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Summation convention

  • To: mathgroup at
  • Subject: [mg204] Summation convention
  • From: corcoran (Stephen Corcoran) <corcoran%markov.stats at>
  • Date: Sat, 19 Nov 1994 14:50:11 +0000

Dear Mathgroupers,

I wonder if you could help me,

I need to set up a rule of the following form,

rule = {b[a[x_]] -> d[a[y],a[x]] c[a[y]]},

where a[y] must differ from all other indices a[k] used so far.
My application involves expressions involving use of the summation
convention which I would like to manipulate using Mma.  Thus, in "rule"
given above, the RHS is interpreted as being summed over the index a[y].
I need to ensure that, in any given complicated expression,
that if 

e = b[a[1]] b[a[2]]

and each b[a[j]] (j=1,2) is to be replaced by a term involving summation using
the above "rule", that the indices using in each summation are different.  One 
thing I thought of involved incrementing the summation index y in "rule" each 
time I used it, but this would not work as if I write

f = e /. rule

"rule" is applied twice before I have a chance to increment y.

Any suggestions?
(I am actually away for the next week, but I look forward to reading
email on my return!),


Stephen Corcoran,		email:	corcoran at (internet)
Dept. of Statistics,			corcoran at (janet)
University of Oxford,
1, South Parks Road		phone:  (0865) 272879
OXFORD, OX1 3TG			fax:	(0865) 272595

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