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

Posets -- a package for working with posets

Description

The 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.

Contributors

The following people have generously contributed code or worked on our code.

Authors

Version

This documentation describes version 0.2 of Posets.

Source code

The source code from which this documentation is derived is in the file Posets.m2.

Exports

  • Types
    • Poset -- a class for partially ordered sets (posets)
  • Functions and commands
    • atoms -- returns the atoms of a poset
    • closedInterval -- returns the closed interval in the poset between two elements
    • compare -- returns boolean value for whether an element is less than another
    • coveringRelations -- returns a list of all relations (a < b) with no intermediates
    • divisorPoset -- returns the poset of all divisors of a given monomial
    • dropElements -- returns the poset obtained by removing a list of elements
    • filter -- returns a principal filter generated by the given element
    • hasseDiagram -- returns Hasse diagram for the poset
    • isAntichain -- checks whether a subposet is an anti-chain
    • isLattice -- determines if a poset is a lattice
    • joinExists -- determines if the join exists
    • lcmLattice -- returns the LCM lattice of an ideal
    • maximalChains -- returns all maximal chains of a poset
    • maximalElements -- returns all maximal elements of a poset
    • meetExists -- determines if the meet exists
    • meetIrreducibles -- returns the meet-irreducibles of a poset
    • minimalElements -- returns all minimal elements of a poset
    • moebiusFunction -- returns Moebius function values
    • openInterval -- returns the open interval in the poset between two elements
    • orderComplex -- returns the simplicial complex with faces given by chains
    • 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
    • subPoset -- returns the subposet supported on elements in a given list
    • transitiveClosure -- computes the transitive closure of a given set of relations.
  • Methods
    • atoms(Poset), see atoms -- returns the atoms of a poset
    • closedInterval(Poset,Thing,Thing), see closedInterval -- returns the closed interval in the poset between two elements
    • compare(Poset,Thing,Thing), see compare -- returns boolean value for whether an element is less than another
    • coveringRelations(Poset), see coveringRelations -- returns a list of all relations (a < b) with no intermediates
    • dropElements(Poset,Function), see dropElements -- returns the poset obtained by removing a list of elements
    • dropElements(Poset,List), see dropElements -- returns the poset obtained by removing a list of elements
    • filter(Poset,Thing), see filter -- returns a principal filter generated by the given element
    • hasseDiagram(Poset), see hasseDiagram -- returns Hasse diagram for the poset
    • height(Poset) (missing documentation)
    • isAntichain(Poset,List), see isAntichain -- checks whether a subposet is an anti-chain
    • isLattice(Poset), see isLattice -- determines if a poset is a lattice
    • joinExists(Poset,Thing,Thing), see joinExists -- determines if the join exists
    • maximalChains(Poset), see maximalChains -- returns all maximal chains of a poset
    • maximalElements(Poset), see maximalElements -- returns all maximal elements of a poset
    • meetExists(Poset,Thing,Thing), see meetExists -- determines if the meet exists
    • meetIrreducibles(Poset), see meetIrreducibles -- returns the meet-irreducibles of a poset
    • minimalElements(Poset), see minimalElements -- returns all minimal elements of a poset
    • moebiusFunction(Poset) -- returns the Moebius function values for the unique minimal element to each element of the poset
    • moebiusFunction(Poset,Thing,Thing) -- returns the Moebius function values for the minimal element of a closed interval to each element of the interval
    • openInterval(Poset,Thing,Thing), see openInterval -- returns the open interval in the poset between two elements
    • orderComplex(Poset), see orderComplex -- returns the simplicial complex with faces given by chains
    • 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
    • subPoset(Poset,List), see subPoset -- returns the subposet supported on elements in a given list
  • Symbols
    • 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
    • VariableName (missing documentation)