random choices: random.Random(136631), consumed in the order of the script; the attempts used are printed
  h = 6: six general fifth powers: attempts used (D_3, w_i, L) = (0, 0, 0); D_3 = [59/24*X^3 - 527/8*X^2*Y + 167/8*X*Y^2 - 809/24*Y^3 + Z^3, 37/72*X^3 - 289/24*X^2*Y + 97/24*X*Y^2 - 415/72*Y^3 + Y*Z^2, -43/18*X^3 + 349/6*X^2*Y - 109/6*X*Y^2 + 535/18*Y^3 + X*Z^2, -11/12*X^3 + 71/4*X^2*Y - 27/4*X*Y^2 + 113/12*Y^3 + Y^2*Z, -29/144*X^3 + 113/48*X^2*Y - 41/48*X*Y^2 + 95/144*Y^3 + X*Y*Z, 47/24*X^3 - 211/8*X^2*Y + 75/8*X*Y^2 - 325/24*Y^3 + X^2*Z]; L = 7*x + 9*y + 5*z; w_1, w_2, w_3 + L^4 = [2375/693*x^3 - 59/63*x^2*y - 563/231*x*y^2 + 103/231*y^3 - 2683/693*x^2*z + 1817/693*x*y*z - 3*y^2*z - 5*x*z^2 + y*z^2 + 3*z^3, -3394/231*x^3 + 16/21*x^2*y + 681/77*x*y^2 + 13/77*y^3 + 7013/231*x^2*z - 1594/231*x*y*z + y^2*z - 4*x*z^2 - y*z^2 - 3*z^3, 2401*x^4 + 12348*x^3*y + 23814*x^2*y^2 + 20412*x*y^3 + 6561*y^4 + 6860*x^3*z + 26460*x^2*y*z + 34020*x*y^2*z + 14580*y^3*z + 7350*x^2*z^2 + 18900*x*y*z^2 + 12150*y^2*z^2 + 3500*x*z^3 + 4500*y*z^3 + 625*z^4 - 10942/693*x^3 + 334/63*x^2*y + 985/231*x*y^2 - 881/231*y^3 + 26111/693*x^2*z - 15010/693*x*y*z - y^2*z - 4*x*z^2 + 5*y*z^2 - 3*z^3]
PASS h = 6: six general fifth powers: concise, h = 6, H = [1, 3, 6, 6, 3, 1], (c1) True, (c2) True, w_1, w_2, w_3 + L^4 in I, colength 36  [1.0s]
  h = 5: five fifth powers: attempts used (D_3, w_i, L) = (0, 0, 0); D_3 = [Z^3, 6/7*X^2*Y + 1/7*X*Y^2 + 3/14*X^2*Z + 11/7*X*Y*Z + Y*Z^2, 15/14*X^2*Y - 1/14*X*Y^2 + 9/14*X^2*Z + 5/7*X*Y*Z + X*Z^2, -13/14*X^2*Y + 13/14*X*Y^2 + 1/7*X^2*Z - 2/7*X*Y*Z + Y^2*Z, Y^3, X^3]; L = 9*x + 7*y + z; w_1, w_2, w_3 + L^4 = [73/6*x^2*y + 27/2*x*y^2 - 59/3*x^2*z - 4*x*y*z + y^2*z + 2*x*z^2 - 5*y*z^2, 21/4*x^2*y + 41/4*x*y^2 - 31/2*x^2*z + 3*x*y*z - 2*y^2*z + 4*x*z^2 - 5*y*z^2, 6561*x^4 + 20412*x^3*y + 23814*x^2*y^2 + 12348*x*y^3 + 2401*y^4 + 2916*x^3*z + 6804*x^2*y*z + 5292*x*y^2*z + 1372*y^3*z + 486*x^2*z^2 + 756*x*y*z^2 + 294*y^2*z^2 + 36*x*z^3 + 28*y*z^3 + z^4 + 1/4*x^2*y + 21/4*x*y^2 - 11/2*x^2*z - x*y*z - 4*y^2*z + 4*x*z^2 + y*z^2]
PASS h = 5: five fifth powers: concise, h = 5, H = [1, 3, 6, 6, 3, 1], (c1) True, (c2) True, w_1, w_2, w_3 + L^4 in I, colength 36  [1.4s]
  h = 4, V without common factor: four fifth powers: attempts used (D_3, w_i, L) = (0, 0, 0); D_3 = [Z^3, 10/19*X^2*Y - 11/19*X*Y^2 - 31/38*X^2*Z - 43/38*X*Y*Z + Y*Z^2, -6/19*X^2*Y + 18/19*X*Y^2 + 15/19*X^2*Z + 30/19*X*Y*Z + X*Z^2, 15/19*X^2*Y + 12/19*X*Y^2 + 39/38*X^2*Z + 59/38*X*Y*Z + Y^2*Z, Y^3, X^3]; L = 4*x + 2*y + 8*z; w_1, w_2, w_3 + L^4 = [-29/12*x^2*y + 3/4*x*y^2 - 13/3*x^2*z + 5*x*y*z + 2*y^2*z - 2*x*z^2 + y*z^2, 11/12*x^2*y + 31/4*x*y^2 - 8/3*x^2*z - 5*x*y*z + y^2*z - x*z^2 - y*z^2, 256*x^4 + 512*x^3*y + 384*x^2*y^2 + 128*x*y^3 + 16*y^4 + 2048*x^3*z + 3072*x^2*y*z + 1536*x*y^2*z + 256*y^3*z + 6144*x^2*z^2 + 6144*x*y*z^2 + 1536*y^2*z^2 + 8192*x*z^3 + 4096*y*z^3 + 4096*z^4 + 77/12*x^2*y + 25/4*x*y^2 - 14/3*x^2*z + x*y*z - 5*y^2*z - x*z^2 - 3*y*z^2]
PASS h = 4, V without common factor: four fifth powers: concise, h = 4, H = [1, 3, 6, 6, 3, 1], (c1) True, (c2) True, w_1, w_2, w_3 + L^4 in I, colength 36  [1.7s]
  h = 4, V = x<y, z>: X^5 + Y^5 + Z^5 + (Y + Z)^5: attempts used (D_3, w_i, L) = (0, 0, 0); D_3 = [Z^3, 1/2*X*Y^2 - X^2*Z + 3*X*Y*Z + Y*Z^2, 4/5*X^2*Y + X^2*Z - 8/5*X*Y*Z + X*Z^2, -1/2*X*Y^2 + X^2*Z - 3*X*Y*Z + Y^2*Z, Y^3, X^3]; L = 7*x + 4*y + 7*z; w_1, w_2, w_3 + L^4 = [-7/2*x^2*y + 11*x*y^2 - x^2*z - x*y*z + 5*y^2*z + 3*x*z^2 - 5*y*z^2, -11/2*x^2*y + 13*x*y^2 - 2*x^2*z - 3*x*y*z + 4*y^2*z + 4*x*z^2 - 4*y*z^2, 2401*x^4 + 5488*x^3*y + 4704*x^2*y^2 + 1792*x*y^3 + 256*y^4 + 9604*x^3*z + 16464*x^2*y*z + 9408*x*y^2*z + 1792*y^3*z + 14406*x^2*z^2 + 16464*x*y*z^2 + 4704*y^2*z^2 + 9604*x*z^3 + 5488*y*z^3 + 2401*z^4 + 1/2*x^2*y + 6*x*y^2 - 3*x^2*z - 2*x*y*z + 3*y^2*z + x*z^2 - 3*y*z^2]
PASS h = 4, V = x<y, z>: X^5 + Y^5 + Z^5 + (Y + Z)^5: concise, h = 4, H = [1, 3, 6, 6, 3, 1], (c1) True, (c2) True, w_1, w_2, w_3 + L^4 in I, colength 36  [2.0s]
  h = 3: X^5 + Y^5 + Z^5: attempts used (D_3, w_i, L) = (0, 0, 0); D_3 = [Z^3, 19/4*X^2*Y + 17/3*X*Y^2 + 21/2*X^2*Z + 83/12*X*Y*Z + Y*Z^2, 13/4*X^2*Y + 10/3*X*Y^2 + 15/2*X^2*Z + 61/12*X*Y*Z + X*Z^2, 3/4*X^2*Y - X*Y^2 - 1/2*X^2*Z + 1/4*X*Y*Z + Y^2*Z, Y^3, X^3]; L = 6*x + 5*y + 2*z; w_1, w_2, w_3 + L^4 = [620/101*x^2*y + 381/101*x*y^2 - 438/101*x^2*z - 3*y^2*z - 5*y*z^2, -627/202*x^2*y - 109/101*x*y^2 + 177/101*x^2*z + x*y*z + 2*y^2*z - 2*x*z^2 - y*z^2, 1296*x^4 + 4320*x^3*y + 5400*x^2*y^2 + 3000*x*y^3 + 625*y^4 + 1728*x^3*z + 4320*x^2*y*z + 3600*x*y^2*z + 1000*y^3*z + 864*x^2*z^2 + 1440*x*y*z^2 + 600*y^2*z^2 + 192*x*z^3 + 160*y*z^3 + 16*z^4 - 331/101*x^2*y + 46/101*x*y^2 + 68/101*x^2*z + 2*x*y*z + 3*y^2*z - x*z^2 - y*z^2]
PASS h = 3: X^5 + Y^5 + Z^5: concise, h = 3, H = [1, 3, 6, 6, 3, 1], (c1) True, (c2) True, w_1, w_2, w_3 + L^4 in I, colength 36  [2.4s]
total time 2.4 s
ALL CHECKS PASSED
