Re: Differentiating sums
- To: mathgroup at smc.vnet.net
- Subject: [mg63814] Re: [mg63770] Differentiating sums
- From: Pratik Desai <pdesai1 at umbc.edu>
- Date: Sun, 15 Jan 2006 05:43:27 -0500 (EST)
- References: <200601140732.CAA00260@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Zvi Tarem wrote:
>How can I use Mathematica to represent sums in a way that can be
>differentiated correctly? Here is a trivial example:
>
>If x and y are both vectors of length N then the derivative of the product
>of the vectors with respect to any element x[i] is simply y[i]. I cannot
>make Mathematica 'understand' the concept of indexing. Here is what I tried:
>
>prod = Sum[x[i] y[i], {i, N}]
>D[prod, x[j]]
>I get 0
>
>D[prod, x[i]]
>I get Sum[y[i],{i,N}] which is wrong.
>
>
I don't think that is wrong. I am no mathematician, but I have used
Fourier Series /ad nauseam /and this is what is called as Term by Term
Differentiation. I am not quite sure mathematica understands what you
mean when you say you want to differentiate with respect to x[i]?, I
think mathematica thinks that this applies to all x[i]'s. If you want
to differentiate with particular x[i]'s then, I think, you must give a
finite N. Maybe something like this
In[90]:=
Clear[x,y,prod]
prod[N_,j_,var_]:= D[Sum[Subscript[x,i]*Subscript[y,i], {i,
N}],Subscript[var,j]]
prod[10,2,y]
Out[92]=
\!\(x\_2\)
Hope this helps
Pratik
>The same for subscript notation.
>
>Then I tried Array[] and Part[], but they require constants as the limit and
>selectors.
>
>Can anyone help?
>
>
>
>
- References:
- Differentiating sums
- From: "Zvi Tarem" <zvi.tarem@cern.ch>
- Differentiating sums