coordinates.coordinate_systems.OblateHomoeoidalCoordinateSystem.metric_tensor

property OblateHomoeoidalCoordinateSystem.metric_tensor: Callable

Returns the callable function for the metric tensor of the coordinate system.

The metric tensor \(g_{ij}\) defines the inner product structure of the coordinate system. It is used for measuring distances, computing derivatives, and raising/lowering indices. This function returns the precomputed metric tensor as a callable function, which can be evaluated at specific coordinates.

Returns:

A function that computes the metric tensor \(g_{ij}\) when evaluated at specific coordinates. The returned function takes numerical coordinate values as inputs and outputs a NumPy array of shape (ndim, ndim).

Return type:

Callable

Example

cs = MyCoordinateSystem()
g_ij = cs.metric_tensor(x=1, y=2, z=3)  # Evaluates the metric at (1,2,3)
print(g_ij.shape)  # Output: (ndim, ndim)