摘要
本文基于微分形式吴方法理论及算法给出无需确定对称Lie代数本身而事先构造其同构像(具有同结构常数的Lie代数)的机械化算法.该算法有效提高构造(偏)微分方程(组)对称Lie代数的效率,并可应用于对称Lie代数各类性质的机械化分析和判定.最后给出算例验证算法的有效性.
A mechanical algorithm for constructing an isomorphism image(a Lie algebra with the same structural constants)of the Lie algebra of symmetry of a differential equations without solving maximum symmetry of the equations is given based on differential form Wu’s method.The algorithm increases the efficiency of computing whole symmetry and can be applied to mechanical analysis and decision of various properties of the Lie algebra of symmetry of a(partial)differential equation.The illustrative examples show the efficiency and extensive applications of the given algorithm.
出处
《中国科学：数学》
CSCD
北大核心
2019年第5期751-764,共14页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11571008
11771279和11661060)资助项目
关键词
微分形式吴方法
(偏)微分方程
对称Lie代数
确定方程组
机械化算法
differential form Wu’s method
(partial)differential equations
Lie algebra of symmetry
determining equations
mechanical algorithm
