[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:

| > | > | We want to be able to write:
| > | > |
| > | > |   DirectProduct(4,1..9)
| > | > |
| > | > | but this does not work because '1..9' is not a type - it is an object
| > | > | of 'Segment PositiveInteger'.
| > | >
| > | > If it worked, what would you have liked the mathematical meaning to
| > | > be, and why?
| > | >
| > |
| > | I would like the result to be a finite domain.
| >
| > that says what property the result would have, but it does not tell me
| > what the meaning of the result is.  I would like to underdstand
| > the mathematical meaning.
| >
| 
| I think the concept of an interval (segment) on the domain Integer is
| a fairly well-defined concept, no?

The notion of interval domain is well-understood.  But, the algebra you
presented in not one of the well-understood algebra I can link to.
So, I would appreciate your effort in elaborating on what you have ini mind.

The Segment (and UniversalSegment) domain is already in the Axiom
faimily, but you seem to be wanting something else.  So, yes, the
`concept of segment' may be a fairly well-defined concept;
apparently you're considering a different definition.  I would like to
understand it. 

-- Gaby