In sagemanifolds, I would like to change from an initial chart to a second and then, from the second to the third. My attempts fail. Is this my fault or a sagemanifolds problem? (Apologies if I already asked this.)
Here is a minimal (not) working example. I run the following file:
theManifold = Manifold(1, 'M', r'\mathcal{M}')
theOpenSet = theManifold.open_subset('U')
theFirstChart.<x> = theOpenSet.chart(r'x')
g = theManifold.riemannian_metric('g')
g[0,0] = 1
show(g.display())
theSecondChart.<y> = theOpenSet.chart(r'y')
ChangeFirst_to_Second = theFirstChart.transition_map(theSecondChart,[x])
show(g.display(theSecondChart.frame()))
theThirdChart.<z> = theOpenSet.chart(r'z')
ChangeSecond_to_Third = theSecondChart.transition_map(theThirdChart,[y])
show(g.display(theThirdChart.frame()))
The output is
g=dx⊗dx
g=dy⊗dy
and then a few screens of error messages, of which the most clear is "no common chart for the multiplication".
