(S1) actual algebras in normal form
    sample 0 (secant): H = [1, 3, 6, 5, 2, 2, 1, 1, 1, 1], skipped
    sample 1 (tangent): H ok; X^5 in M: True; x^5y, x^5z in Ann(M): True
  [ok] sample 1: ray conditions of Lemma 5.4 with k = 5
    sample 2 (secant): H ok; X^5 in M: True; x^5y, x^5z in Ann(M): True
  [ok] sample 2: ray conditions of Lemma 5.4 with k = 5
    sample 3 (tangent): H = [1, 3, 6, 4, 2, 2, 1, 1, 1, 1], skipped
    sample 4 (secant): H = [1, 3, 6, 4, 2, 2, 1, 1, 1, 1], skipped
    sample 5 (tangent): H ok; X^5 in M: True; x^5y, x^5z in Ann(M): True
  [ok] sample 5: ray conditions of Lemma 5.4 with k = 5
    sample 6 (secant): H = [1, 3, 6, 5, 2, 2, 1, 1, 1, 1], skipped
    sample 7 (tangent): H ok; X^5 in M: True; x^5y, x^5z in Ann(M): True
  [ok] sample 7: ray conditions of Lemma 5.4 with k = 5
    sample 8 (secant): H = [1, 3, 6, 4, 2, 2, 1, 1, 1, 1], skipped
    sample 9 (tangent): H = [1, 3, 6, 4, 2, 2, 1, 1, 1, 1], skipped
    sample 10 (secant): H = [1, 3, 6, 4, 2, 2, 1, 1, 1, 1], skipped
    sample 11 (tangent): H ok; X^5 in M: True; x^5y, x^5z in Ann(M): True
  [ok] sample 11: ray conditions of Lemma 5.4 with k = 5
    accepted samples (S1): 5
  [ok] at least 4 accepted samples in (S1)
(S3) negative control at s = 8
    H = [1, 3, 6, 3, 2, 2, 1, 1, 1]
  [ok] s = 8, Gamma_0, delta != 0: X^5 not in M (straight ray criterion fails, so s >= 2k0-1 is needed)
7 checks, 0 failed
ALL CHECKS PASSED
