next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Posets :: openInterval

openInterval -- returns the open interval in the poset between two elements

Synopsis

Description

This routine returns the intreval between the elements a and b in P, not including a and b, and an error message if the two elements are not comparable in 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 : openInterval(P,a,g)

o2 = Poset{cache => CacheTable{}                                                                }
           GroundSet => {b, c, d, e, f}
           RelationMatrix => | 1 0 0 1 0 |
                             | 0 1 0 1 1 |
                             | 0 0 1 0 1 |
                             | 0 0 0 1 0 |
                             | 0 0 0 0 1 |
           Relations => {(b, b), (b, e), (c, c), (c, e), (c, f), (d, d), (d, f), (e, e), (f, f)}

o2 : Poset

Ways to use openInterval :

  • openInterval(Poset,Thing,Thing)