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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: "JensPeer Kuska" <kuska at informatik.unileipzig.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.

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