1 | initial version |

The first problem arises because the domain of `ginv`

is `M`

and not `U`

(since `g`

is defined as `g = M.riemannian_metric('g')`

) and the default frame of `M`

is `Rho.frame()`

. So, you should set:

```
sage: M.set_default_frame(Tau.frame())
```

The second problem lies in the definition of `psi`

:

```
sage: psi = U.scalar_field({Rho: function('Psi')(u1,u2,u3)}, name='psi',latex_name='\Psi')
```

You are declaring the coordinate expression of `psi`

in the chart `Rho`

, but `(u1,u2,u3)`

are coordinates of the chart `Tau`

, so that `function('Psi')(u1,u2,u3)`

appears as a constant function. For instance, one has `diff(function('Psi')(u1,u2,u3), r12) = 0`

. Hence the Laplace-Beltrami operator applied to `psi`

yields zero.

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