Dear Martin,
> what does a looping construct have to do with a Cartesian product?
The construct arround reduce/concat isn't so usual in order to
built several overlapped loops.
cartesian product and repeat keyword are two possibilities.
> > The * isn't the better operator because this locks
> > {1,2,3} * {1,2,3} = {1,2,3,4,6,9}
> > and {1,2,3} + {1,2,3} = {2,3,4,5,6}
>
> I actually wondered already once, why "+" is not union$Set, "-" not
> difference$Set.
I think that operator for sets are missing.
union (union (E, F), G) is less clever than E union F union G.
But why do you want a +. It might be possible to have more operators
than only +, -, *, /, ^, ::, $, # and @.
> I didn't think of the possibility above, although I doubt that
> it would be too useful.
For finite set it's not useful,
but very useful for intervals ; and intervals and set are close.
I like to use it for chaotic systems, with numerical instability.
or in order to separate root of a function.
newton methods can forget some mutiple roots.
interval methods, with operations over intervals, can add false roots.
> After all, you can even define it only if the elements
> understand "+" and "*".
I meet this needs for functions.
axiom doesn't understand that sin+cos is the fuction x +-> (sin x + cos x)
François
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