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tensor

  

lin_com

  

linear combination of any number of tensor_types

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

lin_com(c1, T1, c2, T2, ...., cN, TN)

Parameters

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

Description

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:

c1T1+c2T2+c3T3+....+cNTN.

  

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](..).

Examples

Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.  See DifferentialGeometry algebraic operations and Physics[`*`].

withtensor:

Aarray1..3,1..3,a,0,0,0,a,0,0,0,a:

Barray1..3,1..3,0,b,0,0,0,0,0,b,0:

Carray1..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].

T1tableindex_char=1,1,compts=opA:

T2tableindex_char=1,1,compts=opB:

T3tableindex_char=1,1,compts=opC:

SUMlin_comx,T1,T2,z,T3

SUMtableindex_char=−1,−1,compts=axbcz0ax0czbax

(1)

Form the linear combination of some scalars:

T4create,x:T5create,y:T6create,z:

SUMlin_comT4,b+c,T5,ca,T6

SUMtableindex_char=,compts=caz+yb+yc+x

(2)

See Also

DifferentialGeometry

DifferentialGeometry algebraic operations

Physics

Physics[`*`]

tensor(deprecated)

tensor(deprecated)[simp]