PASS (A) w o F = 0 for w = x^3, F = Y^4 + Z^4 + X^2 Y Z (so S_1 o F lies in D_3 = w^perp)  [0.0s]
PASS (A) x o F, z o F, Y^3 linearly independent: the open condition (no (v, lambda) != 0 with v o F = lambda P^3)  [0.1s]
PASS (A) random tail 0: H = [1, 3, 6, 9, 1], inverse-system ray along Y with k = 3  [0.3s]
PASS (A) random tail 1: H = [1, 3, 6, 9, 1], inverse-system ray along Y with k = 3  [0.6s]
PASS (A) random tail 2: H = [1, 3, 6, 9, 1], inverse-system ray along Y with k = 3  [0.8s]
PASS (B) 13682 anchor: H = [1, 3, 6, 8, 2], x^3, y^3, z^4 in I, local length 36, residual 16 with H = [1, 3, 6, 6]  [3.2s]
PASS (C) alpha anchor: H = [1, 3, 6, 5, 5], Q = x o X^2Y has rank 2, dim D_3' = 5  [6.8s]
PASS (C) alpha anchor: f_1, f_2, f_3 of the (1,3,6,4,5) anchor lie in I, local length 36 < 40, residual 16 with H = [1, 3, 6, 4, 2]  [6.8s]
PASS (D) D_3' = C[Y,Z]_4 + C X^4 (P = X), = C[Y,Z]_4 + C X Y^3 (P = Y on the line): dimensions 6, 6  [6.9s]
PASS (D) rank(Q) = 2: dim D_3' = 5 (so D_4 = C[Y,Z]_4)  [6.9s]
PASS (D) rank(Q) = 3: dim D_3' = 5 (so D_4 = C[Y,Z]_4)  [7.0s]
PASS (D) beta, P = X, random D_4 and tails: H = [1, 3, 6, 5, 5], ray along X with k = 3  [7.1s]
PASS (D) beta, P = X, random D_4 and tails: H = [1, 3, 6, 5, 5], ray along X with k = 3  [7.3s]
PASS (D) beta, P = X, random D_4 and tails: H = [1, 3, 6, 5, 5], ray along X with k = 3  [7.5s]
PASS (D) degeneration P_t = Y + tX: D_3(t) = C[Y,Z]_3 + C g_t, D_3'(t) = C[Y,Z]_4 + C h_t of dimensions 5, 6 at t = 0, 1/3, -2, 5  [7.7s]
  (E) random choices: random.Random(2020), consumed in the order of the script
  (E) (c, e) = (7, 3): attempt 0 used (w_1, w_2 from try 0); points [X + Y, 4*X - Y + 2*Z, -5*Y - 3*Z], L = 8*x + 9*y + 6*z; w_1, w_2, w_3 + L^4 = [137592217/22406975*x^3 - 4881277/22406975*x^2*y - 195648852/22406975*x*y^2 + 62937912/22406975*y^3 - 70127859/4481395*x^2*z - 95038292/22406975*x*y*z - 88763498/22406975*y^2*z + 5*x*z^2 - 3*y*z^2 + 3*z^3, -56409599/22406975*x^3 - 10844506/22406975*x^2*y + 79485069/22406975*x*y^2 - 12230964/22406975*y^3 + 24168913/4481395*x^2*z - 55794426/22406975*x*y*z + 68784006/22406975*y^2*z - 4*x*z^2 - 3*y*z^2 - z^3, 4096*x^4 + 18432*x^3*y + 31104*x^2*y^2 + 23328*x*y^3 + 6561*y^4 + 12288*x^3*z + 41472*x^2*y*z + 46656*x*y^2*z + 17496*y^3*z + 13824*x^2*z^2 + 31104*x*y*z^2 + 17496*y^2*z^2 + 6912*x*z^3 + 7776*y*z^3 + 1296*z^4 - 44037409/22406975*x^3 + 29076679/22406975*x^2*y + 35631054/22406975*x*y^2 - 20670324/22406975*y^3 + 30150133/4481395*x^2*z - 66591716/22406975*x*y*z + 2184496/22406975*y^2*z - 5*x*z^2 + 3*y*z^2 - z^3]
PASS (E) global linkage sanity (1,3,6,7,3): H = [1, 3, 6, 7, 3], w1, w2 coprime True, CI in I True, global colength 36  [8.0s]
  (E) (c, e) = (6, 4): attempt 0 used (w_1, w_2 from try 0); points [3*X + Y - 4*Z, -3*X - 5*Y + 4*Z, -2*X - 3*Y + 4*Z, -X + 4*Y + 4*Z], L = x + 8*y + 6*z; w_1, w_2, w_3 + L^4 = [183069676/35455887*x^3 - 62411876/11818629*x^2*y + 13326860/3939543*x*y^2 - 45684500/11818629*y^3 + 87291035/35455887*x^2*z - 669127856/35455887*x*y*z + 3*y^2*z - 5*x*z^2 - 3*y*z^2 - z^3, 8389744/1313181*x^3 - 11174828/437727*x^2*y + 777436/145909*x*y^2 - 2332076/437727*y^3 - 4362424/1313181*x^2*z - 31846112/1313181*x*y*z - y^2*z - 2*x*z^2 - y*z^2 + 4*z^3, x^4 + 32*x^3*y + 384*x^2*y^2 + 2048*x*y^3 + 4096*y^4 + 24*x^3*z + 576*x^2*y*z + 4608*x*y^2*z + 12288*y^3*z + 216*x^2*z^2 + 3456*x*y*z^2 + 13824*y^2*z^2 + 864*x*z^3 + 6912*y*z^3 + 1296*z^4 - 13546472/3939543*x^3 + 40607644/1313181*x^2*y - 3933412/437727*x*y^2 + 4246036/1313181*y^3 + 29431238/3939543*x^2*z + 58041106/3939543*x*y*z + y^2*z + x*z^2 - y*z^2 - 4*z^3]
PASS (E) global linkage sanity (1,3,6,6,4): H = [1, 3, 6, 6, 4], w1, w2 coprime True, CI in I True, global colength 36  [8.3s]
  (E) (c, e) = (5, 5): attempt 0 used (w_1, w_2 from try 0); points [X + 5*Y + 2*Z, -4*X - 3*Y, X - Y - Z, 4*X + 5*Y - Z, 5*X + 5*Y + 3*Z], L = x + 4*y + 9*z; w_1, w_2, w_3 + L^4 = [344919/190250*x^3 - 435646/475625*x^2*y - 4218871/951250*x*y^2 + 1543098/475625*y^3 + 670582/95125*x^2*z - x*y*z - 4*y^2*z + 3*x*z^2 - 5*y*z^2 - z^3, 1784259/761000*x^3 - 5727603/951250*x^2*y + 15775569/3805000*x*y^2 - 362811/951250*y^3 + 465463/95125*x^2*z - 3*x*y*z - 4*x*z^2 + z^3, x^4 + 16*x^3*y + 96*x^2*y^2 + 256*x*y^3 + 256*y^4 + 36*x^3*z + 432*x^2*y*z + 1728*x*y^2*z + 2304*y^3*z + 486*x^2*z^2 + 3888*x*y*z^2 + 7776*y^2*z^2 + 2916*x*z^3 + 11664*y*z^3 + 6561*z^4 - 118077/76100*x^3 + 454384/95125*x^2*y - 1934307/380500*x*y^2 + 186833/95125*y^3 + 30897/19025*x^2*z + x*y*z - y^2*z + 4*x*z^2 - 4*y*z^2 - 5*z^3]
PASS (E) global linkage sanity (1,3,6,5,5): H = [1, 3, 6, 5, 5], w1, w2 coprime True, CI in I True, global colength 36  [8.5s]
total time 8.5 s
ALL CHECKS PASSED
