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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: [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


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