[Python-ideas] Support multiplication for sets

[Steven D'Aprano]

Jakob Bowyer wrote:
> There is that but from a math point of view the syntax a * b does make
> sence.
> Its slightly clearer and makes more sense to people from outside of a
> programming background.


I realise that the consensus is that the lack of associativity is a 
fatal problem with a Cartesian product operator, but there are at least 
two other issues I haven't seen.

(1) "Using * for set product makes sense to mathematicians" -- maybe so, 
but those mathematicians already have to learn to use | instead of ∪ 
(union) and & instead of ∩ (intersection), so learning to use 
itertools.product() for Cartesian product is not a major burden for them.


(2) Cartesian product is potentially very expensive. The Cartesian 
product of a moderate-sized set and another moderate-sized set could 
turn out to be a HUGE set.

This is not a fatal objection, since other operations in Python are 
potentially expensive:

alist*10000000

but at least it looks expensive. You're multiplying by a big number, of 
course you're going to require a lot of memory. But set multiplication 
can very easily creep up on you:

aset*bset

will have size len(aset)*len(bset) which may be huge even if neither set 
on their own is. Better to keep it as a lazy iterator rather than try to 
generate a potentially huge set in one go.


-- 
Steven