EulerAffine -- The Euler Characteristic of an affine variety.

• Usage:

  EulerAffine I

• Inputs:
  • I, an ideal, an ideal in a polynomial ring over a field defining an affine variety.
• Outputs:
  • a ring element, the Euler characteristic

i1 : kk=ZZ/32749;

i2 : R=kk[x_1..x_3]

o2 = R

o2 : PolynomialRing

i3 : I=ideal(x_1^2+x_2^2+x_3^2-1)

            2    2    2
o3 = ideal(x  + x  + x  - 1)
            1    2    3

o3 : Ideal of R

i4 : time EulerAffine I
 -- used 0.0760285s (cpu); 0.068047s (thread); 0s (gc)

o4 = 2