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MathGroup Archive 2007

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Re: Differentiation w.r.t. elements of lists

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79712] Re: Differentiation w.r.t. elements of lists
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 2 Aug 2007 03:54:58 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <f8pi48$1l4$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

and you are shure that

 > Another, even shorter test case would be
 >
 > D[x[[i]], x[[j]]]
 >
 > which "should", IMHO, return KroneckerDelta[i,j].

??

Than
D[x[[1]],x[[2]]]

should be zero ? right ?? but what is

with

x = {Sin[y], y}

D[x[[1]], x[[2]]]

the result is not 0 ..

may be that you are wrong.

Regards
   Jens

Daniel Hornung wrote:
> Hello,
> I don't know if what I want to do is impossible to do neatly (probably not)
> or whether I simply chose the wrong way (maybe).
> 
> Basically I want to do componentwise differentiation.  Here's a short test
> case:
> ----
> In[1] := h[x_]:=Sum[x[[j]]^2,{j,1,Length[x]}]
> 
> In[2] := dh[x_,i_]=D[h[x],x[[i]]]
>>From In[2]:=
> Part::pspec: Part specification i is neither an integer nor a list of 
> integers. Mehr...
> Out[2]= 0
> 
> In[3]:= Assuming[i\[Element]Integers&&i>0&&i<=n,dh[x_,i_]=D[h[x],x[[i]]]]
>>From In[3]:=
> Part::pspec: Part specification i is neither an integer nor a list of 
> integers. Mehr...
> Out[3]= 0
> ----
> 
> What I would want is a result like dh[x_,i_]=2x[[i]], of course.
> 
> Another, even shorter test case would be 
> 
> D[x[[i]], x[[j]]]
> 
> which "should", IMHO, return KroneckerDelta[i,j].
> 
> Any ideas or hints how to solve these problems in a nice way?
> 
> Thank you in advance,
> Daniel Hornung
> 


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