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MathGroup Archive 2004

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Re: Sum question and general comment

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50664] Re: Sum question and general comment
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 15 Sep 2004 07:54:42 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <ci8m99$bpg$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

atleast fir the Sum[] over i (belonging to) {1,2,3,5,7,8,21}
I have a possible solution

Unprotect[Sum]

Sum[expr_, {i_, indexlist_List}] :=
  Plus @@ ( (expr /. i -> #) & /@ indexlist)

Protect[Sum]

The first case "Sum over i=1 to 100 except i!= 23 and 36"
can be done if you create a list and remove the indicies
that you don't need.

For the last case with the double sum and  i!=j I
would use (1-KroneckerDelta[i,j]) because that is a
very common notation.

Regards
  Jens


Steve Gray wrote:
> 
> I don't want to overload the group with my questions, so I only post after
> not being able to find the answer in the Help or at the site. Part of the
> problem of course is that it isn't clear how to state the question so that
> I can look it up*. Anyway, the current question has to do with Sum and
> similar "indexed" operations:
> 
> I find no way to do, for example,
> "Sum over i=1 to 100 except i!= 23 and 36", etc., or Sum over values belonging to a list, such as
> "Sum over i (belonging to) {1,2,3,5,7,8,21}", etc., or
> "Sum ( i=1 to 10) Sum (0ver j=1 to 10 but j !=i)", etc. (this can be awkwardly done with j=1 to i-1
> and j=i+1 to 10)
> In some cases there can be workarounds using things like
> (1- KroneckerDelta[i,j]), etc., but these can get complicated and obscure.
> I would have thought that Mathematica could do operations like these directly,
> but ??. Thank you for any information.
> 
> Steve Gray
> 
> * Someone who makes major progress on the problem of letting users communicate with a computer in
> ordinary, appropriate technical "people" language will have big success. Currently in almost all
> software one must ask using exactly the right terms. (I realize that Microsoft and others are trying
> to make progress here, but it's negligible so far in my opinion.) Part of the answer would be a
> greatly expanded index, compiled knowing what terms people are likely to use for their questions.


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