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CharacteristicClasses :: probabilistic algorithm

probabilistic algorithm

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.

An example that is known to be susceptible to errors, especially if ResidualStrategy=>Bertini is used, is the following.
i1 : R=QQ[x,y,z,w]

o1 = R

o1 : PolynomialRing
i2 : I=ideal(x^3+y*z*w,x*y+z*w,x^5+y^5+z^5+w^5)

             3                      5    5    5    5
o2 = ideal (x  + y*z*w, x*y + z*w, x  + y  + z  + w )

o2 : Ideal of R

To get a feeling, the user is recommended to compute characteristic classes of this scheme several times, using the two different strategies.