table test: 300 random SL(2,Z) pairs, u_1..u_3 both conventions: all agree with matrices
h(-t) (monic): t**3 - t**2 - 2*t + 1
L1 (K): line (0,t,t), conv K, relation u_3 = - u_2
   degrees of coords of u_3 - (-1) u_2: [68, 68, 69, 69]
   gcd of the four coordinates: (2, [(2*t**4 - 4*t**2 + 1, 1)])
   2*t**4 - 4*t**2 + 1 divides all four coordinates: True
   kappa = tr[x,y] = 2*t**2 - 2 ; Res(g, kappa - 2) = 16 = {2: 4}
   gcd_k Res(g, coords of u_2 - 1) = 1024 ; of u_2 + 1 = 1024 ; factorizations: {2: 10} {2: 10}
   leading coefficient of g: 2
L1 (O): line (0,t,t), conv O, relation u_4 = + u_3
   degrees of coords of u_4 - (1) u_3: [914, 914, 913, 913]
   gcd of the four coordinates: (64, [(t - 1, 2), (t + 1, 2), (t, 5), (t**2 - 2, 3), (2*t**4 - 4*t**2 + 1, 1)])
   2*t**4 - 4*t**2 + 1 divides all four coordinates: True
   kappa = tr[x,y] = 2*t**2 - 2 ; Res(g, kappa - 2) = 16 = {2: 4}
   gcd_k Res(g, coords of u_3 - 1) = 5192296858534827628530496329220096 ; of u_3 + 1 = 5192296858534827628530496329220096 ; factorizations: {2: 112} {2: 112}
   leading coefficient of g: 2
L2 (K), h(t): line (1,t,t), conv K, relation u_4 = + u_2
   degrees of coords of u_4 - (1) u_2: [312, 314, 313, 315]
   gcd of the four coordinates: (1, [(t - 1, 1), (t, 1), (t + 1, 1), (t**2 - 3, 1), (t**3 - t**2 - 2*t + 1, 1), (t**3 + t**2 - 2*t - 1, 1)])
   t**3 + t**2 - 2*t - 1 divides all four coordinates: True
   kappa = tr[x,y] = t**2 - 1 ; Res(g, kappa - 2) = 1 = {}
   gcd_k Res(g, coords of u_2 - 1) = 1 ; of u_2 + 1 = 1 ; factorizations: {} {}
   leading coefficient of g: 1
L2 (K), h(-t): line (1,t,t), conv K, relation u_4 = + u_2
   degrees of coords of u_4 - (1) u_2: [312, 314, 313, 315]
   gcd of the four coordinates: (1, [(t - 1, 1), (t, 1), (t + 1, 1), (t**2 - 3, 1), (t**3 - t**2 - 2*t + 1, 1), (t**3 + t**2 - 2*t - 1, 1)])
   t**3 - t**2 - 2*t + 1 divides all four coordinates: True
   kappa = tr[x,y] = t**2 - 1 ; Res(g, kappa - 2) = 1 = {}
   gcd_k Res(g, coords of u_2 - 1) = 1 ; of u_2 + 1 = 1 ; factorizations: {} {}
   leading coefficient of g: 1
control: g | coords of u_3 - u_2 on (0,t,t) (should be False): False
ALL DIVISIBILITY CLAIMS: True
nice -n 10 $PY -I vA_families.py  109.22s user 0.51s system 99% cpu 1:49.83 total
