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First initialize a manifold M with local coordinates [x, y, z].
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Example 1.
First we calculate the Lie derivative of a function f and note that it agrees with the directional derivative f.
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Example 2.
First we calculate the Lie derivative of a vector field and check that it coincides with the Lie bracket.
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Example 3.
First we calculate the Lie derivative of a differential form and check the result against Cartan's formula.
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Example 4.
We calculate the Lie derivative of a tensor field.
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Example 5.
We calculate the Lie derivative of the zero connection.
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Example 6.
The Lie derivative with respect to a list of vectors can be calculated simultaneously.
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The Lie derivative of a list of tensors can be calculated simultaneously.
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Both arguments to LieDerivative can be lists.
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The Lie derivative of a Matrix of differential 2-forms can be calculated simultaneously.
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Example 7.
The Lie derivative can be calculated in anholonomic frames. Use FrameData to find the structure equations for an anholonomic frame and initialize with DGsetup.
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Example 8.
The Lie derivative can be calculated for abstract forms.
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Example 9.
The Lie derivative can be calculated for tensors on a Lie algebra. Use LieAlgebraData and DGsetup to initialize a Lie algebra.
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Calculate the Killing form for the Lie algebra and show that its Lie derivative is zero for all vectors in the Lie algebra.
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