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

*To*: mathgroup at smc.vnet.net*Subject*: [mg69544] Re: partials of Sum[x[i]^2, {i,1,n}] (e.g.)*From*: dh <dh at metrohm.ch>*Date*: Fri, 15 Sep 2006 06:45:09 -0400 (EDT)*References*: <eebfke$4d8$1@smc.vnet.net>

Ji, for this kind of things, Mathematica has the pattern: __ meaning at least one, or ___ meaning zero or one. Daniel kj wrote: > 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