[PASS] R in the certificate = rotation of the quaternion (100,5,-18,7) (|q|^2 = 10398, common denominator 5199)
[PASS] R^T R = I and det R = 1 
[PASS] a1' = t a1 with t > 0, and a1' - x' = s R(a1 - x) with s > 0 
[PASS] a2' = t a2 with t > 0, and a2' - x' = s R(a2 - x) with s > 0 
[PASS] a3' = t a3 with t > 0, and a3' - x' = s R(a3 - x) with s > 0 
[PASS] A_12(x) = ((R-I)N).M = 0 at the x of P 
[PASS] A_23(x) = ((R-I)N).M = 0 at the x of P 
[PASS] A_31(x) = ((R-I)N).M = 0 at the x of P 
[PASS] the conditions A_kl(x) = 0 are affine-linear in x 
numerator factors over Q: [(1, 1), (1, 1), (1, 1), (1, 1), (2, 1)]
rational roots: [-4637560805/313396006, 0, 489410995/393950054, 23003637315/13356891878]
[PASS] linear factors: lam and the three printed rational roots 
[PASS] the only higher factor is the printed quadratic c2 t^2 + c1 t + c0 (up to a constant) degrees of all factors: [1, 1, 1, 1, 2]
[PASS] the printed quadratic is irreducible over Q (discriminant D not a square) 
[PASS] x(lambda*) from Cramer's rule equals the x of P in the certificate 
   root -4637560805/313396006: a_k parallel to R(a_k - x) for k = [3]
[PASS] rational root -4637560805/313396006 degenerate (some a_k parallel to R(a_k - x)) 
   root 0: a3 = 0 = y (degenerate)
   root 489410995/393950054: a_k parallel to R(a_k - x) for k = [2]
[PASS] rational root 489410995/393950054 degenerate (some a_k parallel to R(a_k - x)) 
   root 23003637315/13356891878: a_k parallel to R(a_k - x) for k = [1]
[PASS] rational root 23003637315/13356891878 degenerate (some a_k parallel to R(a_k - x)) 
RUN2 CONSTRUCTION: ALL OK
