euler(MultiprojectiveVariety) -- topological Euler characteristic of a (smooth) multi-projective variety

• Function: euler

• Usage:

  euler X

  euler(X,Verify=>b)

• Inputs:
  • X, a multi-projective variety, which is assumed to be smooth, and b is a boolean value, that is, true or false (the default value is true)
• Outputs:
  • an integer, the topological Euler characteristics of the variety X, generally calculated as EulerCharacteristic(ideal X,Certify=>b)

i1 : X = PP_QQ^(2,2); -- Veronese surface

o1 : ProjectiveVariety, surface in PP^5

i2 : euler X

o2 = 3

i3 : X4 = X^4;

o3 : ProjectiveVariety, X x X x X x X

i4 : euler X4

o4 = 81