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

Synopsis

Usage:

CMStats(List)
Inputs:
- ideals, a list, of objects of type MonomialIdeal, or any type to which isCM can be applied
Optional inputs:
- Verbose => ..., default value false, optional input to request verbose feedback
Outputs:
- a rational number, 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 a method function with options.