quorum_i.py

from sympy import *

# ni is smaller UNL size, o is common unl size, pi/pj is extra size of ni/nj, qi is ni's quorum, ti is fault tolerance of all UNLs
ni, pi, pj, qi, ti = symbols("ni, pi, pj, qi, ti")

oij = ni - pi
nj = oij + pj


fork_safei = oij > (nj/2 + ni - qi + ti)
fork_firsti = (1-qi/ni)*ni <= ti

print solve(fork_safei,ti)

# For what qi are they equal?
qi = solve(solve(fork_safei,ti).args[1] - solve(fork_firsti, ti).args[1],qi)[0]

print 'qi >', qi

fork_firsti = (1-qi/ni)*ni > ti

print solve(fork_firsti,ti)

fork_safei = oij > (nj/2 + ni - qi + ti)

print solve(fork_safei,ti)