This command computes the topological Euler characteristic of closed subschemes of Pk, even singular ones. We compute the topological Euler characteristic of the singular cubic x3 + x2z = y2z.
i1 : setRandomSeed 4386;
|
i2 : R = QQ[x,y,z]
o2 = R
o2 : PolynomialRing
|
i3 : eulerChar ideal(x^3 + x^2*z - y^2*z)
o3 = 1
|
All the examples were done using symbolic computations with Gröbner bases. Changing the option ResidualStrategy to Bertini will do the main computations numerically, provided Bertini is installed and configured .
Observe that the algorithm is a probabilistic algorithm and may give a wrong answer with a small but nonzero probability. Read more under
probabilistic algorithm.