Re: [Axiom-developer] about Expression Integer

[Ralf Hemmecke]

> > Martin Rubey wrote: 
> > > I could imagine that some innocent looking computation
> > > would not be correct in the situation above. 
> > As Martin I already imagine this error :
> >
> > 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:
>
> (5) -> differentiate(b::EXPR INT,x)::P
>
>    (5)  0
>    Type: DistributedMultivariatePolynomial([x,y],Expression Integer)

Well, Bill, imagine you had to programm DistributedMultivariatePolynomial.
In gdpoly.spad we see

      differentiate(p: %,v: OV) ==
            multivariate(differentiate(univariate(p,v)),v)

where univariate just converts p to an element of
SparseUnivariatePolynomial(%). (BTW, that's already a trick!)
However, it seems the most obvious thing to do.

Now you suggest to do that differently, since the coefficients of that 
univariate polynomial might also contain the variable x. Well, would be 
possible, but obviously the designer of DMP (or rather GDMP) did not 
think of such a strange thing like having the same variable as the 
indeterminate of the polynomial and at the same time in the domain of 
coefficients.

Still, it's a bug, because that behaviour should at least be very vell 
documented. It is, however, not so clear where to do this. I suggest 
there should be a note in DMP rather than the category 
PartialDifferentialRing (where the signature comes from).

Ralf