Poset -- a class for partially ordered sets (posets)

Description

This class is a type of HashTable which represents finite posets. It consists of a ground set, a set of sequences (a,b) representing relationships where a is less than or equal to b, a matrix encoding these relations.

i1 : G = {a,b,c,d,e}; -- the ground set

i2 : R = {(a,b),(b,c),(a,c),(a,d),(d,e)}; --a set of sequences representing relations that "generate" all other relations

i3 : P = poset (G,R) -- the matrix encoding these relations is computed by calling this function

o3 = Poset{cache => CacheTable                                  }
           GroundSet => {a, b, c, d, e}
           RelationMatrix => | 1 1 1 1 1 |
                             | 0 1 1 0 0 |
                             | 0 0 1 0 0 |
                             | 0 0 0 1 1 |
                             | 0 0 0 0 1 |
           Relations => {(a, b), (b, c), (a, c), (a, d), (d, e)}

o3 : Poset

Functions and methods returning an object of class Poset :

lcmLattice(Ideal), see lcmLattice -- returns the LCM lattice of an ideal
lcmLattice(MonomialIdeal), see lcmLattice -- returns the LCM lattice of an ideal

Methods that use an object of class Poset :

adjacencyMatrix(Poset), see adjacencyMatrix -- returns adjacency matrix of a directed graph
compare(Poset,Thing,Thing), see compare -- returns boolean value for whether an element is less than another
filter(Poset,Thing), see filter -- returns a principal filter generated by the given element
isLattice(Poset), see isLattice -- determines if a poset is a lattice
joinExists(Poset,Thing,Thing), see joinExists -- determines if the join exists
meetExists(Poset,Thing,Thing), see meetExists -- determines if the meet exists
orderIdeal(Poset,Thing), see orderIdeal -- returns a principal order ideal generated by the given element
posetJoin(Poset,Thing,Thing), see posetJoin -- returns the join of two elements
posetMeet(Poset,Thing,Thing), see posetMeet -- returns the meet of two elements

For the programmer

The object Poset is a type, with ancestor classes HashTable < Thing.

Poset -- a class for partially ordered sets (posets)

Description

See also

Functions and methods returning an object of class Poset :

Methods that use an object of class Poset :

For the programmer