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tensor

  

permute_indices

  

Permutation of the indices of a tensor_type

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

permute_indices(T, permutation)

Parameters

T

-

tensor_type on which to perform permutation

permutation

-

permutation according to which the re-indexing of the indices is to be done

Description

Important: The tensor package has been deprecated. Use the superseding command DifferentialGeometry[Tensor][RearrangeIndices].

• 

This procedure allows you to change the way a given tensor_type is indexed.  Given any permutation of the indices of a tensor_type and a tensor, the routine will re-index the tensor according to the given permutation.

• 

T must be of rank 2 or more.

• 

permutation is a list of indices (integers ranging from 1 to rank(T)) with no duplications and size equal to the rank of T.  It is used to specify the re-indexing of the tensor in the following way: The `nth' index of the original tensor is moved to the position of `n' in the permutation.  For example, a permutation list of  specifies that the third index of the original tensor will be the first index of the re-indexed tensor, the first index of the original tensor will be the second index of the re-indexed tensor, and the second index of the original tensor will be the third index of the re-indexed tensor (that is,  i,j,k --> k,i,j).

• 

This function is occasionally useful because of the rigidity in default indexing of the other utility routines, like prod, contract, and cov_diff, of the tensor package.  Since you can have a preferred indexing different from the default, and switching back and forth between the two conventions could be confusing during a substantial computation, it is advised that you perform a re-ordering of indices of any computed tensor_type to comply with your indexing convention, whenever the default indexing is different from the one with which you are comfortable.

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Note that any symmetrical properties of the indices of the input are not preserved in the re-indexed indices of the result.

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This function is part of the tensor package, and so can be used in the form permute_indices(..) only after performing the command with(tensor) or with(tensor, permute_indices).  The function can always be accessed in the long form tensor[permute_indices](..).

Examples

Important: The tensor package has been deprecated. Use the superseding command DifferentialGeometry[Tensor][RearrangeIndices].

Find the transpose of a rank 2 tensor.

(1)

(2)

Perform a cyclic permutation on a rank 3 tensor.

(3)

(4)

See Also

DifferentialGeometry[Tensor][RearrangeIndices]

tensor(deprecated)

tensor(deprecated)/cov_diff

tensor(deprecated)[contract]

tensor(deprecated)[prod]

 


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