=== Part U ===
  [ok] (Bx) {P : z.P in nu_4(B), xy.P in nu_3(B)} = C[Y,Z]_5 + C XY^4 + X^4<Y,Z> + C X^5 (dim 10)
  [ok] (Bx) x^2 o P~ = 0 on this space
  [ok] Lambda = V(z), emb[X]: {P : z.P in nu_4(B)} = A_0 + Z A_1 (+ Z^2 L^3, resp. Z^5), A_i binary (dim 12)
  [ok] Lambda = V(z), emb[Y]: {P : z.P in nu_4(B)} = A_0 + Z A_1 (+ Z^2 L^3, resp. Z^5), A_i binary (dim 12)
  [ok] Lambda = V(z), emb[X+Y]: {P : z.P in nu_4(B)} = A_0 + Z A_1 (+ Z^2 L^3, resp. Z^5), A_i binary (dim 12)
  [ok] Lambda = V(z), iso[Z]: {P : z.P in nu_4(B)} = A_0 + Z A_1 (+ Z^2 L^3, resp. Z^5), A_i binary (dim 12)
  [ok] Lambda = V(z), (d): {P : z.P in nu_4(B)} = A_0 + Z A_1 (+ Z^2 L^3, resp. Z^5), A_i binary (dim 11)
  [ok] pure, emb[X]: {P : y.P, z.P in nu_4(B)} = C[X,Y]_5 + [X^4*Z, X^3*Y*Z, X^3*Z^2] (dim 9)
  [ok] pure, emb[Y]: {P : y.P, z.P in nu_4(B)} = C[X,Y]_5 + [X^4*Z, Y^4*Z] (dim 8)
  [ok] pure, emb[X+Y]: {P : y.P, z.P in nu_4(B)} = C[X,Y]_5 + [X^4*Z, X^4*Z + 4*X^3*Y*Z + 6*X^2*Y^2*Z + 4*X*Y^3*Z + Y^4*Z] (dim 8)
  [ok] (Bp) r_t = X^3Y/3 + tX^2Y^2/2 + t^2XY^3/3 has xy o r_t = (X+tY)^2 (t = 1)
  [ok] (Bp) x^2 o r_t and y^2 o r_t are not multiples of (X+tY)^2 (no ray at [X] or [Y] for the active datum)
=== Part S: actual algebras, rays ===
  [ok] (Bx) binary secant, Lambda=V(x)+[X], R in C[Y,Z]_4: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (Bd) binary secant, B = Lambda, general G_3: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (Bc) binary secant, B = Lambda + [Z], R = r + eZ^4: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (Bc) binary secant, B = Lambda + [Z], R = Z^4: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (BeX) binary secant, emb[X], R = r + eX^3Z general: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (BeX) binary secant, emb[X], active datum R = X^3Y + eX^3Z: ray at [Y]: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [y] + colon criterion on 3 of 3
  [ok] (BeX) binary secant, emb[X], R = X^3Z: ray at [Y]: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [y] + colon criterion on 3 of 3
  [ok] (Bp) binary secant, emb[X+Y], general R: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (PeX) pure secant, emb[X], R = r + eX^3Z general: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (PeY) pure secant, emb[Y], R = r + eY^3Z: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (Pep) pure secant, emb[X+Y], R = r + e(X+Y)^3Z: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (P2eX) P2, emb[X], G = G_0 binary (g_z = 0), root a = 1: H ok = True; 3 actual algebras (of 23 tries); Lemma 5.13 at [x + y] + colon criterion on 3 of 3
  [ok] (P2eY) P2, emb[Y], G = G_0 binary (g_z = 0), root a = 1: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x + y] + colon criterion on 3 of 3
  [info] (P2eY) sample skipped: dim D_4 = 4
  [ok] (Bx) binary secant, Lambda=V(x)+[X], R in C[Y,Z]_4: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (Bd) binary secant, B = Lambda, general G_3: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (Bc) binary secant, B = Lambda + [Z], R = r + eZ^4: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (Bc) binary secant, B = Lambda + [Z], R = Z^4: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (BeX) binary secant, emb[X], R = r + eX^3Z general: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (BeX) binary secant, emb[X], active datum R = X^3Y + eX^3Z: ray at [Y]: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [y] + colon criterion on 3 of 3
  [ok] (BeX) binary secant, emb[X], R = X^3Z: ray at [Y]: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [y] + colon criterion on 3 of 3
  [ok] (Bp) binary secant, emb[X+Y], general R: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (PeX) pure secant, emb[X], R = r + eX^3Z general: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (PeY) pure secant, emb[Y], R = r + eY^3Z: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (Pep) pure secant, emb[X+Y], R = r + e(X+Y)^3Z: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [ok] (P2eX) P2, emb[X], G = G_0 binary (g_z = 0), root a = -3: H ok = True; 3 actual algebras (of 27 tries); Lemma 5.13 at [x - 3*y] + colon criterion on 3 of 3
  [ok] (P2eY) P2, emb[Y], G = G_0 binary (g_z = 0), root a = -3: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x - 3*y] + colon criterion on 3 of 3
  [info] (P2eY) sample skipped: dim D_4 = 4
  [info] (Bd-act) binary secant, B = Lambda, G_3 = Z(xy o R), ray at [X]?: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
  [info] (Bp-act) binary secant, emb[X+Y], R = r_1, ray at [X]?: H ok = True; 3 actual algebras (of 3 tries); Lemma 5.13 at [x] + colon criterion on 3 of 3
accepted samples (counted checks): 78
38 checks, 0 failed
ALL CHECKS PASSED
