(R2) r = 2
  ok   (U) (R2) F1 two points of the line (off-line)                  r = 2, dim Syz 4, dim W.Syz 16, tails [16, 16] (expected 16), H ok True   [0.5s]
  ok   (U) (R2) F1 double point on the line (off-line)                r = 2, dim Syz 4, dim W.Syz 16, tails [16, 16] (expected 16), H ok True   [0.9s]
  ok   (U) (R2) F1 two points of the line, not q (embedded)           r = 2, dim Syz 4, dim W.Syz 16, tails [16, 16] (expected 16), H ok True   [1.3s]
  ok   (U) (R2) F1 double point at N != q (embedded)                  r = 2, dim Syz 4, dim W.Syz 16, tails [16, 16] (expected 16), H ok True   [1.8s]
  ok   (U) (R2) W2 {N, q} (off-line)                                  r = 2, dim Syz 4, dim W.Syz 15, tails [17, 17] (expected 17), H ok True   [2.1s]
  ok   (U) (R2) W2 {N, q} (embedded)                                  r = 2, dim Syz 4, dim W.Syz 15, tails [17, 17] (expected 17), H ok True   [2.4s]
  ok   (U) (R2) W2 double point at q along the line                   r = 2, dim Syz 4, dim W.Syz 15, tails [17, 17] (expected 17), H ok True   [2.8s]
  ok   (U) (R2) W2 double point at q transverse                       r = 2, dim Syz 4, dim W.Syz 15, tails [17, 17] (expected 17), H ok True   [3.1s]
(R3) r = 3
  ok   (S) (R3) (B) gradient pencil S_1 o K (off-line)                r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [3.4s]
  ok   (S) (R3) (B) gradient pencil S_1 o K (embedded) [emb]          r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [3.7s]
  ok   (S) (R3) (B) <Y^5, H> (off-line)                               r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [4.1s]
  ok   (S) (R3) (B) <Y^5, H> (embedded) [emb]                         r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [4.4s]
  ok   (U) (R3) (B) pencil in nu_5{Y, Y+Z, Z} [emb]                   r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [4.7s]
  ok   (U) (R3) (B) <YZ^4, Y^2Z^3> [emb]                              r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [5.1s]
  ok   (S) (R3) (Q) <X^5, G> (off-line)                               r = 3, dim Syz 3, dim W.Syz 12, tails [15, 15] (expected 15), H ok True   [5.5s]
  ok   (S) (R3) (Q) <Z^5, H> (embedded) [emb]                         r = 3, dim Syz 3, dim W.Syz 12, tails [15, 15] (expected 15), H ok True   [6.0s]
  ok   (S) (R3) (Q) <Z^5, XZ^4 + G1> [emb]                            r = 3, dim Syz 3, dim W.Syz 12, tails [15, 15] (expected 15), H ok True   [6.3s]
  ok   (U) (R3) (Q) <Z^5, XZ^4 + Y^2Z^3> [emb]                        r = 3, dim Syz 3, dim W.Syz 12, tails [15, 15] (expected 15), H ok True   [6.8s]
  ok   (U) (R3) (U) <Y^5 + X^5, Z^5 + X^5> (off-line)                 r = 3, dim Syz 3, dim W.Syz 14, tails [13, 13] (expected 13), H ok True   [7.1s]
  ok   (U) (R3) (U) <Y^5 + X^5, Y^4Z> (off-line double)               r = 3, dim Syz 3, dim W.Syz 14, tails [13, 13] (expected 13), H ok True   [7.4s]
  ok   (U) (R3) (U) (i) <XZ^4, Y^5 + Z^5> [emb]                       r = 3, dim Syz 3, dim W.Syz 14, tails [13, 13] (expected 13), H ok True   [7.7s]
  ok   (U) (R3) (U) (iii) <XZ^4, YZ^4> [emb]                          r = 3, dim Syz 3, dim W.Syz 14, tails [13, 13] (expected 13), H ok True   [8.1s]
  ok   (U) (R3) (V) <Y^5, Z^5 + X^5> (off-line)                       r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [8.5s]
  ok   (U) (R3) (V) <Y^5, Y^4Z + X^5> (off-line double)               r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [8.9s]
  ok   (U) (R3) (V) <XZ^4, Y^5> (embedded) [emb]                      r = 3, dim Syz 3, dim W.Syz 13, tails [14, 14] (expected 14), H ok True   [9.2s]
  ok   (U) (R3) (U) (ii) c = 1: <YZ^4 + dZ^5, kappa + eZ^5>           r = 3, dim Syz 3, dim W.Syz 14, tails [13, 13] (expected 13), H ok True   [9.6s]
  ok   (U) (R3) (U) (ii) c = 3: <YZ^4 + dZ^5, kappa + eZ^5>           r = 3, dim Syz 3, dim W.Syz 14, tails [13, 13] (expected 13), H ok True   [10.1s]
  ok   (U) (R3) (U) (ii) c = -2: <YZ^4 + dZ^5, kappa + eZ^5>          r = 3, dim Syz 3, dim W.Syz 14, tails [13, 13] (expected 13), H ok True   [10.5s]
(R4) r = 4
  ok   (S) (R4) binary random pencil [off]                            r = 4, dim Syz 2, dim W.Syz 10, tails [12] (expected 12), H ok True   [10.8s]
  ok   (S) (R4) binary random pencil [emb]                            r = 4, dim Syz 2, dim W.Syz 10, tails [12] (expected 12), H ok True   [11.1s]
  ok   (S) (R4) off-line <y o K + X^5, z o K>                         r = 4, dim Syz 2, dim W.Syz 10, tails [12] (expected 12), H ok True   [11.4s]
  ok   (S) (R4) embedded (alpha) <G1 + XZ^4, G2>                      r = 4, dim Syz 2, dim W.Syz 10, tails [12] (expected 12), H ok True   [11.7s]
  ok   (S) (R4) embedded (beta) G2 in nu_5{q, N}: <G1 + XZ^4, Y^5 + Z^5> r = 4, dim Syz 2, dim W.Syz 10, tails [12] (expected 12), H ok True   [12.0s]
  ok   (S) (R4) embedded (beta) G2 in nu_5(double q): <G1 + XZ^4, YZ^4 + 2Z^5> r = 4, dim Syz 2, dim W.Syz 10, tails [12] (expected 12), H ok True   [12.3s]
  ok   (S) (R4) off-line <G + X^5, Y^5> (L = Y)                       r = 4, dim Syz 2, dim W.Syz 8, tails [14] (expected 14), H ok True   [12.6s]
  ok   (S) (R4) embedded <G + XZ^4, Y^5> (L = Y)                      r = 4, dim Syz 2, dim W.Syz 8, tails [14] (expected 14), H ok True   [12.9s]
  ok   (S) (R4) embedded <G + XZ^4, (Y + 2Z)^5>                       r = 4, dim Syz 2, dim W.Syz 8, tails [14] (expected 14), H ok True   [13.2s]
  ok   (S) no pencil containing q^5 has r = 4 (six random members; hand proof in the note)   [13.2s]
(CV) curves for r = 4 without fifth powers
  ok   (A) (alpha) random: relation (1, -1/2, -3/2, 1/2); tail at t = 0: 12; (t, D_5(t) in nu_5(B_t), r(t), relation, tail): [(1/7, True, 4, True, 12), (-1/3, True, 4, True, 12), (1/50, True, 4, True, 12)]   [13.7s]
  ok   (A) (beta) G2 = Y^5 + Z^5: relation (1, 0, 0, -1/5); tail at t = 0: 12; (t, D_5(t) in nu_5(B_t), r(t), relation, tail): [(1/7, True, 4, True, 12), (-1/3, True, 4, True, 12), (1/50, True, 4, True, 12)]   [14.1s]
  ok   (A) (beta) G2 = YZ^4 + 2Z^5: relation (1, 0, -1, 0); tail at t = 0: 12; (t, D_5(t) in nu_5(B_t), r(t), relation, tail): [(1/7, True, 4, True, 12), (-1/3, True, 4, True, 12), (1/50, True, 4, True, 12)]   [14.5s]
  ok   (A) (gamma = delta = 0) y o G1 = Z^4: relation (1, -1, 0, 0); tail at t = 0: 12; (t, D_5(t) in nu_5(B_t), r(t), relation, tail): [(1/7, True, 4, True, 12), (-1/3, True, 4, True, 12), (1/50, True, 4, True, 12)]   [15.0s]
(D) case (d)
  ok   (S) (d) random pencil, G = XYZ: dim K = 1, delta = 4; three random elements of N, 2 tries: local lengths [40, 40]; accepted 2 (closed, H = [1, 3, 6, 5, 4, 2], f in Ann(M), <= 41); minimum 40 <= 36 + delta = 40 (so e(N) <= 40)   [68.5s]
  ok   (S) (d) <Y^5, Z^5>, G = XYZ: dim K = 3, delta = 2; three random elements of N, 2 tries: local lengths [38, 38]; accepted 2 (closed, H = [1, 3, 6, 5, 4, 2], f in Ann(M), <= 41); minimum 38 <= 36 + delta = 38 (so e(N) <= 38)   [90.4s]
44 checks, total time 90.4 s
ALL CHECKS PASSED
