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MathGroup Archive 2005

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Re: Simple Sum does not simplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55490] Re: [mg55472] Simple Sum does not simplify
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sat, 26 Mar 2005 02:39:21 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Alix,

I think that Mathematica would definitely benefit by having a good sum
manipulation package (or maybe it has one that I don't know about?).

In any case, the following, which takes a little work, will simplify your
expression.

Sum[n*a[i] - Sum[a[j], {j, 1, n}], {i, 1, n}];
% /. HoldPattern[Sum[(a_) - Sum[b_, iter2_],
     iter1_]] :> Sum[a, iter1] - Sum[b, iter1, iter2]
% /. HoldPattern[Sum[x_ /; FreeQ[x, n], p___,
     {_, 1, n}, q___]] :> Sum[n*x, p, q]
% /. j -> i

Sum[n*a[i], {i, 1, n}] - Sum[a[j], {i, 1, n},
   {j, 1, n}]
Sum[n*a[i], {i, 1, n}] - Sum[n*a[j], {j, 1, n}]
0

It is quite often the case with Mathematica (or any CAS) that you will have
to write a set of rules or definitions to handle the area of mathematics you
are dealing with - even if that area seems to you to be very common. If
Mathematica had every possible useful relation it would end up with millions
of commands.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/




From: Alix [mailto:ali_tofigh at hotmail.com]
To: mathgroup at smc.vnet.net


Here is a simple symbolic sum:

Sum[n a[i] - Sum[a[j], {j, n}], {i, n}]

This should simplify to 0, but it doesn't. Why and is there a way to
get mathematica to work with these kind of sums? I'm using mathematica
5.0.




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