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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>
*Reply-to*: kuska at informatik.uni-leipzig.de
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.
In your second example
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)
>
> Thanks for your help!
>
>
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