Re: [Axiom-developer] Axiom Design Question / Polymake feedback

[Ralf Hemmecke]

> )abbrev domain POLYTOPE Polytope
> Polytope(R: Ring): Exports == Implementation where
>     Exports == with
> ------------------------------------------------------------
> --               polytope constructions 
         > ------------------------------------------------------------
>       cube: Integer -> %
>       if R is Float then randSphere: (Integer, Integer) -> %
>       vertices: % -> Matrix R

> However, I'm not convinced that this is the best solution. One reason
> being, that I don't really want that the user has to specify the type
> of his polytope all the time.

If you don't like it and you can somehow determine the type of R 
automatically, and it is something simple like Integer then why not writing

Polytope(): Exports == Implementation where
    Exports == with
      vertices: % -> (R: Ring, Matrix R);
      ...

That should work in Axiom (+ dependent types).

By the way, is there a reason for constructing a nullary function 
Polytop() instead of just the constant Polytope? (Sorry, I have not 
looked at polymake.)

Ralf