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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