# eulers(Ring) -- list the sectional Euler characteristics

## Synopsis

• Function: eulers
• Usage:
eulers R
• Inputs:
• Outputs:
• a list, the successive sectional Euler characteristics of a (sheaf of) ring(s).

## Description

Computes a list of the successive sectional Euler characteristics of a ring (sheaf of), the i-th entry in the list being the Euler characteristic of the i-th generic hyperplane restriction of R
 i1 : S = ZZ/101[a,b,c]; i2 : I = ideal(a^3+b^3+c^3) 3 3 3 o2 = ideal(a + b + c ) o2 : Ideal of S i3 : R = S/I o3 = R o3 : QuotientRing i4 : eulers(R) o4 = {0, 3} o4 : List i5 : J = substitute(ideal(b,a+c),R) o5 = ideal (b, a + c) o5 : Ideal of R i6 : eulers(R/J) o6 = {1} o6 : List