       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

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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