Let f(x1,...,xn) and g(x1,...,xn) be polynomials in n variables.
I'd like to define the operation f # g as follows: replace each xi
in f be the corresponding partial derivative operator d/dxi and then
apply the resulting differential operator f(d/dx1,...,d/dxn) to g.
How does one do that? I don't know if it is directly possible in Maxima.
At any rate, it might be possible to speed it up by writing it directly
in Lisp. I don't know how to do that and last time I tried to figure out
how to do so, which was some time ago, I think I ran into a problem about
the number of variables that a user defined function using lisp can have,
which I vaguely recall being 1. (Possibly I'm getting confused with REDUCE,
which I also tried to use.)
Another complication is that Maxima might get confused if some of the
coefficients are subject to let rules, such as some algebraic numbers,
and maybe not properly treated as constants by the differentiations.
--
Ignorantly,
Allan Adler
* Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions and
* comments do not reflect in any way on MIT. Also, I am nowhere near Boston.