macaulayDecomposition -- Compute Macaulay's decomposition of Hilbert polynomial

Synopsis

• Usage:

  macaulayDecomposition hp

• Inputs:
  • hp, a projective Hilbert polynomial, or
  • hp, a ring element, a Hilbert polynomial.
• Outputs:
  • a list

Description

i1 : QQ[t];

i2 : hp = projectiveHilbertPolynomial(3*t+4)

o2 = P  + 3*P
      0      1

o2 : ProjectiveHilbertPolynomial

i3 : mD = macaulayDecomposition hp

o3 = {- P  + P , 8*P  - P , - P  + P , - 6*P  + 4*P  - P }
         0    1     0    1     1    2       0      1    2

o3 : List

i4 : sum mD

o4 = P  + 3*P
      0      1

o4 : ProjectiveHilbertPolynomial