compute the directional derivative
directional_diff( f, V, coord)
contravariant vector field
list of coordinate names
Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.
The function directional_diff(f, V, coord) computes the directional derivative of the scalar field f with respect to the coordinates coord in the direction of the contravariant vector V.
f must be of type algebraic, and V must be a tensor_type with index character  (a contravariant vector field). The result is an algebraic expression.
Simplification: This routine uses the `tensor/directional_diff/simp` routine for simplification purposes. The simplification routine is applied to each component of the gradient of f (an intermediate calculation) and once to the contraction of this gradient with V (the result). By default, `tensor/directional_diff/simp` is initialized to the `tensor/simp` routine. It is recommended that the `tensor/directional_diff/simp` routine be customized to suit the needs of the particular problem.
Compute the directional derivative of f with respect to coord in the direction of V:
Compute the directional derivative of an arbitrary scalar field g(x,y,z) in the direction of an arbitrary vector field U = (u1, u2, u3):
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