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Contraction of Tensors in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112515] Contraction of Tensors in Mathematica
  • From: Sam Takoy <sam.takoy at yahoo.com>
  • Date: Sat, 18 Sep 2010 07:25:16 -0400 (EDT)

Hi,

I this message I will suppress the covariant/contravariant nature of 
tensors.

Suppose I have two tensors A_ijkl and B_rstu (denoted by a and b in 
Mathematica). Each tensor is presented for a 4-deep list. Now, I want to 
form a new tensor:

C_ijklrstu = A_ijkl*B_rstu

and I want C to be represented by an 8-deep list. I've gathered is that 
what I need to do is

c = Outer[Times, a, b];

Great!

Now supposed I want to do some contraction to define a new tensor

D_jklrsu = C_ijklrsiu?


How do I do that?

Many thanks in advance!

Sam


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