to show the insolvability of the quintic by computing nested commutators

arnold.py

import itertools


def reverse(forward: tuple) -> tuple:
    lst = [-1 for _ in forward]
    for idx in range(len(forward)):
        lst[forward[idx]] = idx
    return tuple(lst)


def compose(perm1: tuple, perm2: tuple) -> tuple:
    assert len(perm2) == len(perm1)
    lst = [-1 for _ in perm1]
    for idx in range(len(perm1)):
        lst[idx] = perm2[perm1[idx]]
    return tuple(lst)


def commutator(perms: set) -> set:
    res = []
    for perm1 in perms:
        for perm2 in perms:
            res.append(
                compose(
                    compose(
                        compose(
                            perm1,
                            perm2
                        ),
                        reverse(perm1)),
                    reverse(perm2)
                )
            )
    return set(res)

# https://www.youtube.com/watch?v=RhpVSV6iCko
if __name__ == '__main__':
    n = 3
    perms_set = set(itertools.permutations(range(n)))

    depth = 4
    for i in range(depth):
        print(i, len(perms_set), perms_set)
        perms_set = commutator(perms_set)