an integer, an integer j such that if the Hilbert function of a polynomial ring modulo a homogeneous ideal is a in degree d, the Hilbert function is at most j in degree d+1.
Description
Given a Hilbert function of a in degree d, 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 -- test whether a finite list is a Hilbert function of a polynomial ring modulo a homogeneous ideal