RE: Curl

• To: mathgroup at smc.vnet.net
• Subject: [mg30645] RE: [mg30457] Curl
• From: "Emilio Martin-Serrano Sobrino" <emilio.martin at sema.es>
• Date: Sun, 2 Sep 2001 03:58:52 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

After the Jens-Peer's replay [mg30470] to the Carlo Gabrieli's posting
[mg30457] on (Generalize) Curl, I tried the Jens's implementation without
success and asked the group for valid examples. Since I did not get any
answer, I insisted myself by introducing some minor modifications into the
Jens's code. You can see the modifications by comparing both programs CurlN
(in the  [mg30457] posting) and CurlN1 in this one.

The fact is that I could not put CurlN to work and that my modification
(CurlN1) works well for the example below (for n==3) as you can easily see.

In[1]:= epsilon[index__Integer] := Signature[{index}]
dpos[i_,n_]:= Table[If[k==i,1,0],{k,n}]

CurlN1[f_List, x_List, n_Integer] :=
Module[{index, run},
index = {Sequence @@ Table[Unique[], {n - 2}], j, k};
run = {#, n} & /@ Drop[index, -2];
Table[
Sum[(-epsilon[Sequence @@ index]) D[f[[j]],x[[k]]] dpos[j, n], {j, n},
{k, n}],
Evaluate[Sequence @@ run]
]]
In[2]:= curl=CurlN1[{x z^3,-2x^2 y z, 2y z^4},{x,y,z},3]

In[3]:= Apply[Plus,#]&/@curl
.

Any way, I could not check whether CurlN and CurlN1 are semantically
equivalents or not. But It seems that there is some semantic difference, as
generates an inverted pattern of signs in the results I got in my tests.

I would appreciate any comment on this.

Regards

Emilio

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```

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