Using Sage to Calculate Curvature

SageMath is a powerful, open-source, computer algebra system. You can install your own copy, but computations can also be done in the cloud, using the SageMath cloud server. SageManifolds is a differential geometry and tensor calculus package incorporated into SageMath. Thus, all of the formalism needed to compute curvature is already built in to SageMath.

However, two aspects of SageMath can be daunting for some users. The first is that the syntax is object-oriented, similar to Python. The second is that SageManifolds is designed for experts in differential geometry.

I have therefore created several interactive pages that permit relatively inexperienced users to perform a number of standard computations, at roughly the level of my book. All computations should run in the cloud using any modern browser; no installation is required. Each computation can also be customized by the user. The pages currently available are listed below.