This uses the edge ideal notion of sequential Cohen-Macaulayness; a hypergraph is called SCM if and only if its edge ideal is SCM. The algorithm is based on work of Herzog and Hibi, using the Alexander dual. H is SCM if and only if the Alexander dual of the edge ideal of H is componentwise linear.
i1 : R = QQ[a..f]; |
i2 : G = cycle(R,4) o2 = Graph{edges => {{a, b}, {b, c}, {c, d}, {a, d}}} ring => R vertices => {a, b, c, d, e, f} o2 : Graph |
i3 : isSCM G o3 = false |
i4 : H = graph(monomialIdeal(a*b,b*c,c*d,a*d,a*e)); --4-cycle with whisker |
i5 : isSCM H o5 = true |
i6 : isSCM(H,Gins=>true) --use Gins technique o6 = true |