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

From: Martin Rubey
Subject: [Axiom-developer] Re: [fricas-devel] Re: iterators and cartesian product.
Date: 22 Oct 2007 13:40:26 +0200
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

Francois Maltey <address@hidden> writes:

> >   [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])]

> But what is the signature of this function CartesianProduct ?

Sorry, I didn't bother to think about a good way to specify the Cartesian
product itself, but I think what Bill showed was quite good.

> 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.

I believe it is:

Union_{c\in C} Union_{b\in B} Union_{a\in A} F_{a,b,c}

is the same as

Union_{(a,b,c)\in A x B x C} F_{a,b,c}


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