Algorithm to return if a number is colorful

colorful-numbers.py

'''A number is colorful if all products of the subsets of individual digits are unique
e.g. 263 is colorful:
2 * 6 * 3 = 36
2 * 6 = 12
6 * 3 = 18
'''
def is_colorful(num):
    # Account for negatives (results will be the same)
    num = abs(num)
    
    # Number is trivially colorful if only contains 1 digit
    if num < 10:
        return True
    
    # This is the maximum possible colorful number, contains no repeated digits, no 1s or 0s
    # (although it is not colourful)
    if num > 98765432:
        return False
    
    num_list = [int(digit) for digit in str(num)]
    cache = set(num_list)
    
    '''Trivial cases:
    Number contains a 0 - 0x = 0
    Number contains a 1 - 1x = x
    Length of number is larger than cache - digits are repeats'''
    length = len(num_list)
    if 0 in num_list or 1 in num_list or length > len(cache):
        return False    
    
    # Finally calculate the products after filtering trivial cases
    for i in range(length - 1):
        product = num_list[i]
        for j in range(i + 1, length):
            product *= num_list[j]
            if product in cache:
                return False
            cache.add(product)
    
    return True