next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Depth :: isCM

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



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.


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 :

For the programmer

The object isCM is a method function.