       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,...,x[n]], x[k]]

for

f[x,...,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,...,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,...,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,