partials of Sum[x[i]^2, {i,1,n}] (e.g.)

*To*: mathgroup at smc.vnet.net*Subject*: [mg69520] partials of Sum[x[i]^2, {i,1,n}] (e.g.)*From*: kj <socyl at 987jk.com.invalid>*Date*: Thu, 14 Sep 2006 06:57:04 -0400 (EDT)

In symbolic manipulations, one often needs to leave some of the limits of an expression in symbolic form. E.g. the n in: f[x[1],...,x[n]] = Sum[x[i]^2, {i, 1, n}], (where I've used Mathematica notation loosely). Then one often finds derivations like D[f[x[1],...,x[n]], x[k]] = 2 x[k], for all k in { 1,..., n } Is it possible to do something like this in Mathematica? More generally, can Mathematica fully understand expressions with symbolic limits? Basically, I have a slightly hairier expression that I want to take the partials of, set them all equal to zero to produce a system of n equations. If that weren't enough, I'd like to solve this system of n equations using Mathematica. This kind of manipulation is far more difficult, as far as symbolic math goes, than anything I've seen Mathematica do yet, because it requires Mathematica to understand the notion of an array with a "symbolic cardinality", but I thought I'd ask. Thanks! kj -- NOTE: In my address everything before the first period is backwards; and the last period, and everything after it, should be discarded.