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

[Martin Rubey]

Francois Maltey <address@hidden> writes:

> Hello Martin,
> 
> > > At use, Mupad is almost perfect 
> > > [a $a=0..9] and [10*a+b $a=1..9$b=0..9] and [10*a+b $a=1..9$b=0..9$c=0..9]
> > > $ is a (right to left)? inner operator.
> > > 
> > > Of corse parallel iterations must remain as a pretty pure concept of 
> > > axiom.
> > 
> > So, how do you do parallel iteration in MuPad?
> 
> With a silly 
> 
>     [...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 like the possible new repeat operator :
> 
> [matrix [[a,b,15-a-b],[c,d,15-c-d]] for a in 1..9 repeat for b in 1..9 repeat
> for c in 1..9 repeat for d in 1..9]

I don't.  I'd rather stick to the way I express things as a mathematician,
i.e., (currently not working)

  [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])]

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])]

In fact, it nearly works:

-------------------------------------------------------------------------------

(1) -> l := [[1,2], [3,4]]

   (1)  [[1,2],[3,4]]
                                              Type: List List PositiveInteger
(2) -> [a,b] := first l

   (2)  [1,2]
                                                   Type: List PositiveInteger
(3) -> a

   (3)  1
                                                        Type: PositiveInteger
(4) -> b

   (4)  2
                                                        Type: PositiveInteger
(5) -> [([x,y] := e; matrix [[x,y],[y,x]]) for e in l]
 
   Though x has declared type (or partial type) PositiveInteger it does
      not have an assigned value. You must give it one before it can be
      so used.
(5) -> x

   (5)  1
                                                        Type: PositiveInteger
(6) -> y

   (6)  2
                                                        Type: PositiveInteger
(7) -> [(x := first e; y := second e; matrix [[x,y],[y,x]]) for e in l]

         +1  2+ +3  4+
   (7)  [|    |,|    |]
         +2  1+ +4  3+
                                                    Type: List Matrix Integer

-------------------------------------------------------------------------------

> This command breaks this previous mathematical set
> but build Union_{for a} (Unioun_{for b} (Unioun_{for c} set matrix for d))

Hm, I do not understand this sentence at all.  Which command breaks what?


Martin