Opened 7 years ago

Last modified 6 years ago

#18843 closed enhancement

Differentiable manifolds: vector fields and tensor fields — at Version 8

Reported by: egourgoulhon Owned by: egourgoulhon
Priority: major Milestone: sage-7.4
Component: geometry Keywords: differentiable manifold, tensor field, vector field, differential form
Cc: mbejger, bpillet, bpage Merged in:
Authors: Eric Gourgoulhon, Michal Bejger Reviewers:
Report Upstream: N/A Work issues:
Branch: public/manifolds/diff_manif_tensor_fields Commit: 935a0f741185e30f50ad27750987d7bac63b957f
Dependencies: #15916, #18100, #18783 Stopgaps:

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Description (last modified by 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 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

Change History (8)

comment:1 Changed 7 years ago by git

  • Commit changed from d48210c11f38f90ce656f0fa25ec550d147a1892 to b9c3bc529cdd9e7c11f5f6bd10f6e29b070b7cbc

Branch pushed to git repo; I updated commit sha1. New commits:

b9c3bc5Start to improve documentation on tensor fields on differentiable manifolds

comment:2 Changed 7 years ago by git

  • Commit changed from b9c3bc529cdd9e7c11f5f6bd10f6e29b070b7cbc to a2e0696fc335aa07d0b2ce3f6ab54c45996e6746

Branch pushed to git repo; I updated commit sha1. New commits:

a2e0696Add method display() to tensor components and display_comp() to tensors

comment:3 Changed 7 years ago by git

  • Commit changed from a2e0696fc335aa07d0b2ce3f6ab54c45996e6746 to cad56b1f9b3f4ad59b957d7e8b1b8512bec3ae4d

Branch pushed to git repo; I updated commit sha1. New commits:

cad56b1Improve documentation of tensor fields

comment:4 Changed 7 years ago by git

  • Commit changed from cad56b1f9b3f4ad59b957d7e8b1b8512bec3ae4d to 794c149286b90285cd1d32cd21145b2a2e3e8d53

Branch pushed to git repo; I updated commit sha1. New commits:

794c149Improve documentation of differential forms

comment:5 Changed 7 years ago by git

  • Commit changed from 794c149286b90285cd1d32cd21145b2a2e3e8d53 to 435fb11339a9e00b87de5ceac36ed14085c197e0

Branch pushed to git repo; I updated commit sha1. New commits:

435fb11Improve documentation of vector frames

comment:6 Changed 7 years ago by git

  • Commit changed from 435fb11339a9e00b87de5ceac36ed14085c197e0 to 8f47f64e2eb6411bcc00693f012c63974b3d4e28

Branch pushed to git repo; I updated commit sha1. New commits:

8f47f64More improvements in the documentation of diff. manifolds

comment:7 Changed 7 years ago by git

  • Commit changed from 8f47f64e2eb6411bcc00693f012c63974b3d4e28 to 935a0f741185e30f50ad27750987d7bac63b957f

Branch pushed to git repo; I updated commit sha1. New commits:

935a0f7Improvements in the documentation of class DiffManifold

comment:8 Changed 7 years ago by egourgoulhon

  • Description modified (diff)
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