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Posets :: dropElements

dropElements -- returns the poset obtained by removing a list of elements

Synopsis

Description

This command take a poset P and returns a new poset that contains all elements in P that are not in L. The relations on the remaining elements are all relations that held in P.

Alternately, if a boolean function is given as input instead of a list, all elements for which the function returns true are removed from P.

i1 : S = QQ[a,b];
i2 : P = divisorPoset(a*b^2);
i3 : P.GroundSet

             2             2
o3 = {1, b, b , a, a*b, a*b }

o3 : List
i4 : Q = dropElements(P, {a,a*b^2})

o4 = Poset{cache => CacheTable{}                                                                            }
                                2
           GroundSet => {1, b, b , a*b}
           RelationMatrix => | 1 1 1 1 |
                             | 0 1 1 1 |
                             | 0 0 1 0 |
                             | 0 0 0 1 |
                                              2                          2               2   2
           Relations => {(1, 1), (1, b), (1, b ), (1, a*b), (b, b), (b, b ), (b, a*b), (b , b ), (a*b, a*b)}

o4 : Poset
i5 : R = dropElements(P, m -> first degree m === 2)

o5 = Poset{cache => CacheTable{}                                                                               }
                                     2
           GroundSet => {1, b, a, a*b }
           RelationMatrix => | 1 1 1 1 |
                             | 0 1 0 1 |
                             | 0 0 1 1 |
                             | 0 0 0 1 |
                                                        2                  2                  2       2     2
           Relations => {(1, 1), (1, b), (1, a), (1, a*b ), (b, b), (b, a*b ), (a, a), (a, a*b ), (a*b , a*b )}

o5 : Poset

Ways to use dropElements :

  • dropElements(Poset,Function)
  • dropElements(Poset,List)