# euler(KClass) -- computes the equivariant Euler characteristic of an equivariant K-class

## Synopsis

• Function: euler
• Usage:
euler C
• Inputs:
• C, ,
• Outputs:
• , in the character ring of the torus of the GKM variety on which C is defined

## Description

This method computes the pushforward of a KClass on a GKMVariety $X$ along the structure map $X \to pt$, where $pt$ is a point with trivial torus-action.

 i1 : PP3 = projectiveSpace 3 o1 = a GKM variety with an action of a 4-dimensional torus o1 : GKMVariety i2 : O1 = ampleKClass PP3 o2 = an equivariant K-class on a GKM variety o2 : KClass i3 : euler O1 o3 = T + T + T + T 0 1 2 3 o3 : ZZ[T ..T ] 0 3