Tensor[GenerateTensors] - generate a list of tensors from a list of lists of tensors
Calling Sequences
GenerateTensors(Tlist)
Parameters
Tlist - a list of lists of tensor fields
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Description
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With Tlist = [T_1, T_2, ..., T_r] the command GenerateTensors(Tlist) will generate a list of tensors by forming all possible r-fold tensor products t1 &t t2 ... &t tr, where the first tensor t1 belongs to the list T_1, the second tensor t2 belongs to the list T_2, and so on.
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This command is part of the DifferentialGeometry:-Tensor package, and so can be used in the form GenerateTensors(...) only after executing the command with(DifferentialGeometry) and with(Tensor) in that order. It can always be used in the long form DifferentialGeometry:-Tensor:-GenerateTensors.
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Examples
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Example 1.
First create a 3 dimensional manifold M.
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Create a list L1 of all type (1, 1) tensors on M.
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M >
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M >
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M >
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Example 2.
Create a list L2 of all rank 3 covariant tensors which are symmetric in their first 2 indices.
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M >
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Example 3.
Create a list L3 of all rank 3 covariant tensors which are skew-symmetric in their first 2 indices.
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M >
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