#18843: Differentiable manifolds: vector fields and tensor fields
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: geometry | Resolution:
Keywords: differentiable | Merged in:
manifold, tensor field, vector | Reviewers:
field, differential form | Work issues:
Authors: Eric Gourgoulhon, | Commit:
Michal Bejger | 935a0f741185e30f50ad27750987d7bac63b957f
Report Upstream: N/A | Stopgaps:
Branch: |
public/manifolds/diff_manif_tensor_fields|
Dependencies: #15916, #18100, |
#18783 |
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Description changed by egourgoulhon:
Old description:
> 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
New description:
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
--
--
Ticket URL: <http://trac.sagemath.org/ticket/18843#comment:8>
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