next
| previous |
forward
| backward | up | top |
index
|
toc
|
Macaulay2 web site
Posets -- A package for working with posets.
Description
Posets
package defines Poset as a new data type and provides routines which use or produce posets. A poset or a partially ordered set is a set together with a binary relation satisfying reflexivity, antisymmetry, and transitivity.
Authors
Sonja Mapes
<
mapes@math.columbia.edu
>
Gwyn Whieldon
<
whieldon@math.cornell.edu
>
Josephine Yu
<
jyu@math.mit.edu
>
Version
This documentation describes version
0.1
of Posets.
Source code
The source code from which this documentation is derived is in the file
Posets.m2
.
Exports
Types
DirectedGraph
-- a class for directed graphs
Poset
-- a class for partially ordered sets (posets)
Functions
adjacencyMatrix
-- returns adjacency matrix of a directed graph
allPairsShortestPath
-- computes lengths of shortest paths between all pairs in a directed graph
compare
-- returns boolean value for whether an element is less than another
directedGraph
-- creating a directed graph
filter
-- returns a principal filter generated by the given element
isLattice
-- determines if a poset is a lattice
joinExists
-- determines if the join exists
lcmLattice
-- returns the LCM lattice of an ideal
meetExists
-- determines if the meet exists
orderIdeal
-- returns a principal order ideal generated by the given element
poset
-- creating a poset
posetJoin
-- returns the join of two elements
posetMeet
-- returns the meet of two elements
transitiveClosure
-- computes the transitive closure of a given set of relations.
Methods
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
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
Symbols
DirectedEdges
-- the set of directed edges of a directed graph
GroundSet
-- underlying set of a poset
RelationMatrix
-- the matrix expressing all of the relations between elements in a Poset
Relations
-- a set of relations in the poset that generates all other relations
Vertices
-- the set of vertices a directed graph