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Posets :: facePoset

facePoset -- generates the face poset of a simplicial complex

Synopsis

Description

The face poset of a SimplicialComplex is the poset of faces with partial ordering given by inclusion.
i1 : R = QQ[a..d];
i2 : facePoset simplicialComplex {a*b*c, c*d}

o2 = Poset{cache => CacheTable{...6...}                                                                                                                                                                                                                                                                                                                                                   }
           GroundSet => {{}, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {b, c}, {c, d}, {a, b, c}}
           RelationMatrix => | 1 1 1 1 1 1 1 1 1 1 |
                             | 0 1 0 0 0 1 1 0 0 1 |
                             | 0 0 1 0 0 1 0 1 0 1 |
                             | 0 0 0 1 0 0 1 1 1 1 |
                             | 0 0 0 0 1 0 0 0 1 0 |
                             | 0 0 0 0 0 1 0 0 0 1 |
                             | 0 0 0 0 0 0 1 0 0 1 |
                             | 0 0 0 0 0 0 0 1 0 1 |
                             | 0 0 0 0 0 0 0 0 1 0 |
                             | 0 0 0 0 0 0 0 0 0 1 |
           Relations => {{{}, {a}}, {{}, {b}}, {{}, {c}}, {{}, {d}}, {{}, {a, b}}, {{}, {a, c}}, {{}, {b, c}}, {{}, {c, d}}, {{}, {a, b, c}}, {{a}, {a, b}}, {{a}, {a, c}}, {{a}, {a, b, c}}, {{b}, {a, b}}, {{b}, {b, c}}, {{b}, {a, b, c}}, {{c}, {a, c}}, {{c}, {b, c}}, {{c}, {c, d}}, {{c}, {a, b, c}}, {{d}, {c, d}}, {{a, b}, {a, b, c}}, {{a, c}, {a, b, c}}, {{b, c}, {a, b, c}}}

o2 : Poset

See also

Ways to use facePoset :