(U1) the minimal primes of the incidence over QQ
  [ok] (U1) I has 5 minimal primes: {lam = 0} of dimension [7] and 4 others of dimensions [6, 6, 6, 6]
  [ok] (U1) the four primes are K_1, K_2, K_3, K_D, each once (found ['K_1', 'K_2', 'K_3', 'K_D'])
  [ok] (U1) K_D = (d, e, f, lam2, lam4) (linear)
   K_1: dimension 6, 11 generators: [-l2*l3 + l1*l4, -3*f*l3 + e*l4, -3*f*l1 + e*l2, -e*l3 + c*l4, -e*l1 + c*l2, -e^2 + 3*c*f, -2*d*l3 + b*l4, -2*d*l1 + b*l2, -2*d*e + 3*b*f, -2*c*d + b*e, al]
   K_2: dimension 6, 8 generators: [-3*f*l1 + e*l2, -e*l1 + c*l2, -e^2 + 3*c*f, -2*d*l1 + b*l2, -2*d*e + 3*b*f, -2*c*d + b*e, l4, l3]
   K_3: dimension 6, 14 generators: [-3*f*l3 + e*l4, d*l4*al + 6*f*l1 - 2*e*l2, 3*d*f*l3*al + 6*e*f*l1 - 2*e^2*l2, -e*l3 + c*l4, -d*l3*al - 2*e*l1 + 2*c*l2, -e^2 + 3*c*f, -2*d*l3 + b*l4, -2*d*e + 3*b*f, -2*c*d + b*e, a*l4*al + 2*d*l1 - b*l2, -d^2 + 3*a*f, -b*d + 2*a*e, 2*a*d*l3*al + 2*b*d*l1 - b^2*l2, -b^2 + 4*a*c]
   K_D: dimension 6, 5 generators: [l4, l2, f, e, d]
   [time 0 s]
(U2) absolute primary decomposition (Singular absPrimdecGTZ) of each component
  [ok] (U2) K_1: 1 absolute prime(s), extension degree(s) ['1'], dimension(s) [6] (0 s)
  [ok] (U3) K_1: the absolute prime, with @c eliminated, equals K_i
  [ok] (U2) K_2: 1 absolute prime(s), extension degree(s) ['1'], dimension(s) [6] (0 s)
  [ok] (U3) K_2: the absolute prime, with @c eliminated, equals K_i
  [ok] (U2) K_3: 1 absolute prime(s), extension degree(s) ['1'], dimension(s) [6] (0 s)
  [ok] (U3) K_3: the absolute prime, with @c eliminated, equals K_i
  [ok] (U2) K_D: 1 absolute prime(s), extension degree(s) ['1'], dimension(s) [6] (0 s)
  [ok] (U3) K_D: the absolute prime, with @c eliminated, equals K_i
   [time 0 s]
(U4) each of K_1, K_2, K_3 is the contraction of a graph ideal over the six free coordinates, f inverted
  [ok] (U4) K_1: graph over (a, d, e, f, l2, l4) with f inverted: ['-e^2 + 3*c*f', '-2*d*e + 3*b*f', '3*f*l3 - e*l4', '3*f*l1 - e*l2', 'al']; (G : f^inf) = K: True
  [ok] (U4) K_2: graph over (a, d, e, f, l2, al) with f inverted: ['-e^2 + 3*c*f', '-2*d*e + 3*b*f', '3*f*l1 - e*l2', 'l3', 'l4']; (G : f^inf) = K: True
  [ok] (U4) K_3: graph over (d, e, f, l2, l4, al) with f inverted: ['-d^2 + 3*a*f', '-e^2 + 3*c*f', '-2*d*e + 3*b*f', '3*f*l3 - e*l4', 'd*l4*al + 6*f*l1 - 2*e*l2']; (G : f^inf) = K: True
   [time 0 s]
14 checks, 0 failed
ALL CHECKS PASSED
