meta nums

import itertools

def msum(a):
    return [j for i in a for j in i]

def mprod(a):
    return [msum(i) for i in itertools.product(*a)]

def mpow(a, b):
    return mprod(mprod([[a], b]))

ex = [
    'msum([[[]],[[]]])',  # 1 + 1 = 2
    'msum([[[],[]],[[],[],[]]])',  # 2 + 3 = 5
    'mprod([[[],[]],[[],[],[]]])',  # 2 * 3 = 6
    'mprod([[[],[[]]],[[],[[]]]])',  # (1+x)*(1+x) = 1+2x+x^2
    'mpow([[],[[]]], [[],[],[],[]])',  # (1+x)^4 = 1+4x+6x^2+4x^3+x^4
    'mprod(mprod([[[[],[[]]]], [[],[],[],[]]]))',  # same thing -- (1+x)^4
]

def demo(sort=True):
    for i in ex:
        j = eval(i)
        if sort:
            j = sorted(j)
        print(i, '=', j)