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Re: Curl

  • To: mathgroup at
  • Subject: [mg30652] Re: Curl
  • From: Jens-Peer Kuska <kuska at>
  • Date: Mon, 3 Sep 2001 20:32:27 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <9msos5$plr$>
  • Sender: owner-wri-mathgroup at


sorry for the delay -- a was on a conference.
It was not clear what do you wish.
For a n-dimesional vector field

CurlN[f_List, x_List] := 
  Module[{index, run, n = Length[x]}, 
    index = {Sequence @@ Table[Unique[], {n - 2}], k, j};
    run = {#, n} & /@ Drop[index, -2];
            x\[LeftDoubleBracket]k\[RightDoubleBracket]], {k, n}, {j,
      Evaluate[Sequence @@ run]]

Should work.
The sign is corrected by the order of k and j in index. Because the
definition is
\partial_{x_k} f_{j} k must be the first index in the index list.
I mixed up the post-notation in D[f_j,x_k] where k come on the second


Emilio Martin-Serrano Sobrino wrote:
> Hi,
> After the Jens-Peer's replay  to the Carlo Gabrieli's posting
>  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   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
> 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.
> Regards
> Emilio
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