Given the coordinate variables, coord, a contravariant vector field V, and any tensor T, Lie_diff(T, V, coord) computes the Lie derivative of T with respect to the vector field V using the usual partial derivatives of T and V according to the standard formula:

where the comma denotes a partial derivative, a, b, c, ... are contravariant indices of T and l, m, n, ... are covariant indices of T, and * indicates an inner product on the repeated indices.

It is required that V be a tensor_type with character: [1] (that is, V is a contravariant vector field)

Note that the rank and index character of the result is identical to that of the input tensor, T.

Simplification:  This routine uses the routine `tensor/Lie_diff/simp` routine for simplification purposes.  The simplification routine is applied twice to each component: first, to the first term involving the inner product of the partial of T and the vector V, and second to the entire component once all of the subsequent terms have been added on. By default, this routine is initialized to the `tensor/simp` routine.  It is recommended that the `tensor/Lie_diff/simp` routine be customized to suit the needs of the particular problem.

This function is part of the tensor package, and so can be used in the form Lie_diff(..) only after performing the command with(tensor) or with(tensor, Lie_diff).  The function can always be accessed in the long form tensor[Lie_diff](..).

`tensor/Lie_diff/simp`:=proc(x) simplify(x,trig) end proc: