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

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

Given a Hilbert function of a in degree d, macaulayBound yields the upper bound from Macaulay's Theorem for the Hilbert function in degree d+1.

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

Ways to use macaulayBound:

macaulayBound(ZZ,ZZ)

For the programmer

The object macaulayBound is a method function.

The source of this document is in LexIdeals.m2:595:0.