What is SageManifolds?
SageManifolds is an extension under development for the modern computer algebra system SageMath, implementing differential geometry and tensor calculus.
SageManifolds deals with differentiable manifolds of arbitrary dimension. The basic objects are tensor fields and not tensor components in a given vector frame or coordinate chart. In other words, various charts and frames can be introduced on the manifold and a given tensor field can have representations in each of them.
An important class of treated manifolds is that of pseudo-Riemannian manifolds, among which Riemannian manifolds and Lorentzian manifolds, with applications to General Relativity. In particular, SageManifolds implements the computation of the Riemann curvature tensor and associated objects (Ricci tensor, Weyl tensor). SageManifolds can also deal with generic affine connections, not necessarily Levi-Civita ones.
At present (version 0.9.1), SageManifolds functionalities include:
- maps between manifolds, pullback operator
- submanifolds, pushforward operator
- curves in manifolds
- standard tensor calculus (tensor product, contraction, symmetrization, etc.), even on non-parallelizable manifolds
- taking in charge all monoterm tensor symmetries
- 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)
Open and free software
As SageMath itself, SageManifolds is a free and open source software based on the Python programming language. It is released under the GNU General Public License. To download and install SageManifolds, see here.
If you want to participate in the project, please contact us!