random choices: random.Random(136721), consumed in the order of the script; the attempts used are printed
  G_3: F = X^5 + Y^5 + (X+Y)^5 (dim S_2 o F = 3): attempt 0 used for K = [-X^3 + 3*X^2*Y - 3*X*Y^2 + 3*Y^3 - 5*X^2*Z + 5*X*Y*Z - 2*Y^2*Z + 4*X*Z^2 - 4*Y*Z^2 - 2*Z^3, -3*X^3 - 2*X^2*Y + 3*X*Y^2 + 2*Y^3 - 5*X^2*Z - X*Y*Z - 4*X*Z^2 + 2*Y*Z^2 - 5*Z^3, -X^3 - 2*X^2*Y - X*Y^2 - Y^3 + X^2*Z - 4*X*Y*Z + Y^2*Z + Y*Z^2 - Z^3, 3*X^3 + 2*X^2*Y - 5*X*Y^2 - 3*Y^3 + 2*X^2*Z + X*Y*Z + 2*Y^2*Z + 4*X*Z^2 - 2*Y*Z^2 + 4*Z^3]
  G_3: F = X^5 + Y^5 + (X+Y)^5 (dim S_2 o F = 3): random tail R (attempt 1) = 4*X^4 + 2*X^3*Y - 3*X^2*Y^2 + 3*X*Y^3 + 2*Y^4 - 2*X^3*Z - 361/36*X^2*Y*Z + 2*X*Y^2*Z + 331/18*X^2*Z^2 - 1903/72*X*Y*Z^2 + 2*Y^2*Z^2 + 3*X*Z^3 + 3*Y*Z^3
PASS (A,B) G_3: F = X^5 + Y^5 + (X+Y)^5 (dim S_2 o F = 3): dim S_2 o F = 3, random tails give H = [1, 3, 6, 7, 2, 1], dim (z I*_3)^perp = 12  [0.7s]
  attempts used (w_i, L) = (0, 0); L = 2*x + 8*y + 7*z; w_1, w_2, w_3 + L^4 = [37/47*x^2*y - 37/47*x*y^2 - 1057/141*x^2*z - 1538/141*x*y*z - 354/47*y^2*z + 3*y*z^2 + 3*z^3, -295/141*x^2*y + 295/141*x*y^2 - 5261/423*x^2*z - 7066/423*x*y*z - 426/47*y^2*z + 2*x*z^2 + y*z^2 + 5*z^3, 16*x^4 + 256*x^3*y + 1536*x^2*y^2 + 4096*x*y^3 + 4096*y^4 + 224*x^3*z + 2688*x^2*y*z + 10752*x*y^2*z + 14336*y^3*z + 1176*x^2*z^2 + 9408*x*y*z^2 + 18816*y^2*z^2 + 2744*x*z^3 + 10976*y*z^3 + 2401*z^4 + 620/141*x^2*y - 620/141*x*y^2 + 4246/423*x^2*z + 4928/423*x*y*z + 219/47*y^2*z - 4*x*z^2 + y*z^2 - 4*z^3]
PASS (A) G_3: F = X^5 + Y^5 + (X+Y)^5 (dim S_2 o F = 3): (c1) coprime True, (c2) no linear syzygy True; member of the global linkage construction: H = [1, 3, 6, 7, 2, 1], w1, w2, w3 + L^4 in I, colength 36  [1.3s]
  G_2: F = X^5 + 2 Y^5 (dim S_2 o F = 2): attempt 0 used for K = [-2*X^3 - 4*X^2*Y - 5*X*Y^2 + X^2*Z - X*Y*Z + Y^2*Z + 5*X*Z^2 - 4*Y*Z^2 + 3*Z^3, 5*X^3 + 4*X^2*Y - X*Y^2 - 4*Y^3 + X^2*Z - 2*X*Y*Z + Y^2*Z + 5*X*Z^2 + 2*Y*Z^2 + 2*Z^3, 2*X^3 - 4*X^2*Y + X*Y^2 + 2*Y^3 - 5*X^2*Z + 4*Y^2*Z + 3*X*Z^2 + 3*Y*Z^2 + 4*Z^3, -2*X^3 - X^2*Y + X*Y^2 - 3*X^2*Z + 3*X*Y*Z - Y^2*Z + 4*X*Z^2 + 4*Y*Z^2 - 2*Z^3, -4*X^2*Y - 4*X*Y^2 - Y^3 - 5*X^2*Z - 3*X*Y*Z + 2*Y^2*Z - 3*X*Z^2 + Y*Z^2 + 3*Z^3]
  G_2: F = X^5 + 2 Y^5 (dim S_2 o F = 2): random tail R (attempt 1) = 4*X^3*Y - X^2*Y^2 + 2*X*Y^3 + 2*Y^4 + 3*X^3*Z + 37901/253*X^2*Y*Z + 55337/506*X*Y^2*Z + 11933/253*X^2*Z^2 - Y^2*Z^2 - 2*X*Z^3 + 5*Y*Z^3 - 5*Z^4
PASS (A,B) G_2: F = X^5 + 2 Y^5 (dim S_2 o F = 2): dim S_2 o F = 2, random tails give H = [1, 3, 6, 7, 2, 1], dim (z I*_3)^perp = 12  [1.8s]
  attempts used (w_i, L) = (0, 0); L = 6*x + 2*y + 7*z; w_1, w_2, w_3 + L^4 = [-1273/1747*x^2*y + 9240/1747*x*y^2 - 6865/1747*x^2*z - 19822/1747*x*y*z - 16095/1747*y^2*z + 2*x*z^2 - 3*y*z^2 + z^3, 7992/1747*x^2*y + 1394/1747*x*y^2 - 10907/1747*x^2*z + 13240/1747*x*y*z - 9921/1747*y^2*z - 5*y*z^2 + 2*z^3, 1296*x^4 + 1728*x^3*y + 864*x^2*y^2 + 192*x*y^3 + 16*y^4 + 6048*x^3*z + 6048*x^2*y*z + 2016*x*y^2*z + 224*y^3*z + 10584*x^2*z^2 + 7056*x*y*z^2 + 1176*y^2*z^2 + 8232*x*z^3 + 2744*y*z^3 + 2401*z^4 - 18899/1747*x^2*y + 17654/1747*x*y^2 + 7358/1747*x^2*z - 66814/1747*x*y*z - 19356/1747*y^2*z + 4*x*z^2 + 4*y*z^2 - z^3]
PASS (A) G_2: F = X^5 + 2 Y^5 (dim S_2 o F = 2): (c1) coprime True, (c2) no linear syzygy True; member of the global linkage construction: H = [1, 3, 6, 7, 2, 1], w1, w2, w3 + L^4 in I, colength 36  [2.1s]
total time 2.1 s
ALL CHECKS PASSED
