# euler(ProjectiveHilbertPolynomial) -- constant term of the Hilbert polynomial

## Synopsis

• Function: euler
• Usage:
euler P
• Inputs:
• Outputs:
• an integer, the constant term of the Hilbert polynomial

## Description

The command returns P(0) the constant term of P. This is also the Euler characteristic of the sheaf of rings of a projective variety with Hilbert polynomial P.

 i1 : R = QQ[x_0..x_3] o1 = R o1 : PolynomialRing i2 : C = Proj(R/monomialCurveIdeal(R, {1,3,4})); i3 : P = hilbertPolynomial C o3 = - 3*P + 4*P 0 1 o3 : ProjectiveHilbertPolynomial i4 : euler P o4 = 1