Re: [Axiom-developer] about Expression Integer

[Ralf Hemmecke]

> > 1/ Can I (or cannot) remain Expressions as 
> >
> > x+1/(y+1)             
> > y+1/(x+1)             
> >
> > and do not have a single denominator.

Unfortunately, I have no idea, how to do this. :-(

But, I'd like to warn you. Don't follow Bill's suggestion.

> There are however more complex domains which do include
> expressions of the same form as you wrote above. The interpreter
> is not able to find these automatically, but you can help by
> specifying more exactly what you want. In the compiler you must
> always provide this additional information. For example:
>
> (2) -> (x+1/(y+1))$DMP([x,y],EXPR INT)
>
>               1
>    (2)  x + -----
>             y + 1
>    Type: DistributedMultivariatePolynomial([x,y],Expression Integer)

> In this case your expression is a member of the specified domain and
> no conversion is necessary, but notice that the 2nd term is a monomial
> of degree 0 since this domain has coefficients that can be expressions.
> You might consider this result ambiguous since the entire expression
> could be consider a term degree 0, but apparently the domain DMP
> attempts construct a polynomial of highest degree? To know for sure
> we would probably have to consult the source code for DMP.

Right. In order to know what will happen, a user would have to consult
the source code. That's completely unsatisfactory.

Even more, I think the interpreter should forbid to construct things
like DistributedMultivariatePolynomial([x,y],Expression Integer).

Take, for example (axiom--main--1--patch-47)

P := DistributedMultivariatePolynomial([x,y],Expression Integer)
a: P := x
degree a

Are you sure that you expected

[1,0]
      Type: DirectProduct(2,NonNegativeInteger)

as output, given the fact that x is an element of the coefficient domain?

Now, it is totally clear that

degree(a/x)

also gives

[1,0]
      Type: DirectProduct(2,NonNegativeInteger)

since

a/x

        1
   (5)  - x
        x
  Type: DistributedMultivariatePolynomial([x,y],Expression Integer)

yields also a completely correct output. ;-) However, I guess, most
people find this confusing.

Ralf