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 > > > ========================================================================= > ===== > > "If you can't explain your research to your grandmother, then you > don't understand it yourself" > > Richard Feynman > > > "Update your bumper stickers, kids: Mac OS 8 = Windows 2010" > > David Pogue > > ========================================================================= > ===== > > Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/