibirsky graded algebras of differential system s(3

The generalized and ordinary Hilbert series for Sibirsky graded algebras of comitants and invariants of autonomous polynomial differential systems are of particular importance for some problems of qualitative theory of differential systems. In the Republic of Moldova the computation of these series have their beginnings in the works of Professor M. N. Popa and his disciples. But the construction of these series for some complicated differential systems encounters insurmountable computational difficulties, especially, for the generalized Hilbert series, from which the ordinary Hilbert series can be easily obtained. In this paper, it is shown how the adaptation of Molien’s formula address to the mentioned problem to overcome the enormous calculations, an ordinary Hilbert series were obtained for Sibirsky graded algebras of comitants and invariants for the differential system s(3,5).