Pullback silently fails in some cases with multiple charts #31904
Description
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