Based onWu-Ritt’s characteristic set method and V. Gerdet’s involutive division method,
we defined the involutive characteristic set (abbr. ICS) for a set of non-linear PDEs with
respect to a general involutive direction. The ICS method depends on two factors: the prolongation
direction and the variable ordering. In this paper, we report an implementation
of the ICS method and use it to solve a large set of PDE systems raised from the computation
of symmetric groups for PDEs. Based on the experiments, we try to select the best
prolongation direction and the variable ordering for the ICS algorithm.