id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
22563,Fix treatment of pullback on parallelizable manifolds,egourgoulhon,,"The following is a bug:
{{{
sage: S1 = Manifold(1, 'S^1') # the circle
sage: U = S1.open_subset('U') # the complement of one point
sage: Xt. = U.chart('t:(0,2*pi)') # the standard angle coordinate
sage: V = S1.open_subset('V') # the complement of the point t=pi
sage: Xu.__ = V.chart('u:(0,2*pi)') # the angle t-pi
sage: S1.declare_union(U, V)
sage: e = S1.vector_frame('e') # a global vector frame (makes S^1 parallelizable)
sage: R2 = Manifold(2, 'R^2', start_index=1) # Euclidean space R^2
sage: X2. = R2.chart() # Cartesian coordinates
sage: F = S1.diff_map(R2, {(Xt,X2): [cos(t), sin(t)],
....: (Xu,X2): [-cos(u), -sin(u)]}) # embedding S^1 --> R^2
sage: dx = X2.coframe()[1] # the 1-form dx on R^2
sage: a = F.pullback(dx) ; a
1-form on the 1-dimensional differentiable manifold S^1
sage: a._components
{Coordinate frame (V, (d/du)): 1-index components w.r.t. Coordinate frame (V, (d/du)),
Coordinate frame (U, (d/dt)): 1-index components w.r.t. Coordinate frame (U, (d/dt))}
}}}
As a tensor field on `S^1`, `a` should have components only on frames which domain is `S^1` and not some strict subsets of it, like `U` and `V`. Only restrictions of `a` to `U` and `V` (as stored in `a._restrictions`) shall be initialized in the current case.
This ticket fixes the issue. It also changes the names of the pullback helper function and its arguments for a better readability. It also corrects some typos in the error messages in methods of `DiffMap`.
",defect,closed,major,sage-7.6,geometry,fixed,"pullback, manifolds",tscrim,,Eric Gourgoulhon,Travis Scrimshaw,N/A,,02add83718a340f778b47aacb73a8a61dba2aa18,02add83718a340f778b47aacb73a8a61dba2aa18,,
__