== Thm 1.2(a) over F_3(t), f=t^2+1
  [Thm 1.2(a) over F_3(t), f=t^2+1] net inclusions n=3: 1800 random products tested, failures = 0
  [Thm 1.2(a) over F_3(t), f=t^2+1] net inclusions n=4: 7200 random products tested, failures = 0
  [Thm 1.2(a) over F_3(t), f=t^2+1] witness 1*t*1 = t: in sigma12? False  (must be False)
  [Thm 1.2(a) over F_3(t), f=t^2+1] random triple products sigma12*sigma21*sigma12 outside sigma12: 165 / 500 (nonzero expected)
  [Thm 1.2(a) over F_3(t), f=t^2+1] F_p[f]-module property on random elements: failures = 0
  [Thm 1.2(a) over F_3(t), f=t^2+1] |H| in SL_2(Q) recomputed: 120
  [Thm 1.2(a) over F_3(t), f=t^2+1] pi_*(random word) = diag(h, I) with h in H, n=3: 300 words, failures = 0
  [Thm 1.2(a) over F_3(t), f=t^2+1] pi_*(random word) = diag(h, I) with h in H, n=4: 300 words, failures = 0
  [Thm 1.2(a) over F_3(t), f=t^2+1] exhaustive words n=3, length<=6 over 16 generators: 13017856 words; distinct transvections found = 104; with entry outside sigma_ij = 0  (66.0s)
  [Thm 1.2(a) over F_3(t), f=t^2+1] sample transvections (i,j,entry,first depth): t12((1,))@1; t12((2,))@2; t21((0, 1))@4; t12((2, 0, 1))@5; t21((0, 2))@5; t21((1, 1, 1))@5; t12((0, 0, 0, 0, 1))@6; t12((0, 0, 0, 0, 2))@6; t12((0, 0, 1))@6; t12((0, 0, 1, 0, 1))@6; t12((0, 0, 1, 0, 2))@6; t12((0, 0, 2))@6
== Thm 1.2(b) over F_2(t), f=t^2+t+1
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] net inclusions n=3: 1800 random products tested, failures = 0
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] net inclusions n=4: 7200 random products tested, failures = 0
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] witness 1*t*1 = t: in sigma12? False  (must be False)
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] random triple products sigma12*sigma21*sigma12 outside sigma12: 54 / 500 (nonzero expected)
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] F_p[f]-module property on random elements: failures = 0
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] |H| in SL_2(Q) recomputed: 10
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] pi_*(random word) = diag(h, I) with h in H, n=3: 300 words, failures = 0
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] pi_*(random word) = diag(h, I) with h in H, n=4: 300 words, failures = 0
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] exhaustive words n=3, length<=7 over 8 generators: 1098056 words; distinct transvections found = 34; with entry outside sigma_ij = 0  (6.3s)
  [Thm 1.2(b) over F_2(t), f=t^2+t+1] sample transvections (i,j,entry,first depth): t12((1,))@1; t12((0, 1, 1))@2; t12((1, 1, 1))@3; t21((0, 1))@5; t12((1, 0, 1, 0, 1))@6; t12((1, 1, 0, 0, 1))@6; t13((1, 0, 1, 0, 1))@6; t21((0, 0, 0, 0, 1))@6; t21((1, 0, 1))@6; t23((0, 1, 1, 1))@6; t23((1, 0, 1, 0, 1))@6; t23((1, 1, 0, 1, 1))@6
== Remark 4.2 over Q(i): R = Z[i], J = 3Z[i]
  [Z[i]] net inclusions n=3: 1800 random products tested, failures = 0
  [Z[i]] net inclusions n=4: 7200 random products tested, failures = 0
  [Z[i]] witness 1*i*1 = i in sigma12? False (must be False)
  [Z[i]] x^2+1 has a root mod 3? False (3 inert in Z[i], so Z[i]/3Z[i] = F_9)
  [Z[i]] pi_*(random word) = diag(h, I), h in H (|H| = 120), n=3: 300 words, failures = 0
  [Z[i]] pi_*(random word) = diag(h, I), h in H (|H| = 120), n=4: 300 words, failures = 0
  [Z[i]] i*1 = i in sigma12? False -> sigma12 is not a Z[i]-module; 3i*sigma21 <= sigma21 and 3i*sigma12 <= sigma12 on samples: True
  [Z[i]] exhaustive words n=3, length<=5 over 28 generators: 15452668 words; distinct transvections found = 524; with entry outside sigma_ij = 0  (17.2s)
== Thm 1.1 over F_3(x,y)
  [Thm 1.1 over F_3(x,y)] net inclusions n=3: 900 random products tested, failures = 0
  [Thm 1.1 over F_3(x,y)] net inclusions n=4: 3600 random products tested, failures = 0
  [Thm 1.1 over F_3(x,y)] witness x*x*x = x^3 in sigma12? False (must be False)
  [Thm 1.1 over F_3(x,y)] exhaustive words n=3, length<=5 over 24 generators: 7021464 words; distinct transvections found = 228; with entry outside sigma_ij = 0  (22.7s)
== Thm 1.1 over F_5(x,y)
  [Thm 1.1 over F_5(x,y)] net inclusions n=3: 900 random products tested, failures = 0
  [Thm 1.1 over F_5(x,y)] net inclusions n=4: 3600 random products tested, failures = 0
  [Thm 1.1 over F_5(x,y)] witness x*x*x = x^3 in sigma12? False (must be False)
