MathGroup Archive 2001

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RE: Curl

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


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];
     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
for the minus sign in "(-)epsilon". The lack of this minus sign in CurlN
generates an inverted pattern of signs in the results I got in my tests.

I would appreciate any comment on this.



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