Re: [Axiom-developer] Tuples

[Ralf Hemmecke]

On 06/29/2007 11:36 PM, Franz Lehner wrote:
> Hello
>
> here is an algebra question for a change.
> Do I understand correctly that there is currently no way to implement
> DirectProduct(L: List Group) or DirectProduct(L: Tuple Group)?
> That is, one has to manually iterate DirectProduct(G1,G2)
> if one wants a direct product of more than two groups?
>
> thanks for your consideration
> Franz

Ooops. You seem to be hitting the same problem as me.
If you have a constructor DP which takes a tuple as input, you will run 
into the problem that it is (nearly) impossible to create actual 
elements of that thing.

Let's try do define something... Again that will be Aldor, but I hope 
the problem becomes understandable.

DP(T: Tuple Group): with {
  construct: T -> %
} == add {
  Rep == Array Pointer;
  construct(t: T): % == ...
}

Well the problem is the T here. It is something like (G1, G2, G3) where 
all groups might be different. Now take (g1, g2, g3) where gi is of type 
Gi. That thing is of type (G1, G2, G3) but not a Tuple(A) for some 
domain A, because Tuple constructs homogeneous things. We can only have 
that the type of (g1, g2, g3) is Cross(G1, G2, G3).

Well, if you use Cross, you must give the types at compile time. But 
that you cannot do.

However, you have said "iterate DirectProduct(G1,G2)" and that lets me 
start thinking. I don't claim that I will come up with a good 
"workaround" but the iteration idea might be something that I could 
eventually turn into something I like. You have to wait a bit, though.
Better listen at the aldor-combinat mailing list. I might forget to post 
something to axiom-dev.

Ralf