Summation Convention
- To: mathgroup@smc.vnet.net
- Subject: [mg12268] Summation Convention
- From: Mark Lawrence Storch <mscc+@andrew.cmu.edu>
- Date: Tue, 5 May 1998 03:30:03 -0400
- Organization: Doctoral student, Materials Science and Engineering, Carnegie Mellon, Pittsburgh, PA
Hello,
I am trying to get Mathematica to sum terms with repeated indices as
it is described in section 2.6.5 of the mathematica book. Specifically
I am trying to peform a change of coordinate systems on a fourth rank
tensor. The transformation should take the form
E'(ijkl)=a(im) a(jn) a(ko) a(lp) E(mnop)
Where the parentheses represent the inidices of the tensor and a is the
direction cosine matrix commonly referred to as alpha. I have tried
the following with little success:
M=Table[(\[Alpha][[i,m]] \[Alpha][[j,n]] \[Alpha][[k,o]] \[Alpha][[l,p]]
M[[m,n,o,p]]),{i,3},{j,3},{k,3},{l,3}]
Any ideas that could point me n the right direction would be greatly
appreciated.
Thanks,
Mark Storch