Early attempt at zerocated numbers.

zerocated.py

from itertools import product
from sympy.abc import a,b,c

def phi(x,y):

    if y != 0 and y not in (a,b,c):
        return x / y
    elif y in (a,b,c):
        return x * y
    elif x == 0 and y == 0:
        return b

for prod in product((0,1,a,b,c), repeat=2):
    print(prod, phi(*prod))