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Re: Curl

• To: mathgroup at smc.vnet.net
• Subject: [mg30475] Re: [mg30457] Curl
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Thu, 23 Aug 2001 02:15:39 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

The problem here is not one of Mathematica implementation but of 
mathematical definition. Since curl is normally defined as a vector 
product (cross product) of the gradient operator and a vector field and 
since the cross product of two vectors is defined only in three 
dimensions (you need (n-1) vectors in n-dimensions) it is far from clear 
what such a generalization should be. First tell us what curl in 
n-dimensional euclidean space is and then someone will surely supply a 
Mathematica implementation.

On Wednesday, August 22, 2001, at 02:41  PM, Carlo Gabrieli wrote:

> Hi,
> I found on Roman Maeder "Computer Science with Mathematica" elegant
> implementations of Grad, Div, Laplacian, Jacobian but not of Curl. I
> know that the Mathematica package VectorAnalysis has a Curl function
> but I'd like to learn how to implement a Curl function for an
> arbitrary number of Cartesian coordinates
>
> Thanks in advance to all
> Best Regards
> Carlo Gabrieli
> snail mail: Carlo Gabrieli
> Via San Giovanni d'Acri 15
> 30126 Lido di Venezia (VE)
> Tel.& FAX: 011-39-41-5264157
>
> e-mail: gabrieli at iuav.it
> gabrieli at flux.isdgm.ve.cnr.it
> gabrielic at libero.it
> gabrielic at inwind.it
>
> web pages: http://www.omitech.it/MERLIN/conn.htm
>
>
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Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/