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RandomMonomialIdeals :: CMStats

CMStats -- fraction of monomial ideals in the given list whose quotient ring is Cohen-Macaulay

Synopsis

Description

CMStats simply 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

Note that the method can be run on a list of Ideals, too.

Ways to use CMStats :