One Optimal System swMATH ID: 24718 Software Authors: Zhang, Lin; Han, Zhong; Chen, Yong Description: A direct algorithm Maple package of one-dimensional optimal system for group invariant solutions. To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically, we develop a new Maple package One Optimal System. Meanwhile, we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each classification. Besides, a new conception called invariance set is raised. Moreover, this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples. Homepage: http://iopscience.iop.org/article/10.1088/0253-6102/69/1/14/meta Dependencies: Maple Keywords: symbolic computation; mathematics mechanization; direct algorithm; optimal system Related Software: ONEOptimal; LIE; BIGLIE; Maple Cited in: 3 Publications all top 5 Cited by 7 Authors 1 Chen, Yong 1 Cui, Ping 1 Feng, Yiying 1 Geng, Lu-Lu 1 Han, Zhong 1 Liu, Jiangen 1 Yang, Xiao-Jun Cited in 3 Serials 1 Journal of Geometry and Physics 1 Journal of Optimization Theory and Applications 1 Communications in Theoretical Physics all top 5 Cited in 10 Fields 2 Partial differential equations (35-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year