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RE: [Axiom-developer] Question concerning types...

From: Bill Page
Subject: RE: [Axiom-developer] Question concerning types...
Date: Mon, 18 Sep 2006 15:54:45 -0400

> On September 18, 2006 1:50 PM C Y wrote:
> > 
> > Sorry in advance if this question is a bit daft...
> >
On September 18, 2006 2:16 PM I wrote:
> Not at all. There is not such thing as a daft question -
> however always keep in mind that the same is not true of
> answers. :-)

I am afraid that what I wrote below might be a good example of
a "daft answer" - even if it is in the right spirit... :(

This idea needs more work. On 2nd thought what I wrote below
does not make good sense as it stands. Maybe this is better:

(2) -> a1:MPOLY([a1,a2],INT)
       Type: Void

(3) -> a2:MPOLY([a1,a2],INT)
       Type: Void

(4) -> a1+a2

   (4)  a1 + a2
        Type: MultivariatePolynomial([a1,a2],Integer)

This way it is clear that there are no indeterminants that are
not integers.

Bill Page.

> > --- Earlier I wrote:
> ...
> My proposal is that to define this in algebraic terms what we
> need is a domain like Polynomial which consists of some symbols
> and expressions (of a specific kind) over these symobls. So it
> is clear, right? that the type
>   Polynomial Integer
> consists of a large clase of expressiions of that type. And saying
>   a1:Polynomial Integer
> is just a way of saying that the variable a1 will take values from
> this domain.
> But because the coefficients of the polynomial must come from the
> domain Integer we know that these Integers are embedded in this class
> of expressions as polynomials of degree 0, so we have no problem
> specifying that a certain variable suchs as 'a1' is exact such an
> integer (polynomial of degree 0).
> In general both Integer and Polynomial Integer has Ring so, yes
> it is true that Polynomial Integer can be used in (most) places
> where would like to use Integer (but were no specific value is
> required).
> The only concern I have is whether or not Polynomial Integer is
> "big enough" to model everything that we would want to mean by
> "indefinite integer".
> Regards,
> Bill Page.
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