Ritt-Wu Characteristic Set Method for Laurent Partial Differential Polynomial Systems

In this paper, a Ritt-Wu characteristic set method for Laurent partial differential polynomial systems is presented. The concept of Laurent regular differential chain is defined and its basic properties are proved. The authors give a partial method to decide whether a Laurent differential chain A is Laurent regular. The decision for whether A is Laurent regular is reduced to the decision of whether a univariate differential chain A(1) is Laurent regular. For a univariate differential chain A(1), the authors first give a criterion for whether A(1) is Laurent regular in terms of its generic zeros and then give partial results on deciding whether A(1) is Laurent regular.