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MathGroup Archive 1994

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Re: Summation convention

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg222] Re: [mg204] Summation convention
  • From: Richard Mercer <richard at rmercer.wright.edu>
  • Date: Wed, 23 Nov 1994 12:34:10 -0500

>  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!),
>  

>  Thanks, Stephen
>  

If I understand your question correctly, you will find the Unique
command useful, e.g.

Unique["y"]

will generate a variable of the form yn where n is an integer,
and yn has not been used IN THIS SESSION.

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Richard Mercer                             513-873-2191 office
Department of Mathematics and Statistics   513-873-2785 message
Wright State University                    513-429-2179 fax
Dayton, OH 45435                           NeXTmail welcome!
richard at rmercer.wright.edu        or       rmercer at desire.wright.edu
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