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

*To*: mathgroup at smc.vnet.net*Subject*: [mg69559] Re: partials of Sum[x[i]^2, {i,1,n}] (e.g.)*From*: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>*Date*: Fri, 15 Sep 2006 06:46:06 -0400 (EDT)*Organization*: Uni Leipzig*References*: <eebfke$4d8$1@smc.vnet.net>

Hi, D[f[x[1],...,x[n]], x[k]] for f[x[1],...,x[n]] = Sum[x[i]^2, {i, 1, n}] is 2 x[k]*Sum[KroneckerDelta[k,i],{i,1,n}] and only for the case that 1<=k<=n you get your result, otherwise you get zero. Mathematica can programmed to do that simplification, but it will not do this automatical and if you need that the arguments of you summation will evaluated you should use your own symbol sum[], mySum[] ... and not Sum[] and than you has to do some programming anyway. Regards Jens "kj" <socyl at 987jk.com.invalid> schrieb im Newsbeitrag news:eebfke$4d8$1 at smc.vnet.net... | | | | 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. |