[Axiom-math] Re: [fricas-devel] Re: [open-axiom-devel] [fricas-devel] Re: iterators and cartesian product.

[Gabriel Dos Reis]

On Mon, 22 Oct 2007, Bill Page wrote:

| What I call 'Product' you can call 'Cross', I have no problem with the
| name. If you want 'Cross' to have a signature like:

I believe Cross has a good pedigree in the Axiom family.

|   Cross(x:List Type): with ... appropriate access operations
| 
| that is fine. But still you would not be able to write:
| 
|   Cross [1..9,1..4]

Yes, but why would I have to write that what would be the meaning?

Again, I'm not saying it is bad.  I'm after the semantics.

I can (mathematically) explain that

    cross [l1, l2]

computes the a sequence listing of the elements of the cross product
of the sequence l1 and l2.

I can (mathematically) explain that

    cross [Integer, Float]

returns the cross product of Integer by Float.

How do you matematically explain that, 1..9 is a domain, and still I
can write

      for i in 1..9 repeat
         -- ...

and I do not get a type error?


Again, I'm after the semantics.

-- Gaby