PASS T1a n=3: 6 ordered triples of pairwise distinct indices, all products of spanning monomials (exponents <= 8) lie in sigma_ij
PASS T1a n=4: 24 ordered triples of pairwise distinct indices, all products of spanning monomials (exponents <= 8) lie in sigma_ij
PASS T1b p=3 n=3: 360 random products u*v, u in sigma_ir, v in sigma_rj, all in sigma_ij
PASS T1b p=3 n=4: 1440 random products u*v, u in sigma_ir, v in sigma_rj, all in sigma_ij
PASS T1b p=5 n=3: 360 random products u*v, u in sigma_ir, v in sigma_rj, all in sigma_ij
PASS T1b p=5 n=4: 1440 random products u*v, u in sigma_ir, v in sigma_rj, all in sigma_ij
PASS T1b p=7 n=3: 360 random products u*v, u in sigma_ir, v in sigma_rj, all in sigma_ij
PASS T1b p=7 n=4: 1440 random products u*v, u in sigma_ir, v in sigma_rj, all in sigma_ij
PASS T1c membership predicates behave as intended (x^3, 1 not in V; x not in J; x + y-multiples in V)
PASS T2 p=3: x in sigma_12, x in sigma_21, x^3 = x*x*x not in sigma_12 (and not in sigma_21)
PASS T2 p=5: x in sigma_12, x in sigma_21, x^3 = x*x*x not in sigma_12 (and not in sigma_21)
PASS T2 p=7: x in sigma_12, x in sigma_21, x^3 = x*x*x not in sigma_12 (and not in sigma_21)
PASS T2' p=3: sigma_ij sigma_ji sigma_ij <= sigma_ij for all {i,j} != {1,2} (random elements)
PASS T2' p=5: sigma_ij sigma_ji sigma_ij <= sigma_ij for all {i,j} != {1,2} (random elements)
PASS T3a p=2: all 60 reduced words of length 1..30 checked exhaustively: degree invariant exact, none of length >= 2 upper/lower unitriangular (0.0s)
PASS T3a p=3: all 4194300 reduced words of length 1..20 checked exhaustively: degree invariant exact, none of length >= 2 upper/lower unitriangular (17.4s)
PASS T3a p=5: all 2796200 reduced words of length 1..10 checked exhaustively: degree invariant exact, none of length >= 2 upper/lower unitriangular (7.4s)
PASS T3a p=7: all 4031076 reduced words of length 1..8 checked exhaustively: degree invariant exact, none of length >= 2 upper/lower unitriangular (9.5s)
PASS T3b p=3: 1500 random reduced words of length 2..400: degree invariant exact, none unitriangular (2.0s)
PASS T3b p=5: 1500 random reduced words of length 2..400: degree invariant exact, none unitriangular (2.0s)
PASS T3b p=7: 1500 random reduced words of length 2..400: degree invariant exact, none unitriangular (2.0s)
PASS T3c F = F_9 (non-prime field): 800 random reduced words of length 2..80, degree invariant exact, none unitriangular
PASS T3c F = Q (coefficients in Z\{0}, |c|<=5): 400 random reduced words of length 2..40, degree invariant exact, none unitriangular
PASS T4 n=3 p=3: 4042104 reduced words of length <= 5 in 24 generators of E(sigma); 228 distinct transvections produced, 204 of them are not generators, all with entry in sigma_ij (9.6s)
   examples of non-generator transvections produced (min length, i, j, entry {(xdeg,ydeg):coef}):
      (4, 1, 2, {(0, 1): 1, (1, 0): 1})
      (4, 1, 2, {(0, 1): 1, (1, 0): 2})
      (4, 1, 2, {(0, 1): 2, (1, 0): 1})
      (4, 1, 2, {(0, 1): 2, (1, 0): 2})
      (4, 1, 2, {(0, 2): 1})
      (4, 1, 2, {(0, 2): 2})
PASS T4 n=3 p=3: 6563264 reduced words of length <= 6 in 16 generators of E(sigma); 108 distinct transvections produced, 92 of them are not generators, all with entry in sigma_ij (16.2s)
   examples of non-generator transvections produced (min length, i, j, entry {(xdeg,ydeg):coef}):
      (4, 1, 2, {(0, 1): 1, (1, 0): 1})
      (4, 1, 2, {(0, 1): 1, (1, 0): 2})
      (4, 1, 2, {(0, 1): 2, (1, 0): 1})
      (4, 1, 2, {(0, 1): 2, (1, 0): 2})
      (4, 1, 2, {(0, 2): 1})
      (4, 1, 2, {(0, 2): 2})
ALL AUDIT CHECKS FOR THEOREM 1 PASSED
