Characteristic sets verses generalized characteristic sets

Abstract

The notion of characteristic sets that was developed by Ritt and Wu has been turned into an usual tool for study of set/systems of polynomial equations, algebraic as well as differential equations. By constructing a characteristic sets, one can triangularize an arbitrary set/system of any type of polynomials. It ensures that it can be decomposed into triangular form of a particular set/system. In this manuscript, a comparison of characteristic sets defined by Ritt-Wu’s differential is provided with the generalized characteristic sets defined by author in [5]. Comparison shows that this scheme performs better than earlier method.

Subject Classification:

• Primary 13-XX
• Secondary 14-04

Keywords:

• Characteristic set
• Differential polynomial
• Pseudo division
• Admissible reduction