       Functional differentiation on lattice

• To: mathgroup at smc.vnet.net
• Subject: [mg39759] Functional differentiation on lattice
• From: Norbert Nemec <nobbi_at_theorie3.physik.uni-erlangen.de at NOSPAM.COM>
• Date: Thu, 6 Mar 2003 02:35:38 -0500 (EST)
• Organization: University of Erlangen, Germany
• Sender: owner-wri-mathgroup at wolfram.com

```Hi there,

I've just recently decided that the maths I have to do at the moment really
demand the use of a CAS. I'm absolutely new to Mathematica, but the problem
I have is probably a bit hard to get moving on. Perhaps someone can give me
a simple solution to start out on?

What I need to do could probably be called a "Functional differentiation on
a lattice". To give one very simply example:

I have the functional

S[A] := sum_x (A(x+1)-A(x))^2

(where x is integer - in my case there are periodic boundaries, but that
does not matter at that point)

now I want to calculate

dS/dA(y)

which should result in

- 2(A(y+1)-A(y)) + 2(A(y)-A(y-1))

or simplified

-2A(y+1) + 4A(y) - 2A(y-1)

Lateron, the whole thing will get 4-dimensional and A will get indices that
will be summed over as well.

Is there a simple way to do that in Mathematica? I would really appreciate a
piece of code to get me started on.

Thanks,
Nobbi

```

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