Opened 4 years ago
Last modified 3 years ago
#19147 closed enhancement
Affine connections on smooth manifolds — at Version 6
Reported by:  egourgoulhon  Owned by:  

Priority:  major  Milestone:  sage7.5 
Component:  geometry  Keywords:  differentiable manifold, affine connection, curvature, torsion 
Cc:  mbejger, mmancini  Merged in:  
Authors:  Eric Gourgoulhon, Michal Bjeger, Marco Mancini  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  public/manifolds/diff_manif_connections  Commit:  f86e5db06f2691867a5aed61fa2512300ee396db 
Dependencies:  #18100, #19092  Stopgaps: 
Description (last modified by )
This ticket implements affine connections on infinitely differentiable manifolds (i.e. smooth manifolds) . This is a followup of #19092 within the SageManifolds project (see the metaticket #18528 for an overview). As in #19092, the nondiscrete topological field K over which the smooth manifold is defined is generic, although in most applications, K=R or K=C.
Affine connections are implemented via the Python class AffineConnection
, the user interface being the method DiffManifold.affine_connection()
. At the user choice, CPUdemanding computations (like that of the curvature tensor) can be parallelized, thanks to #18100.
Various methods of the class AffineConnection
allow the computation of
 the connection coefficients with respect to a given vector frame (from those w.r.t. another frame)
 the connection 1forms with respect to a given vector frame
 the torsion tensor
 the torsion 2forms with respect to a given vector frame
 the (Riemann) curvature tensor
 the curvature 2forms with respect to a given vector frame
 the Ricci tensor
 the action of the affine connection on any tensor field
Documentation:
The reference manual is produced by
sage docbuild reference/manifolds html
It can also be accessed online at http://sagemanifolds.obspm.fr/doc/19147/reference/manifolds/
More documentation (e.g. example worksheets) can be found here.
Change History (6)
comment:1 Changed 4 years ago by
 Commit changed from 0e013aee30e3cfc05918943aa419a3d2336c01ec to 477d0577753ca790205ea115053aefad1fed0d0c
comment:2 Changed 4 years ago by
 Description modified (diff)
comment:3 Changed 4 years ago by
 Commit changed from 477d0577753ca790205ea115053aefad1fed0d0c to a14806252bc9f787fec76a0e9dda60ceffa3d172
Branch pushed to git repo; I updated commit sha1. New commits:
a148062  Major improvements in the documentation of diff. manifolds (affine connections part)

comment:4 Changed 4 years ago by
 Commit changed from a14806252bc9f787fec76a0e9dda60ceffa3d172 to a80dcccaf4d8164a23598e986120d48b0fb26008
Branch pushed to git repo; I updated commit sha1. New commits:
a80dccc  Improve TensorField.__eq__ (case with no open cover known)

comment:5 Changed 4 years ago by
 Commit changed from a80dcccaf4d8164a23598e986120d48b0fb26008 to f86e5db06f2691867a5aed61fa2512300ee396db
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
325e832  Corrected error in parallelisation of __mul__. Added parallism for the symmetric __add__

256d268  changed name TensorParallelism to TensorParallelCompute

bea739d  Added Eric corrections to parallelism

a6d4bd4  Merge branch 'public/18100parallelization_tensors' into Sage 6.7

81f662c  Improve documentation of class TensorParallelCompute.

ea38c84  In doc, changed processor with process

819661d  Changed variables name : set_nproc to set_nproc_tensor, get_nproc to get_nproc_tensor

53c248c  Parallelization: corrected doc

0bb79a3  Merge #18100 into #19124

f86e5db  Merge #19147 into (#19124 + #18100)

comment:6 Changed 4 years ago by
 Description modified (diff)
 Milestone changed from sage6.9 to sage6.10
 Status changed from new to needs_review
Branch pushed to git repo; I updated commit sha1. New commits:
Add doctests to AffineConnection; full coverage