Cartesian Product of Sets where No Elements are Identical under Permutations in Python

Question

I have some sets I would like to take the Cartesian product of, which is working well. However, I want to remove all elements of this new set which are identical under a permuta

Answer 1

You want combinations_with_replacement, not product:

itertools.combinations_with_replacement([x, y, z], 3)

Answer 2

Use a dict to map each unique product to the most recently seen tuple.

d = {reduce(operator.mul, f): f for f in flist}

If you would need to treat tuples that aren't permutations of each other as distinct elements, you'll need a more complicated key that incorporates a canonical representation of the tuple.

from operator import mul
d = {(tuple(sorted(f)), reduce(mul, f)): f for f in flist}

Actually, once you do that, you don't need to map the tuple/product pair to a tuple; you can just maintain a set of pairs:

d = {(tuple(sorted(f)), reduce(mul, f)) for f in flist}

In any case, retrieving just the tuples is as simple as

tuples = d.values()  # In the first two cases
tuples = {x for x,y in d} # In the third case