SageMath 8.2 has just been released and is shipped with version 1.2 of SageManifolds code. SageMath is a Python-based free computer algebra system, with some differential geometry and tensor calculus capabilities implemented via the SageManifolds project (http://sagemanifolds.obspm.fr/). See http://sagemanifolds.obspm.fr/examples.html for examples of use, in particular in the context of general relativity.
The new features with respect to version 1.1 of SageManifolds are:
– the possibility to use SymPy instead of SageMath default (Pynac+Maxima) as the symbolic engine for calculus on coordinate expressions
– manifolds equipped with a default metric (i.e. pseudo-Riemannian manifolds)
– operators for vector calculus on any pseudo-Riemannian manifold: gradient, divergence, curl, Laplacian, Dalembertian, dot product, cross product and norm
– more functionalities in the naming of bases and vector frames
See http://sagemanifolds.obspm.fr/changelog.html for details and examples.
It suffices to upgrade to SageMath 8.2 to benefit from these features. Binaries for Linux, MacOS X and Windows are available at http://www.sagemath.org/download.html.
Another option is to run SageMath 8.2 remotely, by creating a free account in CoCalc (https://cocalc.com/): open a Jupyter notebook and select “SageMath 8.2” in the menu Kernel –> Change kernel.
Eric Gourgoulhon,
on behalf of SageManifolds team (http://sagemanifolds.obspm.fr/authors.html)