random choices: random.seed(136442), consumed in the order of the script; retry loops print the attempt used
  gamma = y^2*z + y*z^2 (three roots): triple [z^5 + y^3*z + y^2*z^2 + x^3, y^2*z^2 + y*z^3 + x*y^2, y^5 + y^3*z + y^2*z^2 + x*z^2]; cubic parts independent in x S_2: True; quartic parts in gamma C[y,z]_1: True; local length 39 (dim S/(J + m^N) = 39 for N = 10 and N = 11)
PASS (P) the triple of prop:C for gamma = y^2*z + y*z^2: local length 39 < 40 (stable pair N = 10, 11)
  gamma = y^2*z (double root): triple [z^5 + y^3*z + x^3, y^2*z^2 + x*y^2, y^5 + y^3*z + x*z^2]; cubic parts independent in x S_2: True; quartic parts in gamma C[y,z]_1: True; local length 39 (dim S/(J + m^N) = 39 for N = 10 and N = 11)
PASS (P) the triple of prop:C for gamma = y^2*z: local length 39 < 40 (stable pair N = 10, 11)
  gamma = y^3 (triple root): triple [z^5 + y^4 + x^3, y^3*z + x*y^2, y^5 + y^4 + x*z^2]; cubic parts independent in x S_2: True; quartic parts in gamma C[y,z]_1: True; local length 39 (dim S/(J + m^N) = 39 for N = 10 and N = 11)
PASS (P) the triple of prop:C for gamma = y^3: local length 39 < 40 (stable pair N = 10, 11)
  r = 2, Gamma = V(x, y*z) (two points {Y, Z}), gamma = y^2*z + y*z^2: dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 39 (dim S/(J + m^N) = 39 for N = 10 and N = 11), residual 19 with H = [1, 3, 6, 6, 2, 1]
PASS (R2) r = 2, two points {Y, Z}: gamma kills D_5, realized CI of local length 39, residual 19
  r = 2, Gamma = V(x, y^2) (double point at Z), gamma = y^2*z: dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 39 (dim S/(J + m^N) = 39 for N = 10 and N = 11), residual 19 with H = [1, 3, 6, 6, 3]
PASS (R2) r = 2, double point at Z: gamma kills D_5, realized CI of local length 39, residual 19
  r = 4, D_5 = random: tail dimension 10
PASS (T) r = 4: tails (tau, R) mod trivial = 10 (+12 for E)
  r = 4, D_5 = [Y^4*Z, Y*Z^4]: tail dimension 10
PASS (T) r = 4: tails (tau, R) mod trivial = 10 (+12 for E)
  r = 3, gradient, random K, G = Y^4 + Z^4: tail dimension 13
PASS (T) r = 3 (gradient, random K): tails (tau, R) mod trivial = 13 (+12 for E)
  r = 3, gradient, random K, G = random: tail dimension 13
PASS (T) r = 3 (gradient, random K): tails (tau, R) mod trivial = 13 (+12 for E)
PASS (T) r = 3 (gradient, random K): 2 of 2 choices of G accepted
  r = 3, gradient, K = Y^3Z^3, G = Y^4 + Z^4: tail dimension 13
PASS (T) r = 3 (gradient, K = Y^3Z^3): tails (tau, R) mod trivial = 13 (+12 for E)
  r = 3, gradient, K = Y^3Z^3, G = random: tail dimension 13
PASS (T) r = 3 (gradient, K = Y^3Z^3): tails (tau, R) mod trivial = 13 (+12 for E)
PASS (T) r = 3 (gradient, K = Y^3Z^3): 2 of 2 choices of G accepted
  r = 3, gradient, K = Y^6+Z^6+(Y+Z)^6: G = Y^4 + Z^4 skipped (dim D_4 < 4)
  r = 3, gradient, K = Y^6+Z^6+(Y+Z)^6, G = 4*Y^3*Z + 5*Y^2*Z^2 + 3*Y*Z^3 - 4*Z^4: tail dimension 13
PASS (T) r = 3 (gradient, K = Y^6+Z^6+(Y+Z)^6): tails (tau, R) mod trivial = 13 (+12 for E)
PASS (T) r = 3 (gradient, K = Y^6+Z^6+(Y+Z)^6): 1 of 2 choices of G accepted
  r = 3, <Y^5, H>, random H, G = Y^4 + Z^4: tail dimension 13
PASS (T) r = 3 (<Y^5, H>, random H): tails (tau, R) mod trivial = 13 (+12 for E)
  r = 3, <Y^5, H>, random H, G = random: tail dimension 13
PASS (T) r = 3 (<Y^5, H>, random H): tails (tau, R) mod trivial = 13 (+12 for E)
PASS (T) r = 3 (<Y^5, H>, random H): 2 of 2 choices of G accepted
  r = 4 anchor: dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 36 (dim S/(J + m^N) = 36 for N = 9 and N = 10), residual 16 with H = [1, 3, 6, 5, 1]
PASS (A4) r = 4 anchor: realized (quartic parts do not kill D_5: True), local length 36, residual 16
  r = 3 anchor: dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 36 (dim S/(J + m^N) = 36 for N = 9 and N = 10), residual 16 with H = [1, 3, 6, 4, 2]
PASS (A3) r = 3 anchor: quartic parts kill D_5, realized, local length 36, residual 16
  length-36 criterion, g = y^4, attempt 0 used: p2 = y^3*z - 4*y^2*z^2 + y*z^3 + z^4, p3 = -2*y^4 - y^3*z + 5*y*z^3 + 5*z^4: hypotheses True, local length 36 (N = 10)
PASS (L) length-36 criterion, g = y^4: hypotheses hold, local length 36
  length-36 criterion, g = y^3 z, attempt 3 used: p2 = -3*y^4 + 4*y^3*z + 5*y^2*z^2 - 5*y*z^3 + 4*z^4, p3 = 2*y^4 + 2*y^3*z - 3*y^2*z^2 - 3*y*z^3 + 2*z^4: hypotheses True, local length 36 (N = 10)
PASS (L) length-36 criterion, g = y^3 z: hypotheses hold, local length 36
  length-36 criterion, g = y^2 z^2, attempt 0 used: p2 = -3*y^4 - 5*y^3*z + 3*y^2*z^2 - 3*y*z^3 + 4*z^4, p3 = 3*y^4 - 3*y^2*z^2 - 2*y*z^3 - z^4: hypotheses True, local length 36 (N = 10)
PASS (L) length-36 criterion, g = y^2 z^2: hypotheses hold, local length 36
  length-36 criterion, g = y^2 z (y+z), attempt 0 used: p2 = y^4 + 4*y^3*z + 3*y^2*z^2 + 5*z^4, p3 = -4*y^4 - 4*y^3*z - 2*y^2*z^2 - 5*y*z^3 - 3*z^4: hypotheses True, local length 36 (N = 10)
PASS (L) length-36 criterion, g = y^2 z (y+z): hypotheses hold, local length 36
  length-36 criterion, g = y z (y+z)(y+2z), attempt 0 used: p2 = -4*y^4 + 4*y^3*z - 4*y^2*z^2 - 2*y*z^3 - 3*z^4, p3 = 2*y^4 - 2*y^3*z + 4*y^2*z^2 + 5*y*z^3 + 3*z^4: hypotheses True, local length 36 (N = 10)
PASS (L) length-36 criterion, g = y z (y+z)(y+2z): hypotheses hold, local length 36
  length-36 criterion, g = random, attempt 0 used: p2 = y^4 + 4*y^3*z + 2*y^2*z^2 - 5*z^4, p3 = -y^4 + 2*y^3*z - 3*y^2*z^2 + z^4: hypotheses True, local length 36 (N = 10)
PASS (L) length-36 criterion, g = random: hypotheses hold, local length 36
  (A4') trial 0: attempt 0 used for (p2, p3); D_5 = [-Y^5 + 5*Y^3*Z^2 - 2*Y^2*Z^3 - 3*Y*Z^4 + 4*Z^5, 3*Y^5 + 4*Y^4*Z + 2*Y^3*Z^2 - Y^2*Z^3 - 4*Y*Z^4 - 2*Z^5]; triple [9507/3883*y^4 - 37988/3883*y^3*z + 18852/3883*y^2*z^2 - 12054/3883*y*z^3 + z^4 + x^3, -5*y^3*z - 2*y^2*z^2 + y*z^3 + 4*z^4 + x*y^2, 5*y^4 - 2*y^3*z - 4*y^2*z^2 - 5*y*z^3 + x*z^2]
  r = 4 random D_5 (trial 0): dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 36 (dim S/(J + m^N) = 36 for N = 9 and N = 10), residual 16 with H = [1, 3, 6, 5, 1]
PASS (A4') r = 4, random D_5: beta = <g> one-dimensional, criterion hypotheses, realized CI of local length 36
  (A4') trial 1: attempt 0 used for (p2, p3); D_5 = [-3*Y^5 + 3*Y^4*Z - 4*Y^2*Z^3 + 4*Y*Z^4 + 2*Z^5, -4*Y^4*Z - 5*Y^3*Z^2 - 5*Y^2*Z^3 + 2*Y*Z^4]; triple [-1658/2281*y^4 - 9522/2281*y^3*z + 14346/2281*y^2*z^2 + 2714/2281*y*z^3 + z^4 + x^3, -5*y^4 + 5*y^3*z + 4*y^2*z^2 - 2*y*z^3 + 3*z^4 + x*y^2, -y^4 + y^3*z - 2*y^2*z^2 + 5*y*z^3 + 2*z^4 + x*z^2]
  r = 4 random D_5 (trial 1): dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 36 (dim S/(J + m^N) = 36 for N = 9 and N = 10), residual 16 with H = [1, 3, 6, 5, 1]
PASS (A4') r = 4, random D_5: beta = <g> one-dimensional, criterion hypotheses, realized CI of local length 36
  (A4') trial 2: attempt 0 used for (p2, p3); D_5 = [-4*Y^4*Z - 3*Y^3*Z^2 + 2*Y^2*Z^3 - 2*Z^5, 4*Y^5 + 3*Y^4*Z - 3*Y^3*Z^2 + Y^2*Z^3 + Y*Z^4 - 2*Z^5]; triple [596/407*y^4 - 1932/407*y^3*z + 3556/407*y^2*z^2 - 2394/407*y*z^3 + z^4 + x^3, 5*y^4 + 3*y^3*z + 5*y^2*z^2 + 2*y*z^3 - 3*z^4 + x*y^2, -y^4 - y^3*z - 5*y^2*z^2 + 4*y*z^3 + 3*z^4 + x*z^2]
  r = 4 random D_5 (trial 2): dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 36 (dim S/(J + m^N) = 36 for N = 9 and N = 10), residual 16 with H = [1, 3, 6, 5, 1]
PASS (A4') r = 4, random D_5: beta = <g> one-dimensional, criterion hypotheses, realized CI of local length 36
  r = 3 gradient, random K (trial 0): dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 36 (dim S/(J + m^N) = 36 for N = 9 and N = 10), residual 16 with H = [1, 3, 6, 4, 2]
PASS (L') r = 3 gradient type, random K: <h,K> = 0, criterion hypotheses, realized, local length 36
  r = 3 gradient, random K (trial 1): dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 36 (dim S/(J + m^N) = 36 for N = 9 and N = 10), residual 16 with H = [1, 3, 6, 4, 2]
PASS (L') r = 3 gradient type, random K: <h,K> = 0, criterion hypotheses, realized, local length 36
  (L') type <Y^5, H>, trial 0: attempt 0 used; D_5 = [Y^5, -3*Y^5 - Y^4*Z - 5*Y^3*Z^2 - 2*Y^2*Z^3 - Y*Z^4 - 2*Z^5]; triple [2/7*y^3*z + 2/7*y^2*z^2 - y*z^3 + x^3, 7*y^4 + 2*y^3*z + 4*y^2*z^2 + 2*y*z^3 - z^4 + x*y^2, 4*y^3*z + 3*y^2*z^2 + y*z^3 + 3*z^4 + x*z^2]
  r = 3 type <Y^5, H> (trial 0): dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 38 (dim S/(J + m^N) = 38 for N = 11 and N = 12), residual 18 with H = [1, 3, 6, 4, 3, 1]
PASS (L') r = 3 type <Y^5, H>: h squarefree with simple root (1:0) = only common root with g, c != 0, realized, local length 38
  (L') type <Y^5, H>, trial 1: attempt 2 used; D_5 = [Y^5, 2*Y^5 + 4*Y^3*Z^2 + 3*Y^2*Z^3 - 3*Y*Z^4 + 3*Z^5]; triple [243/16*y^3*z - 9/4*y^2*z^2 - y*z^3 - 2*z^4 + x^3, 7*y^4 + 3*y^3*z - 5*y^2*z^2 - 5*y*z^3 + x*y^2, 5*y^3*z - 2*y^2*z^2 + y*z^3 - 2*z^4 + x*z^2]
  r = 3 type <Y^5, H> (trial 1): dim M = 20, closed True, H = [1, 3, 6, 4, 4, 2], triple in I True, local length 38 (dim S/(J + m^N) = 38 for N = 11 and N = 12), residual 18 with H = [1, 3, 6, 4, 3, 1]
PASS (L') r = 3 type <Y^5, H>: h squarefree with simple root (1:0) = only common root with g, c != 0, realized, local length 38
PASS (L) anchor hypotheses: h = y^6 - z^6 squarefree, g = y^2*z^2 nonzero at its roots
PASS (L) anchor hypotheses: h = y^6 - z^6 squarefree, g = y^4 + z^4 nonzero at its roots
total time 138.9 s
ALL CHECKS PASSED
