hilbPol(RingElement,ZZ,List,List) -- Hilbert polynomial

Synopsis

• Function: hilbPol

• Usage:

  hilbPol(d,n,B,K)

• Inputs:
  • d, a ring element, variable in the polynomial ring
  • n, an integer, type of degree triplet
  • B, a list, the Betti degrees
  • K, a list, integer coefficients of Hilbert polynomial
• Outputs:
  • an expression, Hilbert polynomial of complex of coherent sheaves associated to homology triplet

Description

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 : hilbPol(d,3,{1,2,3},hilbCoeff(T))

       1 3   1 2   2
o3 = - -d  - -d  + -d
       6     2     3

o3 : QQ[d]

See also

• binPol -- product of two binomial polynomials
• chiPol -- Hilbert polynomial of cohomology sheaves
• hilbCoeff -- coefficients of Hilbert polynomial