Part T: actual algebras, turning by b^(s-1)
  (1,3,5,4,4,3,1) F = Y^6, p = z^4: H = [1, 3, 5, 4, 4, 3, 1], p = z^4, roots (V, mu, kappa) = [(Y, 4, 7)]; N1 bound 36, Theorem 3.15 bound 44
  ok   (1,3,5,4,4,3,1) F = Y^6, p = z^4 seed 1 t = 3: closed, H = [1, 3, 5, 4, 4, 3, 1]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 33 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 33; Theorem 3.15 bound 44
  ok   (1,3,5,4,4,3,1) F = Y^6, p = z^4 seed 2 t = 3: closed, H = [1, 3, 5, 4, 4, 3, 1]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 33 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 33; Theorem 3.15 bound 44
  (1,3,5,4,4,3,1) F = Y^6, p = y z^3: H = [1, 3, 5, 4, 4, 3, 1], p = y*z^3, roots (V, mu, kappa) = [(Y, 3, 7), (Z, 1, 6)]; N1 bound 36, Theorem 3.15 bound 43
  ok   (1,3,5,4,4,3,1) F = Y^6, p = y z^3 seed 1 t = 3: closed, H = [1, 3, 5, 4, 4, 3, 1]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 33 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 33; Theorem 3.15 bound 43
  ok   (1,3,5,4,4,3,1) F = Y^6, p = y z^3 seed 2 t = 3: closed, H = [1, 3, 5, 4, 4, 3, 1]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 33 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 33; Theorem 3.15 bound 43
  (1,3,5,4,4,3,1) F = Y^5 Z, p = y z^3: H = [1, 3, 5, 4, 4, 3, 1], p = y*z^3, roots (V, mu, kappa) = [(Y, 3, 6), (Z, 1, 6)]; N1 bound 36, Theorem 3.15 bound 40
  ok   (1,3,5,4,4,3,1) F = Y^5 Z, p = y z^3 seed 1 t = 3: closed, H = [1, 3, 5, 4, 4, 3, 1]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 40
  ok   (1,3,5,4,4,3,1) F = Y^5 Z, p = y z^3 seed 2 t = 3: closed, H = [1, 3, 5, 4, 4, 3, 1]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 40
  (1,3,5,4,4,2,2) tangent Gamma at [Y], p = z^4: H = [1, 3, 5, 4, 4, 2, 2], p = z^4, roots (V, mu, kappa) = [(Y, 4, 7)]; N1 bound 36, Theorem 3.15 bound 44
  ok   (1,3,5,4,4,2,2) tangent Gamma at [Y], p = z^4 seed 1 t = 3: closed, H = [1, 3, 5, 4, 4, 2, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 35 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 35; Theorem 3.15 bound 44
  ok   (1,3,5,4,4,2,2) tangent Gamma at [Y], p = z^4 seed 2 t = 3: closed, H = [1, 3, 5, 4, 4, 2, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 44
  (1,3,5,4,4,2,2) secant Gamma = {[Y],[Z]}, p = y z^3: H = [1, 3, 5, 4, 4, 2, 2], p = y*z^3, roots (V, mu, kappa) = [(Y, 3, 7), (Z, 1, 7)]; N1 bound 36, Theorem 3.15 bound 44
  ok   (1,3,5,4,4,2,2) secant Gamma = {[Y],[Z]}, p = y z^3 seed 1 t = 3: closed, H = [1, 3, 5, 4, 4, 2, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 44
  ok   (1,3,5,4,4,2,2) secant Gamma = {[Y],[Z]}, p = y z^3 seed 2 t = 3: closed, H = [1, 3, 5, 4, 4, 2, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 44
  (1,3,5,4,4,2,2) secant Gamma, p = y^2 z^2: H = [1, 3, 5, 4, 4, 2, 2], p = y^2*z^2, roots (V, mu, kappa) = [(Y, 2, 7), (Z, 2, 7)]; N1 bound 36, Theorem 3.15 bound 44
  ok   (1,3,5,4,4,2,2) secant Gamma, p = y^2 z^2 seed 1 t = 3: closed, H = [1, 3, 5, 4, 4, 2, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 44
  ok   (1,3,5,4,4,2,2) secant Gamma, p = y^2 z^2 seed 2 t = 3: closed, H = [1, 3, 5, 4, 4, 2, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 36
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 44
  (1,3,5,4,3,3,2) Gamma_3 = 3[Y], p = z^3 (y - z): H = [1, 3, 5, 4, 3, 3, 2], p = y*z^3 - z^4, roots (V, mu, kappa) = [(Y, 3, 7), (Y + Z, 1, 4)]; N1 bound 35, Theorem 3.15 bound 41
  ok   (1,3,5,4,3,3,2) Gamma_3 = 3[Y], p = z^3 (y - z) seed 1 t = 3: closed, H = [1, 3, 5, 4, 3, 3, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 35
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 41
  ok   (1,3,5,4,3,3,2) Gamma_3 = 3[Y], p = z^3 (y - z) seed 2 t = 3: closed, H = [1, 3, 5, 4, 3, 3, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 35
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 41
  (1,3,5,4,3,3,2) Gamma_3 = {[Y],[Z],[Y+Z]}, p = y z (y - z)(y + z): H = [1, 3, 5, 4, 3, 3, 2], p = y^3*z - y*z^3, roots (V, mu, kappa) = [(Y, 1, 7), (Z, 1, 7), (Y + Z, 1, 6), (Y - Z, 1, 4)]; N1 bound 35, Theorem 3.15 bound 40
  ok   (1,3,5,4,3,3,2) Gamma_3 = {[Y],[Z],[Y+Z]}, p = y z (y - z)(y + z) seed 1 t = 3: closed, H = [1, 3, 5, 4, 3, 3, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 35
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 40
  ok   (1,3,5,4,3,3,2) Gamma_3 = {[Y],[Z],[Y+Z]}, p = y z (y - z)(y + z) seed 2 t = 3: closed, H = [1, 3, 5, 4, 3, 3, 2]; gamma_f = 0; u = b^5 in (I:m^2); colength I_0 = 21, I_t = 21 (d = 21); G, K_r, P in I_t: True; local length 34 (local standard basis) <= 35
       (info) the same triple at t = 0 (no turning): local length 34; Theorem 3.15 bound 40
Part G: graded members (all tails zero), the extreme cases; certified by ds and by a stable pair
  ok   (1,3,5,4,4,3,1) F = Y^6, p = z^4 graded: closed True, H [1, 3, 5, 4, 4, 3, 1]; t = 0: local length -1 (Theorem 3.15 bound 44); t = 3: 36 (stable N = 10) <= N1 bound 36
  ok   (1,3,5,4,4,2,2) tangent, p = z^4 graded: closed True, H [1, 3, 5, 4, 4, 2, 2]; t = 0: local length -1 (Theorem 3.15 bound 44); t = 3: 36 (stable N = 10) <= N1 bound 36
  ok   (1,3,5,4,4,2,2) secant, p = y z^3 graded: closed True, H [1, 3, 5, 4, 4, 2, 2]; t = 0: local length -1 (Theorem 3.15 bound 44); t = 3: 36 (stable N = 10) <= N1 bound 36
  ok   (1,3,5,4,3,3,2) Gamma_3 = 3[Y], p = z^3 (y - z) graded: closed True, H [1, 3, 5, 4, 3, 3, 2]; t = 0: local length -1 (Theorem 3.15 bound 41); t = 3: 35 (stable N = 10) <= N1 bound 35
accepted samples: 16
total time 21.4 s
ALL CHECKS PASSED
