Physics[Vectors][Curl] - compute the curl by using the nabla differential operator
Physics[Vectors][Divergence] - compute the divergence by using the nabla differential operator
Physics[Vectors][Gradient] - compute the gradient by using the nabla differential operator
Physics[Vectors][Laplacian] - compute the Laplacian by using the nabla differential operator
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Calling Sequence
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Curl(A)
Divergence(A)
Gradient(A)
Laplacian(A)
Remark: these calling sequences are also valid with the inert %Curl, %Divergence, %Gradient, %Laplacian commands
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Parameters
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A
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-
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any algebraic (vector or scalar) expression
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Description
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Curl, Divergence, Gradient and Laplacian, respectively return the curl, the divergence, the gradient and the Laplacian of a given vectorial or scalar function. When the command's name is prefixed by , an unevaluated representation for these operations is returned.
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The %Curl, %Divergence, %Gradient and %Laplacian are the inert forms of Curl, Divergence, Gradient and Laplacian, that is: they represent the same mathematical operations while holding the operations unperformed. To activate the operations use value.
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For the conventions about the geometrical coordinates and vectors see ?conventions
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Examples
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The Gradient of a function
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The Divergence of a Gradient is equal to the Laplacian
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The Laplacian of a vector function in spherical coordinates
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The Curl of a Gradient is identically zero
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Depending on the context the inert representations of these commands, obtained by prefixing the command's name with %, serve better the purpose of representing the mathematical objects
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The Curl of non-projected vector function (note the underscore in 'V_' to represent vectors)
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The Divergence of a Curl is identically zero
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The Divergence and Curl of a projected vector function (projected vectors don't need an "arrow" - the underscore "_" mentioned in the previous example to be represented)
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