tensor
raise
raise a covariant index
lower
lower a contravariant index
Calling Sequence
Parameters
Description
Examples
raise(contravariant_metric_tensor, A, i1, i2, ... )
lower(covariant_metric_tensor, A, i1, i2, ... )
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
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](..).
withtensor:
covariant Euclidean 3-space metric in spherical-polar coordinates:
a≔create−1,−1,array1,0,0,0,r2,0,0,0,r2sinθ2
a≔tablecompts=1000r2000r2sinθ2,index_char=−1,−1
contravariant Euclidean 3-space metric in spherical-polar coordinates:
A≔create1,1,array1,0,0,0,1r2,0,0,0,1r2sinθ2
A≔tablecompts=10001r20001r2sinθ2,index_char=1,1
create a mixed 2-tensor, raise one index, then lower the other
T≔create1,−1,arrayw,x,0,y,z,0,0,y2,xyw
T≔tablecompts=wx0yz00y2xyw,index_char=1,−1
raiseA,T,2
tablecompts=wxr20yzr200y2r2xywcscθ2r2,index_char=1,1
lowera,T,1
tablecompts=wx0r2yr2z00r2sinθ2y2r2sinθ2xyw,index_char=−1,−1
See Also
DifferentialGeometry[Tensor][RaiseLowerIndices]
tensor(deprecated)
tensor(deprecated)/change_basis
tensor(deprecated)/permute_indices
tensor(deprecated)[simp]
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