The free Python-based computer algebra system SageMath 9.4 has been released on 22 August 2021; it includes differential geometry and tensor calculus capabilities developed through the SageManifolds project (https://sagemanifolds.obspm.fr/); see the release tour https://wiki.sagemath.org/ReleaseTours/sage-9.4 for an overview of novelties.
Regarding calculus on manifolds, SageMath 9.4 introduces many new features:
– improved handling of coordinate restrictions while declaring a chart
– many new functionalities regarding generic subsets of manifolds, including
topological closure, image and preimage via a continuous map
– definition of submanifolds and manifold subsets by pullbacks from SageMath sets (polyhedron, lattice, linear subspace, finite set, etc.)
– connection with other real sets defined in SageMath
– new method to create directly a tangent vector at a given manifold point (without having to initialize the tangent space first)
– de Rham cohomology has been implemented, with the algebra of mixed differential forms treated as a de Rham complex
See https://sagemanifolds.obspm.fr/changelog.html for details and examples.
The following people have contributed to these new features :
Ricardo Buring, Eric Gourgoulhon, Michael Jung, Matthias Koeppe, Samuel Lelievre, Travis Scrimshaw
The Linux and macOS binaries for SageMath 9.4 are available at https://www.sagemath.org/download.html. Those for Windows should follow soon. SageMath 9.4 is also available online at https://cocalc.com.