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MathGroup Archive 2004

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Re: Sum question and general comment

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50761] Re: Sum question and general comment
  • From: Janusz Kawczak <jkawczak at math.uncc.edu>
  • Date: Sun, 19 Sep 2004 21:39:17 -0400 (EDT)
  • References: <ci8m99$bpg$1@smc.vnet.net> <ci9b6c$i4n$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Paul,

this is neat, but I cannot reproduce your results. For the first sum
I am getting 5/(i-2) and other will not evaluate at all. What am I
missing?

Janusz.

Paul Abbott wrote:

> In article <ci8m99$bpg$1 at smc.vnet.net>,
>  Steve Gray <stevebg at adelphia.net> 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.,
>
> There is a way to do this (posted to MathGroup in February this year):
> use the Notation package to define your own input notation that accepts
> a lower limit of the form, say i != 1 = p. See
>
>    http://physics.uwa.edu.au/pub/Mathematica/MathGroup/TestSumIterator.nb
>
> > or Sum over values belonging to a list, such as
> > "Sum over i (belonging to) {1,2,3,5,7,8,21}", etc.,
>
> In this case, the most natural operation is to use Map. It is not too
> hard to implement your own notation for this using Element.
>
> > "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.
>
> No matter what notation you define, internally the computation will
> likely have to use constructs such as this. The point is that you would
> like Mathematica to form these constructs automatically and, most
> likely, hide them from view.
>
> > * 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.
>
> Personally, I think the Notation package is a tremendous step in this
> direction.
>
> > Part of the answer would be a greatly expanded index, compiled knowing what
> > terms people are likely to use for their questions.
>
> Uniform notation (or notation conversion is required) also.
>
> Cheers,
> Paul
>
> --
> Paul Abbott                                   Phone: +61 8 9380 2734
> School of Physics, M013                         Fax: +61 8 9380 1014
> The University of Western Australia      (CRICOS Provider No 00126G)
> 35 Stirling Highway
> Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
> AUSTRALIA                            http://physics.uwa.edu.au/~paul


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