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Re: writing tensor in mathematica

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  • Subject: [mg131920] Re: writing tensor in mathematica
  • From: Itai Seggev <itais at>
  • Date: Tue, 29 Oct 2013 02:51:59 -0400 (EDT)
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On Mon, Oct 28, 2013 at 11:22:55PM -0400, Dhaneshwar Mishra wrote:
> Hi 
> I am Dhaneshwar Mishra, new to the Mathematica.
> I would like to write 
> [ab]_(jk) = a_i [C_(ijkm)] b_m 
> in the matrix form, where I,j,k, m varies from 1 to 3. Being a new user, I find 
> little difficult to find proper help from the Mathematica documentations.
> Please suggest me appropriate reading materials so that I can take help of that as well.
> Thanks in advance.
> With regards


I'm not sure exactly what you are asking because you say "in the matrix form"
but you write your equation using indices.  

Assuming you have vectors a and b and a rank-4 tensor c, then a . c. b will
correspond to the contraction you have written.   You might find the resource
tutorial/Tensors in the documentation center helpful.

If you wish to express this relationship symbolically, you can do something
like the following:

$Assumptions =  Element[a | b, Vectors[3, Reals]] && 
  Element[c, Arrays[{3, 3, 3, 3}, Reals]]
TensorContract[TensorProduct[a, c, b], {{1, 2}, {5, 6}}]

In this case, the page tutorial/SymbolicTensors in the documentation center
will give more details, including how to express the symmetry (if any) of the
tensor c. 

If neither of these is what you seek, please let me know.
Itai Seggev
Mathematica Algorithms R&D

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