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

• Function: chiPol

• Usage:

  chiPol(d,p,L,K)

• Inputs:
  • d, a ring element, 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:
  • an expression, 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]