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Posets :: meetIrreducibles

meetIrreducibles -- returns the meet-irreducibles of a poset

Synopsis

Description

An element a of a poset P is meet irreducible if it is not the meet of any set of elements (not containing a). This routine returns a list of all such elements in the poset P.
i1 : P = poset({a,b,c,d,e,f,g}, {(a,b), (a,c), (a,d), (b,e), (c,e), (c,f), (d,f), (e,g), (f,g)})

o1 = Poset{cache => CacheTable{}                                                                }
           GroundSet => {a, b, c, d, e, f, g}
           RelationMatrix => | 1 1 1 1 1 1 1 |
                             | 0 1 0 0 1 0 1 |
                             | 0 0 1 0 1 1 1 |
                             | 0 0 0 1 0 1 1 |
                             | 0 0 0 0 1 0 1 |
                             | 0 0 0 0 0 1 1 |
                             | 0 0 0 0 0 0 1 |
           Relations => {(a, b), (a, c), (a, d), (b, e), (c, e), (c, f), (d, f), (e, g), (f, g)}

o1 : Poset
i2 : meetIrreducibles(P)

o2 = {b, d, e, f, g}

o2 : List

Ways to use meetIrreducibles :