[Axiom-developer] Re: iterators and cartesian product.

[Francois Maltey]

Hello,

> >     [...L[i]...LL[i]... for i in 1 .. min([4, length L, length LL])]
> > vs  the shorter [...x...xx... for x in L for xx in LL for k in 1..4] for
> > axiom
> 
> OK, I don't like MuPad's syntax then :-)

I forget the zip function because I never use it :

   zip ((x,y) -> x+y, [10,20,30], [$1..8]) // answers [11,22,33]
as [x+y for x in [10,20,30] for y in 1..8] -- with axiom

>   [matrix [[a,b,15-a-b],[c,d,15-c-d]] _
>    for (a,b,c,d) in CartesianProduct([1..9, 1..9, 1..9, 1..9])]

Why not ? 
But what is the signature of this function CartesianProduct ?
It must allow any kind of intervals or lists. as CartesianProduct (L, 1..9).
So it might be necessary to have this operator in the kernel, 
Domains might be not enough flexible... 

> or, maybe
> 
>   [((a,b,c,d) := e; matrix [[a,b,15-a-b],[c,d,15-c-d]]) _
>    for e in CartesianProduct([1..9, 1..9, 1..9, 1..9])]

I dislike... Two instructions for one calculus ! 
Matching might be automatic.

> 
> In fact, it nearly works:
> ---------------------------------------------------------------------------
> (1) -> l := [[1,2], [3,4]]
> (2) -> [a,b] := first l
> ...
> > This command breaks this previous mathematical set


> I do not understand this sentence at all.
I explain why I dislike the concat command.

The concat command :

concat 
     [concat [[[matrix [[a,b,15-a-b],[c,d,15-c-d]] for a in 1..9]
              for b in 1..9]
             for c in 1..9]
     for d in 1..9]

builds Union_{for d} (Union_{for c} (Union_{for b} set of matrix for a)
and isn't a mathematic translation of a cartesian product.

but 

>   [matrix [[a,b,15-a-b],[c,d,15-c-d]] _
>    for (a,b,c,d) in CartesianProduct([1..9, 1..9, 1..9, 1..9])]

is exactly the mathematic form of a Cartesian product.
It seems better.

F.