on Completely Integrable System of Linear PDEs with Involutive Characteristic Set Method
确定线性偏微分方程组可积系统的对合特征集方法

Based on the Ritt-Wu's characteristic set method and Riquier-Janet theory, an algorithm to reduce the linear PDE system to a normal form is presented. With this algorithm, we get completely integrable system of linear PDE system by removing redundant terms and adding new integrability conditions. The theorem determining whether a system is completely integrable is given in the paper, and its proof is provided as well. Our algorithm is applicable not only to the linear PDEs with constant coefficients but also to the general case.