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Re: Almost symbolic computations (?)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90499] Re: Almost symbolic computations (?)
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 11 Jul 2008 02:02:13 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g54oim$etu$1@smc.vnet.net>

Barbara Da Vinci wrote:

> This is an example of the problem
> I'm facing.
> 
> The code
> 
>    Needs["VectorAnalysis`"];
>    Head /@ {ax, ay, az}
>    A = {ax, ay, az};
>      Curl[A]
> 
> returns
> 
> {Symbol, Symbol, Symbol}
> {0, 0, 0}
> 
> Instead, I would get the
> well known symbolic form
> 
> d_y az - d_z ay
> ....
> 
> I have been trying, for
> a while, to perform string
> manipulations but that,
> of course, lays to ashes
> the possibility to recognize
> 
> d_y az + d_y az = 2 d_y az
> 
> and so on.
> 
> Any way to get out of it ?

Not sure whether this is what you are looking for:

     Needs["VectorAnalysis`"]

     (* Return the name of the current coordinate system. *)
     CoordinateSystem[]

     (* Return the default symbol names for the coordinates. *)
     Coordinates[]

     (* In Cartesian coordinates, Curl expects to be fed by a
        list of functions that represent the components on the
        x-, y-, and z-axes of a vector field. *)
     Curl[{f[Xx, Yy, Zz], g[Xx, Yy, Zz], h[Xx, Yy, Zz]}]


     Cartesian[]

     {Xx, Yy, Zz}

        (0,0,1)                (0,1,0)
     {-g       [Xx, Yy, Zz] + h       [Xx, Yy, Zz],

        (0,0,1)                (1,0,0)
       f       [Xx, Yy, Zz] - h       [Xx, Yy, Zz],

         (0,1,0)                (1,0,0)
       -f       [Xx, Yy, Zz] + g       [Xx, Yy, Zz]}


HTH,
-- Jean-Marc


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