Changes between Initial Version and Version 2 of Ticket #19147


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Timestamp:
09/07/15 16:00:58 (4 years ago)
Author:
egourgoulhon
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  • Ticket #19147

    • Property Commit changed from 0e013aee30e3cfc05918943aa419a3d2336c01ec to 477d0577753ca790205ea115053aefad1fed0d0c
  • Ticket #19147 – Description

    initial v2  
    11This ticket implements affine connections on infinitely differentiable manifolds (i.e. smooth manifolds) . This is a follow-up of #19092 within the [http://sagemanifolds.obspm.fr/ SageManifolds project] (see the metaticket #18528 for an overview). As in #19092, the non-discrete topological field K over which the smooth manifold is defined is generic, although in most applications, K='''R''' or K='''C'''.
    22
    3 Affine connections are implemented via the Python class `AffineConnection`, the user interface being the method `DiffManifold.affine_connection()`. At the user choice, CPU-demanding computations (like that of the Riemann curvature tensor) can be parallelized, thanks to #18100.
     3Affine connections are implemented via the Python class `AffineConnection`, the user interface being the method `DiffManifold.affine_connection()`. At the user choice, CPU-demanding computations (like that of the curvature tensor) can be parallelized, thanks to #18100.
     4
     5Various methods of the class `AffineConnection` allow the computation of
     6- the connection coefficients with respect to a given vector frame (from those w.r.t. another frame)
     7- the connection 1-forms with respect to a given vector frame
     8- the torsion tensor
     9- the torsion 2-forms with respect to a given vector frame
     10- the (Riemann) curvature tensor
     11- the curvature 2-forms with respect to a given vector frame
     12- the Ricci tensor
     13- the action of the affine connection on any tensor field