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SageManifolds different frames

Hi All,

I have the following code:

sage: M = Manifold(2, 'M')
sage: U = M.open_subset('U')
sage: c_xy.<x,y> = U.chart()
sage: V = M.open_subset('V')
sage: c_uv.<u,v> = V.chart()
sage: M.declare_union(U,V)
sage: xy_to_uv = c_xy.transition_map(c_uv, (x+y, x-y), intersection_name='W', restrictions1= x>0, restrictions2= u+v>0)
sage: xy_to_uv.display()
sage: uv_to_xy = xy_to_uv.inverse()
sage: uv_to_xy.display()
sage: e_xy = c_xy.frame(); e_uv = c_uv.frame()
sage: t = M.tensor_field(1,1, name='t')
sage: t[e_xy,:] = [[x, 1], [y, 0]]
sage: t.add_comp_by_continuation(e_uv, U.intersection(V), c_uv)
sage: t[:]
sage: t[e_uv,:]
sage: w = M.vector_field(name='w')
sage: w[e_xy,:] = [-y, x]
sage: w.add_comp_by_continuation(e_uv, U.intersection(V), c_uv)
sage: w[:]
sage: w[e_uv,:]

What I don't understand is the result in sage: t[e_uv,:] and sage: w[e_uv,:] in view of the transition map uv_to_xy. Shouldn't the result be a direct substitution x=(u+v)/2 and y=(u-v)/2

How is this calculated?