line (a,b,c) = (0+0t, 0+1t, 0+1t), conv=other, relation u_4 = s u_3
  degrees of u_n coordinates: [[2, 2, 1, 1], [14, 14, 13, 13], [114, 114, 113, 113], [914, 914, 913, 913]]
  kappa = tr[x,y] = 2*t**2 - 2
  s=1: gcd degree 19, factors (64, [(t - 1, 2), (t + 1, 2), (t, 5), (t**2 - 2, 3), (2*t**4 - 4*t**2 + 1, 1)])
    factor g = t - 1: exact division OK; Res(g, kappa-2) = {2: 1, -1: 1}; gcd of Res(g, coords of u_3-1) = 0, of u_3+1: {2: 1}; lc(g) = 1
    factor g = t + 1: exact division OK; Res(g, kappa-2) = {2: 1, -1: 1}; gcd of Res(g, coords of u_3-1) = 0, of u_3+1: {2: 1}; lc(g) = 1
    factor g = t: exact division OK; Res(g, kappa-2) = {2: 2, -1: 1}; gcd of Res(g, coords of u_3-1) = 0, of u_3+1: {2: 1}; lc(g) = 1
    factor g = t**2 - 2: exact division OK; Res(g, kappa-2) = 0; gcd of Res(g, coords of u_3-1) = 0, of u_3+1: {2: 2}; lc(g) = 1
    factor g = 2*t**4 - 4*t**2 + 1: exact division OK; Res(g, kappa-2) = {2: 4}; gcd of Res(g, coords of u_3-1) = {2: 112}, of u_3+1: {2: 112}; lc(g) = 2
  s=-1: gcd is constant 2 (no family)
