The ordinary Hilbert series for Sibirsky graded algebras of the differential system s(5,7)

Abstract

In this paper are examined the construction of ordinary Hilbert series for Sibirsky graded algebras of comitants and invariants in autonomous polynomial differential systems. These series are highly significant for addressing specific problems within the qualitative theory of differential systems. However, constructing them for more complex systems typically presents insurmountable computational difficulties, particularly for generalized Hilbert series, from which ordinary Hilbert series are derived. To overcome these massive calculation barriers, this study shows how adapting Molien's formula can effectively solve the problem. Using this approach, the ordinary Hilbert series for the Sibirsky graded algebras of comitants and invariants was obtained for the differential system s(5,7).