Issue in calculus on manifolds with incomplete set of transition maps #28072
Description
In Sage 8.8, we have
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: Y.<u,v> = M.chart()
sage: X_to_Y = X.transition_map(Y, [x+y, x-y])
sage: f = M.scalar_field({X: x*y})
sage: g = M.scalar_field({Y: u*v})
sage: f + g
...
KeyError: (Chart (M, (u, v)), Chart (M, (x, y)))
If one initializes the inverse transition map, things are OK:
sage: X_to_Y.inverse()
Change of coordinates from Chart (M, (u, v)) to Chart (M, (x, y))
sage: f + g
Scalar field on the 2-dimensional differentiable manifold M
sage: _.display()
M --> R
(x, y) |--> x^2 + x*y - y^2
(u, v) |--> 1/4*u^2 + u*v - 1/4*v^2
But even without knowing the inverse transition map, Sage should be capable to compute the value of f + g, with the result expressed in the chart X only.
CC: @tscrim
Component: geometry
Keywords: scalar field
Author: Eric Gourgoulhon
Branch/Commit: 7d13b13
Reviewer: Travis Scrimshaw
Issue created by migration from https://trac.sagemath.org/ticket/28072