Re: Symbolic Curl

• To: mathgroup at smc.vnet.net
• Subject: [mg8555] Re: [mg8532] Symbolic Curl
• From: seanross at worldnet.att.net
• Date: Sat, 6 Sep 1997 23:16:20 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Gary L. Hennigan wrote:
>
> I'm VERY new to mathematica and, unfortunately, it's a site license
> and I'm without a manual. Also pertinent is that I'm using v2.2 NOT
> v3. I'd like to use Mathematica to do some symbolic manipulation for
> me. Something like:
>
>         ans = Curl(v1) Dot Curl(v2)
>
> and get the answer back as the sum of partial derivatives of
> components of v1 and v2 with respect to the Cartesian coordinates. Can
> Mathematica do this?
>
> For example, using the "@" as a partial derivative symbol, Curl[v],
> with
>
>         v={v_x, v_y, v_z}
>
> would result in:
>
>         {(@v_z/@y- at v_y/@z), -(@v_y/@x- at v_x/@y), (@v_y/@x- at v_x/@y)}
>
> I'm new to Mathematica but I did manage to find the VectorAnalysis and
> LinearAlgebra packages. Unfortunately, VectorAnalysis seems to want
> functions of x,y,z for components in order to evaluate Curl[v]. In
> other words, with "v" defined as above I'd get the result {0, 0, 0}.
>
> LinearAlgebra doesn't seem to have the Curl operator.
>
> Last question is should I order the \$50 Mathematica v3.0 manual?
> Again, I'm stuck using what we have, which is v2.2 and don't relish
> the thought of shelling out \$50 for a manual that's useless to me.
>
> Thanks,
> Gary Hennigan

#1- the package Calculus`VectorAnalysis` has Div, Grad and Curl.  Be
aware, though, that there are subtleties at play whenever you get out of
cartesian coordinate systems, so be careful.

#2- If the Hold or HoldAll attribute is not built in to the Div Grad or
Curl, you could define a "pseudo Del" operator like {dx,dy,dz} and then
work out the various combinations yourself.

#3- Some of the items in the 3.0 manual don't apply to version 2.2, but
those items are marked.  A 3.0 manual would certainly be way better than
no manual.  I recommend it.

```

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