isCM -- test whether a polynomial ring modulo a homogeneous ideal is Cohen-Macaulay

Synopsis

Usage:

B=isCM I
Inputs:
- I, an ideal, a homogeneous ideal in a polynomial ring
Outputs:
- B, a Boolean value, true if (ring I)/I is Cohen-Macaulay and false otherwise

Description

isCM takes a homogeneous ideal I in a polynomial ring R and, by computing the projective dimension and codimension of I, determines whether R/I is Cohen-Macaulay. Of course, isCM works only if Macaulay 2 can compute the projective dimension of I.

i1 : R=ZZ/32003[a..c];

i2 : isCM(ideal(a^2,b^4)) --complete intersection

o2 = true

i3 : isCM(ideal(a^3,b^5,c^4,a*c^3)) --Artinian

o3 = true

i4 : isCM(ideal(a^3,a*b^2))

o4 = false

Ways to use isCM :

isCM(Ideal)

For the programmer

The object isCM is a method function.