Initialize a new metric after a change of coordinates

edit

Hi to everyone,

I'm new to SageMath and I use it for some General Relativity implementation.

I have a trouble: I cosntructed a metric g on a Manifold M with a coordinate chart like that

X.>t, x, y, z>

Now, I constructed a change of coordinates defining the transition map from X (original) to Y (new one). I don't have any problem with that

Now, I would like to construct a new metric g' on the same Manifold M, that is g in the new coordinates chart Y. I know that i could visualize that using

g.display(Y.frame(), Y)

but I want the new one like a new metric.

Thank you in advance.