DifferentialGeometry (DG) is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus.
At present, the DG software contains approximately 300 commands, divided into 5 packages. The main DG package contains all the commands for what is often referred to as calculus on manifolds – basic operations with vector fields, differential forms and transformations. The Tensor package contains an extensive set of commands for general algebraic and differential tensor operations as well as commands for specialized computations in general relativity. The Lie algebra package provides commands for creating and manipulating Lie algebras, for calculating various sub-algebras and automorphism groups, and for checking properties of Lie algebras and sub-algebras. The GroupActions package provides functionalities for the symbolic analysis of Lie groups and group actions. The JetCalculus package provides the basis for studying differential equations and the calculus of variations. Finally, the Library package contains tables of Lie algebras, group actions, differential equations and solutions of the Einstein equations. The DG software also contains many utilities to support the creation of new specialized software applications.
Additional information, particularly worksheets which demonstrate functionality, provide code, support reseach results, etc. can be found at the DifferentialGeometry website:
http://digitalcommons.usu.edu/dg/