[Axiom-developer] RE: DistributedExpression (was: How can I get every term of an expression ?)

[Page, Bill]

On Wednesday, September 21, 2005 3:11 PM I wrote:
> ... 
> On the other hand when you input
> 
>   (x+y)*(z+w)::Expression Integer
> 
> and Axiom replies
> 
>   (y + x)z + w y + w x
>                        Type: Expression Integer
> 
> then the display of whatever internal representation is
> used by Axiom for type 'Polynomial Integer' is controlled by
> the implied coercion to the special type OutputForm. This is
> really all that is different between the type Expression Integer
> and Martin's new type DistributedExpression Integer.

Of course I should have written:

        the display of whatever internal representation is
  used by Axiom for type 'Expression Integer' is controlled by
  the implied coercion to the special type OutputForm.

The same applies for all types (domains) in Axiom. Each of them
must supply at least one function named 'coerce' with signatue

  coerce: % -> OutputForm

This function is called by the Axiom interpreter. And it can
be used explicitly like this for example:

(4) -> (a+b)*(c+d)::OutputForm

   (4)  (b + a)(d + c)
                                      Type: OutputForm

Notice that the expression '(a+b)*(c+d)' has not been
interpreted by Axiom in any mathematical sense. OutputForm
is just a way of generating output that "looks like"
mathematics. 

Regards,
Bill Page.