(1) degree and irreducibility over Q of D(X) = Disc_A(prod_j (A+X_j) - A^{n-1})
  n=2: deg D(p+tq) = 2 (n(n-1) = 2), integral=True, extra points ok=True, leading coeff == prod(q_i-q_j)^2: True; irreducible mod 1009 => irreducible over Q
  n=3: deg D(p+tq) = 6 (n(n-1) = 6), integral=True, extra points ok=True, leading coeff == prod(q_i-q_j)^2: True; irreducible mod 1021 => irreducible over Q
  n=4: deg D(p+tq) = 12 (n(n-1) = 12), integral=True, extra points ok=True, leading coeff == prod(q_i-q_j)^2: True; irreducible mod 1097 => irreducible over Q
  n=5: deg D(p+tq) = 20 (n(n-1) = 20), integral=True, extra points ok=True, leading coeff == prod(q_i-q_j)^2: True; irreducible mod 1039 => irreducible over Q
  n=6: deg D(p+tq) = 30 (n(n-1) = 30), integral=True, extra points ok=True, leading coeff == prod(q_i-q_j)^2: True; irreducible mod 1171 => irreducible over Q
  n=7: deg D(p+tq) = 42 (n(n-1) = 42), integral=True, extra points ok=True, leading coeff == prod(q_i-q_j)^2: True; irreducible mod 1009 => irreducible over Q
  n=8: deg D(p+tq) = 56 (n(n-1) = 56), integral=True, extra points ok=True, leading coeff == prod(q_i-q_j)^2: True; irreducible mod 1163 => irreducible over Q
(2) D(X(a)) = 0 on the parametrisation X_j = (1-a_j) prod_{i!=j} a_i, sum a_j = n-1
  n=2: all 5 random rational points give D = 0: True
  n=3: all 5 random rational points give D = 0: True
  n=4: all 5 random rational points give D = 0: True
  n=5: all 5 random rational points give D = 0: True
  n=6: all 5 random rational points give D = 0: True
  n=7: all 5 random rational points give D = 0: True
(3) tau-reduction (degtools, modular) for corner patterns with d_j >= 3:
  3x3            corner at (2, 0): deg f = 2   n(n-1) = 2
  4x5            corner at (1, 1): deg f = 2   n(n-1) = 2
  2x3            corner at (0, 2): deg f = 2   n(n-1) = 2
  3x3x3          corner at (2, 0, 2): deg f = 6   n(n-1) = 6
  2x4x3          corner at (0, 1, 2): deg f = 6   n(n-1) = 6
  4x4x4          corner at (3, 3, 3): deg f = 6   n(n-1) = 6
  2x2x2x3        corner at (1, 0, 1, 0): deg f = 12   n(n-1) = 12
  3x3x3x3        corner at (1, 0, 0, 0): deg f = 12   n(n-1) = 12
  2x2x2x2x2      corner at (1, 1, 0, 1, 0): deg f = 20   n(n-1) = 20
  2x2x3x2x2x2    corner at (1, 1, 1, 1, 0, 1): deg f = 30   n(n-1) = 30
