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tensor

  

raise

  

raise a covariant index

  

lower

  

lower a contravariant index

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

raise(contravariant_metric_tensor, A, i1, i2, ... )

lower(covariant_metric_tensor, A, i1, i2, ... )

Parameters

contravariant_metric_tensor

-

metric tensors used to raise the indices

covariant_metric_tensor

-

metric tensors used to lower the indices

A

-

tensor by which to raise/lower the indices

i1, ...

-

non-empty sequence of indices of A to raise/lower

Description

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

• 

The function raise(con_met, A, 2, 3) computes the tensor A with indices 2 and 3 raised using the contravariant metric con_met.

• 

The function lower(cov_met, A, 1, 4) computes the tensor A with indices 1 and 4 lowered using the covariant metric cov_met.

• 

Each index in the call to raise must be a valid covariant index of A.

• 

Each index in the call to lower must be a valid contravariant index of A.

• 

There must be at least 1 index given and the number of indices cannot exceed the rank of A.

• 

Simplification:  These routines use the `tensor/prod/simp` routine for simplification purposes.  The simplification routine is applied to each component of the result after it is computed.  By default, `tensor/prod/simp` is initialized to the `tensor/simp` routine. It is recommended that the `tensor/prod/simp` routine be customized to suit the needs of the particular problem.

• 

These functions are part of the tensor package, and so can be used in the form raise(..) / lower(..) only after performing the command with(tensor), or with(tensor, raise) / with(tensor, lower).  These functions can always be accessed in the long form tensor[raise](..) / tensor[lower](..).

Examples

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

withtensor:

covariant Euclidean 3-space metric in spherical-polar coordinates:

acreate1,1,array1,0,0,0,r2,0,0,0,r2sinθ2

atableindex_char=−1,−1,compts=1000r2000r2sinθ2

(1)

contravariant Euclidean 3-space metric in spherical-polar coordinates:

Acreate1,1,array1,0,0,0,1r2,0,0,0,1r2sinθ2

Atableindex_char=1,1,compts=10001r20001r2sinθ2

(2)

create a mixed 2-tensor, raise one index, then lower the other

Tcreate1,1,arrayw,x,0,y,z,0,0,y2,xyw

Ttableindex_char=1,−1,compts=wx0yz00y2xyw

(3)

raiseA,T,2

tableindex_char=1,1,compts=wxr20yzr200y2r2xywr2sinθ2

(4)

lowera,T,1

tableindex_char=−1,−1,compts=wx0r2yr2z00r2sinθ2y2r2sinθ2xyw

(5)

See Also

DifferentialGeometry[Tensor][RaiseLowerIndices]

tensor(deprecated)

tensor(deprecated)/change_basis

tensor(deprecated)/permute_indices

tensor(deprecated)[simp]