isCM -- whether a ring or module is Cohen-Macaulay

Synopsis

Usage:

isCM(A)
Inputs:
- A, a Ring or Module
Outputs:
- Boolean

Description

This command merely checks if the depth of A equals the Krull dimension of A.

i1 : A = ZZ/2[x,y,z];

i2 : isCM(A)

o2 = true

i3 : A = ZZ/2[x,y]/(x^2,x*y);

i4 : isCM(A)

o4 = false

i5 : A =  ZZ/101[a_1,a_2,b_1,b_2,c_1]/ideal(a_1*b_1,a_2*b_2,b_1*c_1);

i6 : isCM(A)

o6 = false

This symbol is provided by the package Depth.

Caveat

Typically when one thinks of a Cohen-Macaulay ring or module, one is in the local case. Since the local case is not yet implemented into Macaulay 2, we compute over the ideal generated by by generators(Ring).

Ways to use isCM :

isCM(Module)
isCM(Ring)

For the programmer

The object isCM is a method function.