A bound for the order of characteristic set elements of an ordinary prime differential ideal and some applications
The author recalls some notations, definitions and results on the subject from a differential algebra in the paper. Then he gives an upper bound for the order of characteristic set elements of an ordinary prime differential ideal with respect to an elimination ordering. He also shows that computing characteristic sets of ordinary prime differential ideals, by change of ordering, is single exponential time. The results obtained in the paper are used for the study of the solvability of systems of algebraic differential equations. For an introduction to the subject and references, see \textit{W. Y. Sit} [The Ritt-Kolchin theory for differential polynomials, In: Guo, Li (ed) et al., Proceedings of the international workshop on differential algebra and related topics, New Brunswick, 2000, World Scientific, 1-70 (2002; Zbl 1011.12007)].
scientific article; zbMATH DE number 1441264