Re: [Maxima-discuss] polynomials containing differential operators

[nijso b. <ni...@ho...>]

On Mon, 2016-10-17 at 14:52 -0700, Richard Fateman wrote:
> I haven't responded earlier, but this kind of calculation has been
> approached previously and probably in a variety of ways.
> I think the most successful way relies on defining new operators
> pretty much from top to bottom, and not relying on ^^ + . as built
> in.  I think that it eliminates what is essentially mathematical
> "punning".... e.g. is the number 1  a constant function always returning 
> 1 or is it an identity operator?
> is (D+1).x = D.x +x  or D.x +1.  Could be either.

Some systems use namespaces to avoid this confusion. When we load the
file (say) differentialPolynomial.max, we know (or should at least
expect) that definitions and behavior changes, and that we will be able
to deal with polynomials containing differential operators. We should
then expect the behavior (D+1).x = D.x + x = x.D + 1 + x 

Can you elaborate on your prefered approach? Also, do you have some
reference to a previous approach (in maxima/macsyma)? In this context, I
could only find your paper on computer algebra and operators (Fateman
and Grossman, nasa-cr-185396, 1989). 



Best regards,
Nijso Beishuizen