[Axiom-developer] Re: conditionally defined functions

[Ralf HEMMECKE]

Hi Martin,

> As you might know, I'm experimenting with fixes of the following, superficially
> strange behaviour: 
>
>
> (1) -> (1/x)::UP(x, FRAC POLY INT)
>
>         1
>    (1)  -
>         x
>                     Type: UnivariatePolynomial(x,Fraction Polynomial Integer)

Hmm, when I simply type 1/x, I get:

        1
   (4)  -
        x
                             Type: Fraction Polynomial Integer

So coercing this into UP(x, FRAC POLY INT) is OK. It only looks a bit 
strange, because you might want to get an error message telling you that 
you cannot have x in the denominator.

I made the following experiment:

(5) -> X := monomial(1,1)$UP(x, FRAC POLY INT)
   (5)  x
          Type: UnivariatePolynomial(x,Fraction Polynomial Integer)
(8) -> inv X

        1
   (8)  -
        x
     Type: Fraction UnivariatePolynomial(x,Fraction Polynomial Integer)
(9) -> 1/X

        1
   (9)  -
        x
       Type: UnivariatePolynomial(x,Fraction Polynomial Integer)

That the types are different is really a bit strange.


If I posed the question:

Is UP(x, FRAC POLY INT) = FRAC POLY INT ?

What would you answer? I am not asking for equality of the domains in 
AXIOM, but rather what FRAC POLY INT is mathematically.

Ralf