Template:Seal integer representations/python

Python program to calculate the integer sequence

This code uses the Python library discrete helpers.

from discretehelpers.a import make_linear_binv


arity = 4

depth_to_seals = {depth: None for depth in range(arity)}
depth_to_seals[0] = [make_linear_binv(walsh=0, parity=1, arity=arity)]  # tautology
depth_to_seals[1] = [make_linear_binv(walsh=i, parity=1, arity=arity) for i in range(1, 2 ** arity)]  # negated Walsh functions

for new_depth in range(2, arity+1):
    new_weight = 2 ** (arity - new_depth)
    old_depth = new_depth - 1
    old_seals = depth_to_seals[old_depth]
    new_seals = set()
    for key_a, seal_a in enumerate(old_seals):
        for key_b in range(key_a + 1, len(old_seals)):
            seal_b = old_seals[key_b]
            candidate = seal_a & seal_b
            if candidate.weight == new_weight:
                new_seals.add(candidate)
    depth_to_seals[new_depth] = sorted(new_seals)

lengths = []
sequence = []

for depth, seals in depth_to_seals.items():
    rank = arity - depth
    seal_integers = sorted([seal.intval for seal in seals])
    print(f'{rank}: {seal_integers},')
    lengths.append(len(seal_integers))
    sequence += seal_integers

print('\n', lengths)

print('\n', sorted(sequence))

resulting dictionary

rank_to_seals = {

    4: [65535],

    3: [255, 3855, 13107, 15555, 21845, 23205, 26265, 26985, 38505, 39321, 42405, 43605, 50115, 52275, 61455],
    
2: [15, 51, 85, 105, 153, 165, 195, 771, 1285, 1545, 2313, 2565, 3075, 4369, 4641, 5185, 6273, 8481, 8721, 9345, 10305, 12291, 16705, 17025, 17425, 18465, 20485, 24585, 33153, 33345, 33825, 34833, 36873, 40965, 49155],

    1: [3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769],

    0: [1]

}