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
>