Konwersatorium im. Leopolda Infelda

In this talk I shall discuss the new Differential Geometry package in Maple and illustrate some of the capabilties of this package for computations in mathematical physics. The Differential Geometry package provides a complete, integrated environment for symbolic computations in the areas of calculus on manifolds, tensor algebra and tensor analysis, Lie algebras and Lie groups, jet calculus, and general relativity. I will give a few demonstrations from the areas of integrable systems, Lagrangian reduction in the calculus of variations, homogeneous cosmologies, and equivalence problems to illustrate both the ease of use and versality of the software. Future enhancements of the program will be briefly discussed.