目前很多意义重大的自然科学和工程技术问题都可归结为微分方程的研究，而微分方程研究的主体是偏微分方程（组）（PDEs）。为了求解PDEs人们提出了众多求解方法，诸多方法中Lie对称是公认的普适性最广的方法，它以诸多传统方法为其特例。目前PDEs对称理论和方法的研究在现代数学、物理和力学等学科中有重要的理论和实际意义。本项目将研究基于微分特征列集和Groebner基的PDEs对称机械化算法，在两个算法的框架下深入研究PDEs对称。具体研究内容有：1.利用广义对称(非古典对称和势对称)扩大PDEs拥有的对称，并且利用新的对称构造PDEs的新不变解；2.研究对称分类在PDEs中的应用；3.研究PDEs最优系统，并对PDEs进行分类约化，计算其不变解。这项研究是微分特征列集和Groebner基的最新研究方向。通过该项目的研究，我们将扩展吴方法和Groebner基的应用，并且进一步促进对称理论研究。

At present, Many significant natural sciences and engineering problems can be attributed to the research of differential equations. The main research projects of differential equations are partial differential equations (PDEs). Many methods for solving PDE have been proposed, but there is no a unified and systematic method that can be used to deal with all types of NLPDE, and also various methods have their own scope. We all know that the symmetry method is the most universal method in many methods, many traditional methods become its special cases. The investigations of the symmetry theory and approach have important theoretical and practical significance in modern mathematics, physics, mechanics and so on. In this project, we study the mechanized algorithm to symmetry of PDEs based on differential characteristic set and Groebner basis. Specific studies include: 1. We expand the original symmetries of PDEs by using the generalized symmetries (the nonclassical symmetries and the potential symmetries), and construct new invariant solutions by using new symmetries; 2.We study the applications of symmetry classification to PDEs; 3. We study the optimal system of PDEs and classifying reduce PDEs, calculate invariant solutions. The research is also a new research direction of the differential characteristic set and Groebner basis. We extend the application of Wu’s method and Groebner basis, and further promote the investigations of symmetry theory by studying the project.