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CharacteristicClasses :: eulerChar

eulerChar -- computes the topological Euler characteristic

Synopsis

Description

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 = ZZ/32749[x,y,z]

o2 = R

o2 : PolynomialRing
i3 : eulerChar ideal(x^3 + x^2*z - y^2*z)

o3 = 1

The example was done using symbolic computations with Gröbner bases. The default algorithm computes the projective degrees using Gröbner bases. Changing the option Algorithm to ResidualSymbolic will compute the residual degrees using Gröbner bases. Changing the option Algorithm 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.

Ways to use eulerChar :