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Tensor[GenerateSymmetricTensors] - generate a list of symmetric tensors from a list of tensors
Calling Sequences
GenerateTensors(Tlist, r)
Parameters
Tlist - a list of tensor fields
r - a positive integer, the number of tensors to be chosen from Tlist
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Description
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With Tlist = [t_1, t_2, ..., t_N], the command GenerateSymmetricTensors(Tlist) will generate a list of symmetric tensors by forming all possible r-fold tensor products t_i1 &t t_i2 ... &t t_ir and symmetrizing the result.
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This command is part of the DifferentialGeometry:-Tensor package, and so can be used in the form GenerateSymmetricTensors(...) only after executing the command with(DifferentialGeometry) and with(Tensor) in that order. It can always be used in the long form DifferentialGeometry:-Tensor:-GenerateSymmetricTensors.
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Examples
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Example 1.
First create a 4 dimensional manifold M.
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![DGsetup([w, x, y, z], M)](/support/helpjp/helpview.aspx?si=5609/file05873/math66.png)
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Create a list L1 of all rank 2 covariant symmetric tensors from the 1-forms dx, dy, dz.
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M >
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![T1 := [dx, dy, dz]](/support/helpjp/helpview.aspx?si=5609/file05873/math82.png)
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![T1 := [dx, dy, dz]](/support/helpjp/helpview.aspx?si=5609/file05873/math85.png)
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M >
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![L1 := [dx*dx, dx*dy/2+dy*dx/2, dx*dz/2+dz*dx/2, dy*dy, dy*dz/2+dz*dy/2, dz*dz]](/support/helpjp/helpview.aspx?si=5609/file05873/math92.png)
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M >
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| (2.3) |
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