Part 1: psi = 0 (f = x^2, K = x r), one added element Q = sigma * (form of degree k nonzero at all roots): length = 24 + (k-2)*4
  ok   roots 1111, k = 4: length 32 (bound 32)
  ok   roots 1111, k = 5: length 36 (bound 36)
  ok   roots 1111, k = 6: length 40 (bound 40)
  ok   roots 1111, k = 7: length 44 (bound 44)
  ok   roots 211, k = 4: length 32 (bound 32)
  ok   roots 211, k = 5: length 36 (bound 36)
  ok   roots 211, k = 6: length 40 (bound 40)
  ok   roots 211, k = 7: length 44 (bound 44)
  ok   roots 22, k = 4: length 32 (bound 32)
  ok   roots 22, k = 5: length 36 (bound 36)
  ok   roots 22, k = 6: length 40 (bound 40)
  ok   roots 22, k = 7: length 44 (bound 44)
  ok   roots 31, k = 4: length 32 (bound 32)
  ok   roots 31, k = 5: length 36 (bound 36)
  ok   roots 31, k = 6: length 40 (bound 40)
  ok   roots 31, k = 7: length 44 (bound 44)
  ok   roots 4, k = 4: length 32 (bound 32)
  ok   roots 4, k = 5: length 36 (bound 36)
  ok   roots 4, k = 6: length 40 (bound 40)
  ok   roots 4, k = 7: length 44 (bound 44)
Part 2: different degrees at different roots (psi = 0): q4 = (y-z)(y+z) * (y^2 + y z + 3 z^2) vanishes at the roots 1, -1; Q6 = l^6
  ok   p = z(y-z)(y+z)(y-2z): length 36 <= 36
  ok   p = z^2(y-z)(y+z): length 36 <= 36
  ok   p = z^2 (y-z)^2: length 36 <= 36
Part 3: random higher-order terms, gamma_f = 0, Q = l^k (general sigma): length <= 24 + 4(k-2)
  ok   trial 0, k = 5: length 32 <= 36
  ok   trial 0, k = 6: length 32 <= 40
  ok   trial 0, k = 7: length 32 <= 44
  ok   trial 1, k = 5: length 32 <= 36
  ok   trial 1, k = 6: length 32 <= 40
  ok   trial 1, k = 7: length 32 <= 44
  ok   trial 2, k = 5: length 32 <= 36
  ok   trial 2, k = 6: length 32 <= 40
  ok   trial 2, k = 7: length 32 <= 44
  ok   trial 3, k = 5: length 32 <= 36
  ok   trial 3, k = 6: length 32 <= 40
  ok   trial 3, k = 7: length 32 <= 44
  ok   trial 4, k = 5: length 32 <= 36
  ok   trial 4, k = 6: length 32 <= 40
  ok   trial 4, k = 7: length 32 <= 44
  ok   trial 5, k = 5: length 33 <= 36
  ok   trial 5, k = 6: length 33 <= 40
  ok   trial 5, k = 7: length 33 <= 44
Part 4: psi(v,0) = 0 forced at all roots with nonzero higher terms (K = x r + k4, f = x^2 + x a + beta, beta chosen)
  ok   negative control, no added element: length -1 (infinite = -1, or > 32 expected; psi vanishes at the roots, the three are weighted homogeneous)
  ok   Q = l^5: length 36 <= 36
  ok   Q = l^6: length 40 <= 40
  ok   Q = l^7: length 44 <= 44
  ok   Q quartic nonzero at the roots: length 32 = 32
Part 5 (cor:variants(a)): turning direction W = z h3 with a simple zero at Y = [0:1:0] (a root of p of multiplicity e), P + nu l^7
  ok   roots 1111 (e_Y = 1), tau = 3, nu = 2: length 35 <= 35
  ok   roots 1111 (e_Y = 1), tau = -5, nu = 7: length 35 <= 35
   [info] without nu l^7 (information only; -1 = infinite): -1
  ok   roots 211 (e_Y = 2), tau = 3, nu = 2: length 35 <= 35
  ok   roots 211 (e_Y = 2), tau = -5, nu = 7: length 35 <= 35
   [info] without nu l^7 (information only; -1 = infinite): -1
  ok   roots 22 (e_Y = 2), tau = 3, nu = 2: length 35 <= 35
  ok   roots 22 (e_Y = 2), tau = -5, nu = 7: length 35 <= 35
   [info] without nu l^7 (information only; -1 = infinite): -1
  ok   roots 31 (e_Y = 3), tau = 3, nu = 2: length 35 <= 35
  ok   roots 31 (e_Y = 3), tau = -5, nu = 7: length 35 <= 35
   [info] without nu l^7 (information only; -1 = infinite): -1
  ok   roots 4 (e_Y = 4), tau = 3, nu = 2: length 35 <= 35
  ok   roots 4 (e_Y = 4), tau = -5, nu = 7: length 35 <= 35
   [info] without nu l^7 (information only; -1 = infinite): -1
Part 6: certification of two values by dim S/(C+m^N) = dim S/(C+m^(N+1))
  ok   roots 211, k = 5: certified 36 = 36
  ok   Part 5 roots 4: certified 35 <= 35
total time 0.7 s
ALL CHECKS PASSED
