# macaulayLowerOperator -- the a_<d> operator used in Green's proof of Macaulay's Theorem

## Synopsis

• Usage:
h=macaulayLowerOperator(a,d)
• Inputs:
• Outputs:
• h, an integer, a nonnegative integer representing a_<d>

## Description

Given positive integers a and d, macaulayLowerOperator yields a_<d>, the operation from Green's proof of Macaulay's Theorem. See Bruns and Herzog, Cohen-Macaulay Rings, page 161.

 i1 : macaulayLowerOperator(3,1) o1 = 2 i2 : macaulayLowerOperator(15,5) o2 = 3