DMP([x], DMP([x], Integer)) (was Re: [Axiom-developer] about Expression Integer)

[Ralf Hemmecke]

> > Part of the reason for the confusion, I think, is because the common
> > OutputForm for polynomials does not typographically identify polynomial
> > variables versus coefficients. But if, say the polynomial variables were
> > always printed in bold face roman type but the coefficients were printed in
> > italic, it might be more clear what is going on.
>
> I think that this is a very nice idee. I guess this could be even realized on
> text terminals, couldn't it?

I hope nobody is constructing something like

DMP([x], DMP([x], DMP([x], Integer)))

What are the possible typefaces of x?

Ufff... what's that???

P := DMP([x], DMP([x], Integer))
a:P := x
   DistributedMultivariatePolynomial([x],
      DistributedMultivariatePolynomial([x],Integer)) is not a valid
      type.

Why would Axiom forbid P and allow
Q := DMP([x], Polynomial Integer)
b:Q := x
   (6)  x
     Type: DistributedMultivariatePolynomial([x],Polynomial Integer)

???

And why is that???

(15) -> R := Polynomial Polynomial Integer

   (15)  Polynomial Polynomial Integer
                                                                 Type:
Domain
(16) -> c: R := x

   Polynomial Polynomial Integer is not a valid type.

Yes, now I do my homework and look into the sources of DMP.
Well, my understanding of SPAD is a bit limited, but DMP builds on
GeneralDistributedMultivariatePolynomial (GDMP) and I cannot find
anything that looks like aborting the domain instantiation.

So let's do the following...
Copy the code from DistributedMultivariatePolynomial and just rename the
domain.

--begin aaa.spad
)abbrev domain RHX RHXPolynomial

RHXPolynomial(vl,R): public == private where
  vl : List Symbol
  R  : Ring
  E   ==> DirectProduct(#vl,NonNegativeInteger)
  OV  ==> OrderedVariableList(vl)
  public == PolynomialCategory(R,E,OV) with
      reorder: (%,List Integer) -> %
  private ==
    GeneralDistributedMultivariatePolynomial(vl,R,E)
--end aaa.spad

Then say
)compile aaa.spad
P := RHX([x], RHX([x], Integer))
a:P := x

   (2)  x
        Type: RHXPolynomial([x],RHXPolynomial([x],Integer))

Hmm, just by renaming of DMP to RHX I get a different behaviour?
This tells me that I don't have to look into the Algebra sources to find
why DMP([x], DMP([x], Integer)) is not a valid type. :-(

I hope at some point you agree with me that the interpreter or whoever
forbids to construct DMP([x], DMP([x], Integer)) ) should NOT add
knowledge that is not derivable from the SPAD code in Algebra.

Ralf