Splitting sums in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg126817] Splitting sums in mathematica*From*: jimbo <james.a.gordon1 at googlemail.com>*Date*: Sat, 9 Jun 2012 03:08:02 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

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 Thanks in advance James