tensor
lin_com
linear combination of any number of tensor_types
Calling Sequence
Parameters
Description
Examples
lin_com(c1, T1, c2, T2, ...., cN, TN)
c1, c2, c3, ..., cN
-
algebraic coefficients in the linear combination to be formed
T1, T2, T3, ..., TN
tensor_types of identical characters and sharing the same space dimension
Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead. See DifferentialGeometry algebraic operations and Physics[`*`].
This function forms the following linear combination of tensors:
c1⁢T1+c2⁢T2+c3⁢T3+....+cN⁢TN.
Each * represents a scalar multiplication and each + represents naturally a tensor addition.
There is no limit on how many tensors to be summed; that is, N can be any positive integer.
Any of the algebraic c's can be omitted, in which case it is by default substituted by 1.
Simplification: This routine uses the `tensor/lin_com/simp` routine for simplification purposes. The simplification routine is applied to each component of result after it is computed. By default, `tensor/lin_com/simp` is initialized to the `tensor/simp` routine. It is recommended that the `tensor/lin_com/simp` routine be customized to suit the needs of the particular problem. It should be noted that `tensor/lin_com/simp` is used frequently as a simplifier by other routines. See ?tensor[simp] for a list of simplifiers used by each routine of the package.
This function is part of the tensor package, and so can be used in the form lin_com(..) only after performing the command with(tensor) or with(tensor, lin_com). The function can always be accessed in the long form tensor[lin_com](..).
with⁡tensor:
A≔array⁡1..3,1..3,a,0,0,0,a,0,0,0,a:
B≔array⁡1..3,1..3,0,b,0,0,0,0,0,b,0:
C≔array⁡1..3,1..3,0,0,c,0,0,0,c,0,0:
The following is the direct definitions of the tensor_types T1, T2, T3, without using the function tensor[create].
T1≔table⁡index_char=−1,−1,compts=op⁡A:
T2≔table⁡index_char=−1,−1,compts=op⁡B:
T3≔table⁡index_char=−1,−1,compts=op⁡C:
SUM≔lin_com⁡x,T1,T2,z,T3
SUM≔table⁡index_char=−1,−1,compts=a⁢xbc⁢z0a⁢x0c⁢zba⁢x
Form the linear combination of some scalars:
T4≔create⁡,x:T5≔create⁡,y:T6≔create⁡,z:
SUM≔lin_com⁡T4,b+c,T5,c⁢a,T6
SUM≔table⁡index_char=,compts=c⁢a⁢z+y⁢b+y⁢c+x
See Also
DifferentialGeometry
DifferentialGeometry algebraic operations
Physics
Physics[`*`]
tensor(deprecated)
tensor(deprecated)[simp]
Download Help Document