generate a list of symmetric tensors from a list of tensors - Maple Help

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Tensor[GenerateSymmetricTensors] - generate a list of symmetric tensors from a list of tensors

Calling Sequences

     GenerateSymmetricTensors(Tlist, r)

Parameters

   Tlist    - a list of tensor fields

   r        - a positive integer, the number of tensors to be chosen from Tlist

 

Description

Examples

Description

• 

With Tlist = [t1, t2,...,tN], the command GenerateSymmetricTensors(Tlist) will generate a list of symmetric tensors by forming all possible r-fold tensor products ti1ti2...tir and symmetrizing the result.

• 

This command is part of the DifferentialGeometry:-Tensor package, and so can be used in the form GenerateSymmetricTensors(...) only after executing the command with(DifferentialGeometry) and with(Tensor) in that order. It can always be used in the long form DifferentialGeometry:-Tensor:-GenerateSymmetricTensors.

Examples

withDifferentialGeometry:withTensor:

 

Example 1.

First create a 4-tensional manifold M.

DGsetupw,x,y,z,M:

 

Create a list L1 of all rank 2 covariant symmetric tensors from the 1-forms dx, dy, dz.

M > 

T1dx,dy,dz

T1:=dx,dy,dz

(2.1)
M > 

L1GenerateSymmetricTensorsT1,2

L1:=dxdx,12dxdy+12dydx,12dxdz+12dzdx,dydy,12dydz+12dzdy,dzdz

(2.2)
M > 

nopsL1

6

(2.3)

See Also

DifferentialGeometry

Tensor

GenerateForms

GenerateTensors

 


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