set_default_chart seems to fail

edit

I load the following file

theManifold = Manifold(1,'M',r'\mathcal{M}')
theManifold = Manifold(1,'M',r'\mathcal{M}')

theOpenSet = theManifold.open_subset('U')

firstChart.<x> = theOpenSet.chart(r'x')

g=theManifold.riemannian_metric('g')
g[0,0] = x

show("g with first chart")
show(g.display())

secondChart.<y> = theOpenSet.chart('y')

first_to_second = firstChart.transition_map(secondChart,[2*x])
second_to_first = first_to_second.inverse()

show("g with secondChart.frame() and secondChart as arguments to display")
show(g.display(secondChart.frame(),secondChart))

theManifold.set_default_frame(secondChart.frame())
theManifold.set_default_chart(secondChart)

show("g with secondChart.frame() and secondChart as defaults")
show(g.display())

The output is

𝚐 𝚠𝚒𝚝𝚑 𝚏𝚒𝚛𝚜𝚝 𝚌𝚑𝚊𝚛𝚝
g=x dx⊗dx
𝚐 𝚠𝚒𝚝𝚑 𝚜𝚎𝚌𝚘𝚗𝚍𝙲𝚑𝚊𝚛𝚝.𝚏𝚛𝚊𝚖𝚎() 𝚊𝚗𝚍 𝚜𝚎𝚌𝚘𝚗𝚍𝙲𝚑𝚊𝚛𝚝 𝚊𝚜 𝚊𝚛𝚐𝚞𝚖𝚎𝚗𝚝𝚜 𝚝𝚘 𝚍𝚒𝚜𝚙𝚕𝚊𝚢
g=1/8 y dy⊗dy
𝚐 𝚠𝚒𝚝𝚑 𝚜𝚎𝚌𝚘𝚗𝚍𝙲𝚑𝚊𝚛𝚝.𝚏𝚛𝚊𝚖𝚎() 𝚊𝚗𝚍 𝚜𝚎𝚌𝚘𝚗𝚍𝙲𝚑𝚊𝚛𝚝 𝚊𝚜 𝚍𝚎𝚏𝚊𝚞𝚕𝚝𝚜
g=1/4 x dy⊗dy

In particular, when the secondChart and secondChart.frame() have been set as defaults, the metric g is expanded with respect to the second frame, but the components are still expressed in the first coordinates.

Is there a way to set defaults so that g appears as 1/8 y dy ⊗dy?