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tensor

  

partial_diff

  

compute the partial derivatives of a tensor_type with respect to given coordinates

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

partial_diff( U, coord)

Parameters

U

-

tensor_type whose partial derivatives are to be found

coord

-

list of names representing the coordinate variables

Description

Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.

• 

Given the coordinate variables, coord, and any tensor_type U, partial_diff(U, coord) constructs the partial derivatives of U, which will be a new tensor_type (not necessarily a tensor, of course) of rank one higher than that of U.

• 

The extra index due to differentiation is of covariant character, by convention. Thus the index_char field of the result is Uindex_char,−1.

• 

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

• 

When computing the first and second partial derivatives of the covariant metric tensor components, it is suggested that the tensor[d1metric] and tensor[d2metric] routines be used instead of the partial_diff routine so that the symmetries of the first and second partials be implemented using the tensor package indexing functions. The partial_diff routine does not preserve any symmetric properties that the indices of its input may have.

• 

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

Examples

Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.

withtensor:

coordr,θ,ψ:

Aarray1..3,fr,gθ,hψ:

Ucreate1,opA

Utablecompts=frgθhψ,index_char=1

(1)

part_Upartial_diffU,coord

part_Utablecompts=ⅆⅆrfr000ⅆⅆθgθ000ⅆⅆψhψ,index_char=1,−1

(2)

Vcreate,Hr,θ,ψ

Vtablecompts=Hr,θ,ψ,index_char=

(3)

part_Vpartial_diffV,coord

part_Vtablecompts=rHr,θ,ψθHr,θ,ψψHr,θ,ψ,index_char=−1

(4)

See Also

tensor(deprecated)

tensor(deprecated)/cov_diff

tensor(deprecated)/directional_diff

tensor(deprecated)/exterior_diff

tensor(deprecated)/Lie_diff

tensor(deprecated)[d1metric]

tensor(deprecated)[d2metric]

tensor(deprecated)[indexing]

tensor(deprecated)[simp]