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



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 :

For the programmer

The object isCM is a method function.