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18843 Differentiable manifolds: vector fields and tensor fields egourgoulhon egourgoulhon "This ticket implements tensor fields (among which vector fields and differential forms) on differentiable manifolds. This is a follow-up of #18783 within the [http://sagemanifolds.obspm.fr/ SageManifolds project] (see the metaticket #18528 for an overview). As in #18783, the non-discrete topological field K over which the differentiable manifold is defined is generic, although in most applications, K='''R''' or K='''C'''.
This ticket implements the following Python classes:
1/ Parent classes:
- `VectorFieldModule`: module of vector fields on a differentiable manifold
- `VectorFieldFreeModule`: free module of vector fields on a parallelizable differentiable manifold
- `TensorFieldModule`: module of tensor fields of a given type (k,l) on a differentiable manifold
- `TensorFieldFreeModule`: free module of tensor fields of a given type (k,l) on a parallelizable
differentiable manifold
- `DiffFormModule`: module of differential forms of a given degree p (p-forms) on a differentiable
manifold
- `DiffFormFreeModule`: free module of differential forms of a given degree p (p-forms) on a
parallelizable differentiable manifold
- `AutomorphismFieldGroup`: general linear group of the module of vector fields on a differentiable
manifold
- `AutomorphismFieldParalGroup`: general linear group of the free module of vector fields on a
parallelizable differentiable manifold
2/ Element classes:
- `TensorField`: tensor field on a differentiable manifold
- `VectorField`: vector field on a differentiable manifold
- `DiffForm`: p-form on differentiable manifold
- `AutomorphismField`: field of tangent-space automorphisms on a differentiable manifold
- `TensorFieldParal`: tensor field on a parallelizable differentiable manifold
- `VectorFieldParal`: vector field on a parallelizable differentiable manifold
- `DiffFormParal`: p-form on parallelizable differentiable manifold
- `AutomorphismFieldParal`: field of tangent-space automorphisms on a parallelizable differentiable
manifold
3/ Other classes:
- `VectorFrame`: vector frame on a differentiable manifold
- `CoordFrame`: coordinate vector frame on a differentiable manifold
- `CoFrame`: coframe (frame of 1-forms) on a differentiable manifold
- `CoordCoFrame`: coordinate coframe on a differentiable manifold
'''Documentation''':
The reference manual is produced by
`sage -docbuild reference/manifolds html`
It can also be accessed online at http://sagemanifolds.obspm.fr/doc/18843/reference/manifolds/
More documentation (e.g. example worksheets) can be found [http://sagemanifolds.obspm.fr/documentation.html here].
" enhancement closed major sage-7.4 geometry fixed differentiable manifold, tensor field, vector field, differential form mbejger bpillet bpage Eric Gourgoulhon, Michal Bejger Travis Scrimshaw N/A fb7f4dd6e483f9956f49475bc16707f739f1129a fb7f4dd6e483f9956f49475bc16707f739f1129a #15916, #18783, #20770