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Simplification with subscripted variables and anonymous functions

• To: mathgroup at smc.vnet.net
• Subject: [mg81580] Simplification with subscripted variables and anonymous functions
• From: Rick Warfield <walrus2049 at gmail.com>
• Date: Fri, 28 Sep 2007 02:12:22 -0400 (EDT)

Hi,

This is probably a very basic question but I wasn't able to find an
answer in the archives.  I am trying to use Mathematica to combine and
simplify some sums, for example:

FullSimplify[ (Sum[Subscript[r, j], {j, 1, n}] - Sum[Subscript[r, k],
{k, 1, d}])^2, Element[d | n, Integers] && d < n ]

Is equivalent to

Sum[Subscript[r, m], {m, k+1, d}]

But Mathematica doesn't make the simplification.

A related problem I have is with expressions that use a variable as an
anonymous function, such as g in the following expression:

FullSimplify[g[p]*g[q], ForAll[{p, q}, g[p]*g[q] == 0]]

Should simplify to 0, but does not (of course I could also have
written this with subscripts, but that also doesn't work)

Thanks for your help!

• Follow-Ups:
  • Re: Simplification with subscripted variables and anonymous functions
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>