L1  Lemma 3.1 (top coefficient of {p,q})
  ok    L1 Theorem A bracket, Q(sqrt2,sqrt3)  520/520 (pairs x orders, 13 compatible orders); where lambda(LE p, LE q) != 0 also LE{p,q} = LE p + LE q: 402/402
  ok    L1 CONTROL Theorem A bracket, Q(sqrt2,sqrt3)  identity fails in 22 of 75 cases (dense pairs x three non-compatible orders)
  ok    L1 Theorem D bracket, Q(theta)  775/775 (pairs x orders, 31 compatible orders); where lambda(LE p, LE q) != 0 also LE{p,q} = LE p + LE q: 694/694
  ok    L1 CONTROL Theorem D bracket, Q(theta)  identity fails in 40 of 75 cases (dense pairs x three non-compatible orders)
  ok    L1 random integer lambda, n = 3  520/520 (pairs x orders, 13 compatible orders); where lambda(LE p, LE q) != 0 also LE{p,q} = LE p + LE q: 403/403
  ok    L1 CONTROL random integer lambda, n = 3  identity fails in 33 of 75 cases (dense pairs x three non-compatible orders)
  ok    L1 random integer lambda, n = 5  325/325 (pairs x orders, 13 compatible orders); where lambda(LE p, LE q) != 0 also LE{p,q} = LE p + LE q: 225/225
  ok    L1 CONTROL random integer lambda, n = 5  identity fails in 31 of 75 cases (dense pairs x three non-compatible orders)
L2  Lemma 3.2: |LE(W)| = dim W
  ok    L2  60/60 random subspaces: echelon gives rank-many distinct leading exponents; LE of random combinations lies in that set
L3  Lemma 3.3 / Proposition 3.4 on algebras C[f,g]
  ok    L3 random f = x+y+z, g = xy+z^2 (algebraically independent)  d <= 14: dim W_d = 64 = |LE(W_d)| = 64, r = 2, projection to coordinates (0, 1) injective: True, |LE| <= (d+1)^r: True
  ok    L3 f = x^2+y, g = y^2+z (lex)  d <= 14: dim W_d = 36 = |LE(W_d)| = 36, r = 2, projection to coordinates (0, 1) injective: True, |LE| <= (d+1)^r: True
  ok    L3 (a,b,c) = (1,2,3): f = x + x^2y^3z, g = x^2 + 5x^2y^3z + (x^2y^3z)^2  d <= 14: dim W_d = 4 = |LE(W_d)| = 4, r = 2, projection to coordinates (0, 1) injective: True, |LE| <= (d+1)^r: True; pairwise lambda-orthogonal: True
  ok    L3 (1,2,3): kernel vector (2,3,1) lies in span LE  
  ok    L3 (a,b,c) = (1,1,sqrt2): f = xz + y, g = x^2z^2 + 2y^3  d <= 12: dim W_d = 16 = |LE(W_d)| = 16, r = 2, projection to coordinates (0, 1) injective: True, |LE| <= (d+1)^r: True; pairwise lambda-orthogonal: True
  ok    L3 Theorem A bracket: f = x+y+z, g = f^2 + f (commuting, dependent)  d <= 12: dim W_d = 13 = |LE(W_d)| = 13, r = 1, projection to coordinates (0,) injective: True, |LE| <= (d+1)^r: True
TOTAL failures: 0
running time: 5 s
