#18843: Differentiable manifolds: vector fields and tensor fields
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: geometry | Keywords: differentiable
Merged in: | manifold, tensor field, vector
Reviewers: | field, differential form
Work issues: | Authors: Eric Gourgoulhon,
Commit: | Michal Bejger
d48210c11f38f90ce656f0fa25ec550d147a1892| Report Upstream: N/A
Stopgaps: | Branch:
|
public/manifolds/diff_manif_tensor_fields
| Dependencies: #15916, #18100,
| #18783
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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 topological
field K over which the differentiable manifold is defined is generic (with
sufficient structure to define differentiability, e.g. a complete metric
field), 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
--
Ticket URL: <http://trac.sagemath.org/ticket/18843>
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