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.

Eric Gourgoulhon,
on behalf of SageManifolds team (https://sagemanifolds.obspm.fr/authors.html)

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)

SageMath 8.1 has just been released and is shipped with version 1.1 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 1.0.2 of SageManifolds are:
– computation of geodesics (and more generally integrated curves)
– exterior powers of free modules of finite rank
– multivector fields and the Schouten-Nijenhuis bracket
– some performance improvements

See http://sagemanifolds.obspm.fr/changelog.html for details and examples.

It suffices to upgrade to SageMath 8.1 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 8.1 remotely, by creating a free account in CoCalc (https://cocalc.com/): open a Jupyter notebook and select “SageMath 8.1” in the menu Kernel -> Change kernel.

Eric Gourgoulhon,
on behalf of SageManifolds team (http://sagemanifolds.obspm.fr/authors.html)

The SageManifolds project aims at extending the modern computer algebra system SageMath (http://www.sagemath.org/) towards differential geometry and tensor calculus. All SageManifolds 1.0 code is included in SageMath 7.5, so that it does not require any separate installation. Key features of SageMath are being open-source, using the Python language and running in the powerful Jupyter Notebook (http://jupyter.org/).

SageManifolds is devoted to explicit tensor calculus (as opposed to “abstract tensor calculus”): the dimension of the manifold must be specified and some atlas must be provided. SageManifolds 1.0 functionalities include
– topological manifolds: charts, open subsets, maps between manifolds, scalar fields
– differentiable manifolds: tangent spaces, vector frames, tensor fields, curves, pullback and pushforward operators
– standard tensor calculus (tensor product, contraction, symmetrization, etc.), even on non-parallelizable manifolds
– taking into account any monoterm tensor symmetry
– exterior calculus (wedge product, exterior derivative, Hodge duality)
– Lie derivatives of tensor fields
– affine connections (curvature, torsion)
– pseudo-Riemannian metrics
– some plotting capabilities (charts, points, curves, vector fields)

Example of use, in particular in the context of general relativity, are posted at
http://sagemanifolds.obspm.fr/examples.html
Visit http://sagemanifolds.obspm.fr/ for free download and run.

Eric Gourgoulhon (on behalf of the SageManifolds team: http://sagemanifolds.obspm.fr/authors.html )