SageMath 8.3 has just been released and is shipped with version 1.3 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 (https://sagemanifolds.obspm.fr/). See https://sagemanifolds.obspm.fr/examples.html for examples of use, in particular in the context of general relativity.
The new features with respect to version 1.2 of SageManifolds are:
– submanifolds and their geometry (induced metric, extrinsic curvature, etc.)
– Euclidean spaces as Riemannian manifolds diffeomorphic to R^n and equipped with a flat metric, with predefined coordinate charts (Cartesian, spherical, cylindrical); this allows for elementary vector calculus in standard curvilinear coordinates, see https://sagemanifolds.obspm.fr/vector_calculus.html
– tensor fields along a submanifold
See https://sagemanifolds.obspm.fr/changelog.html for details and examples.
It suffices to upgrade to SageMath 8.3 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 8.3 remotely, by creating a free account in CoCalc (https://cocalc.com/): open a Jupyter notebook and select “SageMath 8.3” in the menu Kernel -> Change kernel.
on behalf of SageManifolds team (https://sagemanifolds.obspm.fr/authors.html)