Hi, Michal Bejger and I have started a project regarding differential geometry in Sage. At present, differential geometry in Sage is limited to the class DifferentialForm created by Joris Vankerschaver. The project SageManifolds extends it in at least two directions: - general tensors (and not only differential forms) and metric structures - various charts can be defined on a given manifold and tensor fields are manipulated as such, namely independently of any chart or vector frame. It borrows from DifferentialForm the storage of tensor components as a dictionary whose keys are the indices and that contains only the nonzero and non-redundant values.
The project is still at a very early stage; current functionalities include: - differentiable mappings and submanifolds - standard tensor calculus (tensor product, contraction, (anti)symmetrization) - exterior calculus (wedge product, exterior derivative of differential forms) - Lie derivatives - affine connections - curvature and torsion - pseudo-Riemannian metrics - Hodge duality More details on the page http://sagemanifolds.obspm.fr The package is also posted on the Sage trac server: http://trac.sagemath.org/sage_trac/ticket/14865 The package is still very preliminary. Future developments will focuss on - the implementation of Sage Parent/Element scheme for a better integration in Sage - adding new functionalities (e.g. extrinsic geometry of submanifolds, spinors) - producing faster code by migrating some parts to Cython Volunteers are welcome ! -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
