       Re: Simplification with subscripted variables and anonymous functions

• To: mathgroup at smc.vnet.net
• Subject: [mg81618] Re: Simplification with subscripted variables and anonymous functions
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 29 Sep 2007 02:32:42 -0400 (EDT)
• Organization: Uni Leipzig
• References: <fdi6cc\$rl8\$1@smc.vnet.net>

```Hi,

you missunderstand the role of Sum[]. Sum[] try to find a
closed expression for the summation and transform

Sum[1/r^i, {i, 1, Infinity}] to 1/(r-1)

but it makes *no* formal transformations when it
can't find such a closed form. The reason is, that
such a transformation can destroy the convergence of the
Sum[]. You have to wrote your own rules
for the transformations of the sum.

FullSimplify[g[p]*g[q], g[p]*g[q] == 0]

work as expected.

Regards
Jens

Rick Warfield wrote:
> 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)
>