On Wed, Jul 9, 2008 at 9:06 AM, Bill Page <[EMAIL PROTECTED]> wrote:
> On Wed, Jul 9, 2008 at 7:19 AM, Gabriel Dos Reis wrote:
>> Bill Page writes:
>> | In a previous email you said you thought SubDomain was "half-baked".
>>
>> Indeed.
>>
>> | If you meant this in the sense of "not fully implemented" then I agree
>>
>> Not just fully implemented, but also not fully specified, and in fact
>> the semantics seems fuzzy (at best) once one starts using it. For
>> example, the SubDomain constructor takes two arguments: The
>> parent domain and the predicate that test whether to consider an
>> object a member of the subdomain. Yet, you have use it with only
>> one argument without specficifying what that would mean.
>>
>
> Are we talking about the same "SubDomain constructor"?
I do not know of many SubDomain constructors in OpenAxiom, Axiom or
FriCAS.
> The one to
> which I was referring is produced by Axiom and FriCAS when you create
> a value referring to a category. E.g.
>
> (1) -> c:=INS
>
> (1) IntegerNumberSystem
> Type: SubDomain Domain
Yes, but what is it?
I canot find a description of it in the Axiom book.
>
> As far as I can see 'SubDomain' here is is a category constructor that
> takes only one argument.
>
> There is another "subdomain constructor" that one can find in the source
> code for PositiveInteger and NonNegativeInteger:
That constructor is also spelled SubDomain, not subdomain.
>
> PositiveInteger: Join(OrderedAbelianSemiGroup,Monoid) with
> gcd: (%,%) -> %
> ++ gcd(a,b) computes the greatest common divisor of two
> ++ positive integers \spad{a} and b.
> commutative("*")
> ++ commutative("*") means multiplication is commutative
> : x*y = y*x
> == SubDomain(NonNegativeInteger,#1 > 0) add
>
> This construction presumably returns a domain.
Then, how do you distinguish this SubDomain from that SubDomain?
As far as I can tell, both are spelled the same.
>
> I think these are related, as I speculated in my previous email, but
> they are certainly not the same.
How do I know that?
-- Gaby
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