SageMath 9.4 is out

More info:  external link

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 (; see the release tour 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 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 Those for Windows should follow soon. SageMath 9.4 is also available online at