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

## Synopsis

• Function: euler
• Usage:
euler X
euler(X,Verify=>b)
• Inputs:
• X, , 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,MathMode=>b)

## Description

 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