differential_geometry.symbolic.compute_tensor_laplacian

differential_geometry.symbolic.compute_tensor_laplacian(tensor: MutableDenseNDimArray | ImmutableDenseNDimArray | ImmutableDenseMatrix | MutableDenseMatrix, coordinate_axes: Sequence[Symbol], inverse_metric: ImmutableDenseMatrix | MutableDenseMatrix | ImmutableDenseNDimArray | MutableDenseNDimArray, l_term: ImmutableDenseMatrix | MutableDenseMatrix | ImmutableDenseNDimArray | MutableDenseNDimArray | None = None, metric_density: Basic | None = None) → MutableDenseNDimArray | ImmutableDenseNDimArray | ImmutableDenseMatrix | MutableDenseMatrix

Compute the Laplacian of each component of a symbolic tensor field.

Parameters:

• tensor (sympy.Array) – A symbolic tensor field of arbitrary shape.

• coordinate_axes (list of sympy.Symbol) – The coordinate variables.

• inverse_metric (sympy.Matrix or Array) – Inverse metric tensor.

• l_term (sympy.Array, optional) – Precomputed L-term (otherwise derived from metric_density).

• metric_density (sympy.Basic, optional) – Used to compute L-term if not provided.

Returns:

A symbolic tensor of the same shape, with Laplacian applied component-wise.

Return type:

sympy.Array