The LCM lattice of an Ideal is the set of all LCMs of subsets of the generators of the ideal with partial ordering given by divisibility. These are particularly useful in the study of resolutions of monomial ideals. Note that the minimal element of an LCM lattice will always be defined to be $1$ in the ring $R$ containing $I$ rather than $1$ in ZZ.
i1 : R = QQ[x,y]; |
i2 : L = lcmLattice monomialIdeal(x^2, x*y, y^2) o2 = L o2 : Poset |
i3 : compare (L, 1_R, x^2*y); |
Note that if $I$ is not a MonomialIdeal, then the method automatically uses the Strategy "subsets."
The object lcmLattice is a method function with options.