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