This method returns the order complex of a poset P. The order complex is the simplicial complex whose faces are chains of P (and whose facets are maximal chains of P).
i1 : S = QQ[a,b,c]; |
i2 : P = divisorPoset(a*b*c); |
i3 : C = maximalChains P o3 = {{1, c, b*c, a*b*c}, {1, c, a*c, a*b*c}, {1, b, b*c, a*b*c}, {1, b, a*b, ------------------------------------------------------------------------ a*b*c}, {1, a, a*c, a*b*c}, {1, a, a*b, a*b*c}} o3 : List |
i4 : D = orderComplex P o4 = | v_0v_4v_6v_7 v_0v_2v_6v_7 v_0v_4v_5v_7 v_0v_1v_5v_7 v_0v_2v_3v_7 v_0v_1v_3v_7 | o4 : SimplicialComplex |