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Matrix/tensor algebra shortcuts?

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  • Subject: [mg119615] Matrix/tensor algebra shortcuts?
  • From: Hauke Reddmann <fc3a501 at>
  • Date: Mon, 13 Jun 2011 05:18:16 -0400 (EDT)

Two questions. My tensors are very sparse, in fact if
it has e.g. two upper and one lower index T_ab_c, then
the only nonzero elements have a+b=c. (This is general,
always sum of upper=sum of lower.) Clearly, if I could
avoid carrying through all the zeroes I could save
a factor n (and already at dimension n=10 Mathematica
chokes on time and space ressources for my problems). 
Do you have a more elegant way than throwing all Outer[] 
and Dot[] and so on out of the window and programming 
everything with Do[] loops?
Another thing. Sometimes I don't even want to specify
the matrices and just need a formal noncommutative 
multiplication "knowing" that Z°(l*(Y+W))°(X*m)=
l*m*Z°Y°X+l*m*Z°W°X (where of course ° is some matrix
multiplication sign, * is normal scalar multiplication,
and scalar, distributive and associative properties
should be executed latest on an Expand[] command. 
How can I define me a ° with these properties?
Please answer n00b-friendly. :-)
Hauke Reddmann <:-EX8    fc3a501 at
Leierklang und ein flammendes Inferno grüßen dich
auf das Allerzärtlichste

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