atlas
Atlas is a Maple toolbox which allows users to solve a variety of differential geometry problems using a simple computational scheme. The computational process is highly automated. For low dimensional (2-D and 3-D) problems it contains atlasWizard, a Maplet tool which generates corresponding atlas package code and allows users to formulate and solve problems in seconds. The package allows users to do differential geometry calculations with symbolic dimension. All the results are given in standard mathematical notations and all calculations are as coordinate-free as possible. The software is able to work with manifolds and mappings; users can define N-dimensional manifold as a set of charts and mappings and then do calculations on defined charts.