  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)
  F = 2*Y^5 - 5*Y^4*Z + 10*Y^3*Z^2 - 10*Y^2*Z^3 + 5*Y*Z^4, gamma = y^2*z + y*z^2: dim M = 20, closed True, H = [1, 3, 6, 4, 5, 1], 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 (R) realization for F = 2*Y^5 - 5*Y^4*Z + 10*Y^3*Z^2 - 10*Y^2*Z^3 + 5*Y*Z^4 (gamma = y^2*z + y*z^2): complete intersection of local length 39, residual 19
  F = Y^5, gamma = y^2*z + y*z^2: dim M = 20, closed True, H = [1, 3, 6, 4, 5, 1], 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 (R) realization for F = Y^5 (gamma = y^2*z + y*z^2): complete intersection of local length 39, residual 19
  F = Y^5 + Y*Z^4 + Z^5, gamma = y^2*z: dim M = 20, closed True, H = [1, 3, 6, 4, 5, 1], 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 (R) realization for F = Y^5 + Y*Z^4 + Z^5 (gamma = y^2*z): complete intersection of local length 39, residual 19
  F = Y^2*Z^3 + Z^5, gamma = y^3: dim M = 20, closed True, H = [1, 3, 6, 4, 5, 1], 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 (R) realization for F = Y^2*Z^3 + Z^5 (gamma = y^3): complete intersection of local length 39, residual 19
PASS (Q) sanity: random binary quintic F = 4*Y^5 - 4*Y^4*Z - 5*Y^3*Z^2 + Y^2*Z^3 + 4*Y*Z^4 - 2*Z^5 (Python random.seed(136451) at the start): dim C[y,z]_2 o F = 3 <= 3, so a binary cubic kills F
total time 52.4 s
ALL CHECKS PASSED
