Martin was kind enough to answer some of my questions in a newsgroup, and to
direct me towards Maxima, and thereby here.
I need to work with vector & tensor (dyad) derivatives (grad, div, curl,
tensor div) abstractly. I don't want the CAS program to try to evaluate the
derivative itself, rather it should be left as an operator. Thereby
something like
DECLARE([u,v],nonscalar);
VECTORSIMP(CURL(v ~ u));
should return something akin to
u*div(v)-v*div(u)+(v dot del)u-(u dot del)v
We have been discussing some elementary forms related to my larger problem;
baby steps are always a good idea. But, to put my problem into perspective,
I'll state it here.
I am looking for an alternate form of the expression on the LHS. The first
term on the RHS is an educated guess (and may well be quite wrong), and
I would like to see how it pans out. I need to figure out exactly what
those
other terms are.
curl ( u dot vv ) = u cross div (vv) + other terms...
Where (vv) is the tensor dyad formed from the arbitrary vector (v); and (u)
is a vector such that div(u)=0 and curl(u)=0.
I have just downloaded 5.9.0 binaries, and have poked around a bit, but like
Martin, I have not been able to make much progress following what vect.mac
and vector.mac from CVS would suggest.
Thanks for your time and any suggestions,
Rob McDonald
> I couldn't reproduce the desired equation using the (patched) vect.mac.
> However I don't know ANYTHING about this stuff...
>
> Martin
>
> > From: "Rob McDonald" <robm at asdl>
> > Subject: Re: Different sort of CAS problem
> > Newsgroups: sci.math.symbolic
> > Date: Wed, 5 Mar 2003 15:18:20 -0500
> > Organization: Georgia Institute of Technology
> >
> > Can maxima do this with vector field entities?
> >
> > For example, if u and v are vector fields, how will maxima handle
> >
> > curl(v cross u)
> >
> > if it can return something like
> >
> > u*div(v)-v*div(u)+(v dot del)u-(u dot del)v
> >
> > and similar expressions for
> >
> > divergence(v cross u)
> > grad(v dot u)
> >
> > I would jump to it in a heartbeat...
> >
> > Rob
> >