Re: [Axiom-developer] about Expression Integer

[Martin Rubey]

Dear Bill, Ralf, *

I'm currently out of time. But I'm a little afraid of the direction the
discussion takes currently.

I believe that the intension of a constructor like DMP is to cover
*polynomials*.

If we allow (2*x+1/x)::DMP([x], EXPR INT), i.e., allowing 1/x as a coefficient,
then it must be clear that the "x" in 1/x is something different than the "x"
in 2*x. Otherwise we don't get a polynomial, obviously.

So, I think that

> > P := DMP([x,y], EXPR INT) 
> > a :P := x 
> > b := a/x 
> > 
> > differentiate(b,x)                    -- 1/x
> 
> (4) -> differentiate(b,x)
> 
>         1
>    (4)  -
>         x
>    Type: DistributedMultivariatePolynomial([x,y],Expression Integer)
> 
> I think this result should be classed a bug. The 'differentiate'
> operation apparently makes some incorrect assumptions about the
> coefficient domain. I think the result should be the same as:

is not a bug. If you want to have axiom output 0, then I imagine that you will
get into trouble with writing packages, variable capture might well occur.

I'd rather say that b::EXPR INT giving one is troublesome. I wouldn't really
classify it as a bug though, given the nature of EXPR INT. Note that b::UP([x],
INT) or b::POLY INT give errors!

PLEASE don't change the behaviour of DMP and company. What should be documented
(and I think Ralf did, but I hadn't time) is that domains like POLY EXPR INT
and friends can lead to "surprising" results. This should go into the section
"types" of the axiom book.

Martin