# CMStats -- fraction of monomial ideals (or other objects) in the given list whose quotient ring is Cohen-Macaulay

## Synopsis

• Usage:
CMStats(List)
• Inputs:
• Optional inputs:
• Verbose => ..., default value false, optional input to request verbose feedback
• Outputs:
• , the fraction of Cohen-Macaulay ideals in the list

## Description

The function checks whether the coordinate ring of each ideal in the given sample is arithmetically Cohen-Macaulay and returns the proportion that are.

 i1 : R=ZZ/101[a,b,c]; i2 : ideals = {monomialIdeal"a3,b,c2", monomialIdeal"a3,b,ac"} 3 2 3 o2 = {monomialIdeal (a , b, c ), monomialIdeal (a , b, a*c)} o2 : List i3 : CMStats(ideals) 1 o3 = - 2 o3 : QQ

## Ways to use CMStats :

• "CMStats(List)"

## For the programmer

The object CMStats is .