Pullback silently fails in some cases with multiple charts

[egourgoulhon]

In Sage 9.3, we have

sage: E.<x,y> = EuclideanSpace()
sage: polar.<r,ph> = E.polar_coordinates()
sage: g = E.metric()
sage: M = Manifold(1, 'M')
sage: Ct.<t> = M.chart()
sage: F = M.diff_map(E, coord_functions={(Ct, polar): (1 + cos(t), t)})
sage: gM = F.pullback(g)
sage: gM
Field of symmetric bilinear forms on the 1-dimensional differentiable
manifold M

So far so good, but

sage: gM.display()
ValueError: no basis could be found for computing the components in 
 the Coordinate frame (M, (d/dt)

Actually, gM has been initialized as a tensor field object, but its components have not been evaluated in any frame:

sage: gM._components
{}

Forcing the coordinate expression of the map F in the Cartesian chart (for instance by a call to F.display()) fixes the issue:

sage: F.display()
M --> E^2
   t |--> (x, y) = (cos(t)^2 + cos(t), (cos(t) + 1)*sin(t))
   t |--> (r, ph) = (cos(t) + 1, t)
sage: gM = F.pullback(g)
sage: gM.display()
(2*cos(t) + 2) dt*dt

However, the expression of F in Cartesian coordinates should not be required to compute the pullback of g since the latter is known in polar coordinates, where F has been defined:

sage: g.display(polar)
g = dr*dr + r^2 dph*dph

This bug has been reported at https://ask.sagemath.org/question/57431/

CC: @tscrim @mjungmath @mkoeppe

Component: manifolds

Keywords: pullback

Author: Eric Gourgoulhon

Branch/Commit: aea4554

Reviewer: Ricardo Buring

Issue created by migration from https://trac.sagemath.org/ticket/31904

[egourgoulhon]

New commits:

8455aab

Fix bug #31904 in pullback

[egourgoulhon]

Author: Eric Gourgoulhon

[egourgoulhon]

Commit: 8455aab

[egourgoulhon]

Branch: public/manifolds/pullback_bug-31904

[egourgoulhon]

comment:4

The fix consisted in making the internal function _pullback_chart of the method pullback to operate for a single pair of charts (now added as arguments), which is determined in the main part of pullback, based on the knowledge of the map's coordinate expressions.

[rburing]

comment:5

The return partial statement in the parallel code has seemingly accidentally been indented too far.

[sagetrac-git]

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

aea4554

#31904: Fix indentation in _pullback_chart

[sagetrac-git]

Changed commit from 8455aab to aea4554

[egourgoulhon]

comment:7

Replying to @rburing:

The return partial statement in the parallel code has seemingly accidentally been indented too far.

Good catch, thanks! (it was not revealed by the parallel doctest because local_list_ind had a single element in that case).
This is corrected in the above commit (as well as a pyflakes error reported by the patchbot).

[egourgoulhon]

comment:8

Ricardo, do you agree with the last version?

[rburing]

Reviewer: Ricardo Buring

[rburing]

comment:9

Yes, looks good now.

[egourgoulhon]

comment:10

Thank you!

[vbraun]

Changed branch from public/manifolds/pullback_bug-31904 to aea4554