The algorithm used for the computation of characteristic classes is probabilistic. Theoretically it calculates the classes correctly in all cases outside a lower-dimensional subset, i.e., with probability one. In the implementation, however, the probability of not computing the correct class is strictly larger than zero, although small. Sceptical users should repeat calculations to increase the probability of computing the correct class.
i1 : setRandomSeed 121; |
i2 : R = QQ[x,y,z,w] o2 = R o2 : PolynomialRing |
i3 : I = minors(2,matrix{{x,y,z},{y,z,w}}) 2 2 o3 = ideal (- y + x*z, - y*z + x*w, - z + y*w) o3 : Ideal of R |
i4 : chernClass I 2 o4 = 4H ZZ[H] o4 : ----- 4 H |
i5 : chernClass I 3 2 o5 = 2H + 3H ZZ[H] o5 : ----- 4 H |
i6 : chernClass I 3 2 o6 = 2H + 3H ZZ[H] o6 : ----- 4 H |