[Python-ideas] Support multiplication for sets

[Stephen J. Turnbull]

Terry Reedy writes:

 > If the elements of A*B are sequences, then A*B is also not commutative. 
 > But it would be if the elements were sets instead of pairs.

But that's not a Cartesian product.  By definition in a Cartesian
product order of element components matters.  I don't think I've ever
seen a set product like that, and have trouble imagining applications
for it unmodified (typically when squaring a set the diagonal would
cause problems).

 > In math, *...* is a ternary operator with 3 args, like if...else in 
 > Python or ;...: in C, but it generalizes to an n-ary operator.

A better analogy is to the comma or string concatenation.  I don't
know if that would lead to an associative implementation, though.

 > In most situations, one really needs an iterator that produces the
 > pairs one at a time rather than a complete collection.

I don't see why you couldn't have an operator on two iterables that
produces an iterator.  But of course comprehension notation is hard to
beat for that.

 > And when one does want a complete collection, one might often want
 > it ordered as a list rather than unordered as a set.

I don't understand this.  Sets are unordered; any order you impose on
the product would be arbitrary.  So iterate the product as a set, what
else might be (commonly) wanted?