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Macaulay2 web site
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
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)