# chiPol(RingElement,ZZ,List,List) -- Hilbert polynomial of cohomology sheaves

## Synopsis

• Function: chiPol
• Usage:
chiPol(d,p,L,K)
• Inputs:
• d, , variable in polynomial ring
• p, an integer, for the -p'th cohomology sheaf
• L, a list, pair {B,H} of Betti degrees and homology degrees
• K, a list, integer coefficients of the Hilbert polynomial
• Outputs:
• , Hilbert polynomial of the -p'th cohomology sheaf of the complex of coherent sheaves associated to a homology triplet

## Description

Computes the Hilbert polynomial of the -p'th cohomology sheaf of the complex of coherent sheaves associated to a homology triplet
 i1 : QQ[d] o1 = QQ[d] o1 : PolynomialRing i2 : T = triplet({1,2,3}, {1,3}, {0,2,3}) o2 = {{1, 2, 3}, {1, 3}, {0, 2, 3}} o2 : Triplet i3 : chiPol(d,0,{T#0,T#1},hilbCoeff(T)) o3 = d o3 : QQ[d] i4 : chiPol(d,1,{T#0,T#1},hilbCoeff(T)) 1 3 1 2 1 o4 = -d + -d + -d 6 2 3 o4 : QQ[d]