Re: Splitting sums in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg126818] Re: Splitting sums in mathematica
• From: Ray Koopman <koopman at sfu.ca>
• Date: Sun, 10 Jun 2012 02:14:18 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jqusrg\$rnm\$1@smc.vnet.net>

```On Jun 9, 12:09 am, jimbo <james.a.gord... at googlemail.com> wrote:
> Hello,
>
> Does anyone know of a way to algebraically split sums (if that is the
> correct name for it) in mathematica? I need to do the following (and
> higher-order versions of the same)...
>
> Sum_over_p [  Sum_over_q (  a_p * a_q  )   ] = Sum_over_p_equal_q
> (a_p^2) + Sum_over_p_not_equal_q (a_p*a_q)
>
> ...in other words, turn a nested sum running over two indices into two
> sum, one for when the indices are equal, and one for when they are
> different?
>
> I then need to make some substitutions once there are no nested sums
> and simplify my answer. I have an equation with many hundreds of terms
> in it, so doing it by hand is not an option. I can send a typeset
> example if anyone needs clarification
>
> I have version 5.2 for students
>
>
> James

Let a = {a1,a2,...}. Then a.a gives the sum of the terms with p == q,
and 2*Dot@@Transpose@Subsets[a,{2}] gives the sum of the terms with
p != q.

```

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