R1 (2,2): 2000 random curves v = (v_1, v_2), Gaussian integer coefficients in [-5,5], degree 2: {'NS': 1996, 'not NS': 4}; dim U(V_R): {2: 1996, 3: 4}; dim K_v = dim U(V_R) - 2 for every curve: True (so (NS) fails exactly when K_v != 0, as in Proposition 4.4)   (0.6 s)
R1 control (real v_1, v_2): property (NS) fails, as it must: True
R2 check on Example 4.5(b): K_v = R H_0 with the printed H_0 and det H_0 = -20: True
R2 (2,4): 300 random curves, Gaussian integer coefficients in [-3,3], degree 4: {'NS (dim K_v = 1, det != 0)': 300, 'dim K_v > 1': 0, 'det = 0': 0}   (0.2 s)
R3 (2,6): 12 random Gaussian curves: dim K_v = 4; smallest value found of sigma_3/sigma_1 on the unit sphere of K_v: 6.062e-05 (a zero would be a matrix of rank <= 2; information only)   (4.3 s)
R3x (2,6), exact: 10 random curves, Gaussian integer coefficients in [-3,3], degree 6: dim K_v = 4 in 10 cases; Macaulay matrix in degree 5 of the 3x3 minors has full column rank 56 (no non-zero complex matrix of rank <= 2 in K_v, hence (NS)) in 10 cases   (270.9 s)
R3x control (real v_1, v_2): dim K_v = 4, Macaulay rank 55 of 56 (must be smaller than 56 if dim K_v = 4)
R4 (4,2) curve 0: best lambda_min (floating point, normalized) 6.069e-02; exact certificate (multipliers / 1000), smallest pivot 0.14
R4 (4,2) curve 1: best lambda_min (floating point, normalized) 1.502e-01; exact certificate (multipliers / 1000), smallest pivot 0.467
R4 (4,2) curve 2: best lambda_min (floating point, normalized) 1.347e-01; exact certificate (multipliers / 1000), smallest pivot 0.231
R4 (4,2) curve 3: best lambda_min (floating point, normalized) 4.859e-02; exact certificate (multipliers / 1000), smallest pivot 0.133
R4 (4,2) curve 4: best lambda_min (floating point, normalized) 9.745e-02; exact certificate (multipliers / 1000), smallest pivot 0.194
R4 (4,2) curve 5: best lambda_min (floating point, normalized) 3.753e-02; exact certificate (multipliers / 1000), smallest pivot 0.114
R4 (4,2) curve 6: best lambda_min (floating point, normalized) 3.097e-02; exact certificate (multipliers / 1000), smallest pivot 0.0878
R4 (4,2) curve 7: best lambda_min (floating point, normalized) 3.659e-03; exact certificate (multipliers / 1000), smallest pivot 0.0223
R4 (4,2): exact certificates of property (NS) for 8 of 8 random complex curves (Gaussian integer coefficients in [-3,3])   (2.1 s)
ALL: PASS
