macaulayBound -- the bound on the growth of a Hilbert function from Macaulay's Theorem

Synopsis

• Usage:

  h=macaulayBound(a,d)

• Inputs:
  • a, an integer, a positive integer
  • d, an integer, a positive integer
• Outputs:
  • h, an integer, the Macaulay upper bound for the Hilbert function in degree d+1 given that it is a in degree d.

Description

i1 : macaulayBound(3,1)

o1 = 6

i2 : macaulayBound(15,5)

o2 = 18

See also

• macaulayRep -- the Macaulay representation of an integer
• macaulayLowerOperator -- the a_<d> operator used in Green's proof of Macaulay's Theorem
• isHF -- is a finite list a Hilbert function of a polynomial ring mod a homogeneous ideal