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! > >