tensor[directional_diff] - compute the directional derivative
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Calling Sequence
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directional_diff( f, V, coord)
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Parameters
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f
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scalar field
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V
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contravariant vector field
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coord
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list of coordinate names
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Description
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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.
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f must be of type algebraic, and V must be a tensor_type with index character [1] (a contravariant vector field). The result is an algebraic expression.
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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.
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Examples
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Compute the directional derivative of f with respect to coord in the direction of V:
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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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