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

[Bill Page]

On 10/27/07, Ralf Hemmecke wrote:
>
> Let me cite the documentation from stream.spad.pamphlet
>
> ++ A stream is an implementation of an infinite sequence using
> ++ a list of terms that have been computed and a function closure
> ++ to compute additional terms when needed.
>
> First, a stream is an infinite sequence. If we get
>
> (6) -> s:=construct([1,2,3])$Stream(Integer)
> (6) ->
>     (6)  [1,2,3]
>                                                           Type: Stream
> Integer
> (7) -> s.4
>   7) ->
>     >> Error detected within library code:
>     elt: no such element
>
> Then there is either something wrong with the code or with the
> documentation.
>

I think it is the documentation. Given the exports of Stream, it
obviously should say only "potentially infinite".

> Second, according to the documentation a Stream is a pair (A,B) where A
> is a list of precomputed functions and B is a function that computes the
> next value.
>
> If you would like to know the difference between Stream and Generator,
> then think of a Generator as the B part above.
>

Ok.

> ...
> > The larger question remains however: When to use a domain to directly
> > model something that is "set-like" and when to define a higher-order
> > domain whose objects are "set-like"? To me this is not clear in either
> > Spad or Aldor.
>
> I don't think you gain very much if you only consider set-like domains.
> If, however, you are looking at finite fields, for sure, you will think
> of a domain, since it is more important that there are some operations
> that connect the elements.
>

So you say it is natural to define "PrimeField 7" as a domain itself
rather than defining a general domain of "PrimeFields" and
constructing "PrimeField 7" as an element of that domain? Yes, I think
that makes sense. But there are of course some operations that connect
elements of any well defined set, no? If it is only a matter of
degree, then I still think it is rather confusing that Axiom (and
Aldor) provides these two rather different alternative implementation
of something that is essentially the same.

I suppose what I am saying is that (maybe) there should really be no
distinction between domains and members of domains (objects) - that
all objects should also be domains in and of themselves. But of course
that is not the way Axiom was designed.

Regards,
Bill Page.