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MathGroup Archive 2006

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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: "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.
| 



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