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Posets :: orderComplex

orderComplex -- returns the simplicial complex with faces given by chains

Synopsis

Description

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

Ways to use orderComplex :

  • orderComplex(Poset)