Characteristic sets verses generalised characteristic sets for ordinary differential polynomial sets

Abstract

The concept of characteristic sets developed initially by Ritt and Wu has turned into a standard tool for the study of sets or systems of polynomial and algebraic differential equations. With the help of constructing characteristic sets, an arbitrary set or system of polynomials or differential polynomials can be triangularised. It means that it can be decomposed into a particular set or system of triangular forms. In this paper, a comparison of Ritt–Wu’s characteristic sets by Wang for the ordinary differential polynomial sets with the generalised characteristic sets of the ordinary differential polynomial sets by the authors has been presented. Keywords: Characteristic set, differential polynomial, pseudo-division, admissible reduction.