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 list of relationships $\{a,b\}$ where $a \leq b$, and a matrix encoding these relations.
i1 : G = {1,2,3,4}; -- the ground set
i2 : R = {{1,2},{1,3},{2,4},{3,4}}; -- a list of cover relations
i3 : P = poset(G, R) -- the poset with its relations matrix computed
o3 = P
o3 : Poset
projectivizeArrangement(List,Ring) -- see projectivizeArrangement -- computes the intersection poset of a projectivized hyperplane arrangement
randomPoset(List) -- see randomPoset -- generates a random poset with a given relation probability
randomPoset(ZZ) -- see randomPoset -- generates a random poset with a given relation probability
resolutionPoset(ChainComplex) -- see resolutionPoset -- generates a poset from a resolution
resolutionPoset(Ideal) -- see resolutionPoset -- generates a poset from a resolution
resolutionPoset(MonomialIdeal) -- see resolutionPoset -- generates a poset from a resolution
standardMonomialPoset(MonomialIdeal) -- see standardMonomialPoset -- generates the poset of divisibility in the monomial basis of an ideal
standardMonomialPoset(MonomialIdeal,ZZ,ZZ) -- see standardMonomialPoset -- generates the poset of divisibility in the monomial basis of an ideal
subposet(Poset,List) -- see subposet -- computes the induced subposet of a poset given a list of elements
transitiveOrientation(Graph) -- see transitiveOrientation -- generates a poset whose comparability graph is the given graph
union(Poset,Poset) -- see union -- computes the union of two posets
youngSubposet(List) -- see youngSubposet -- generates a subposet of Young's lattice
youngSubposet(List,List) -- see youngSubposet -- generates a subposet of Young's lattice
youngSubposet(ZZ) -- see youngSubposet -- generates a subposet of Young's lattice
Methods that use an object of class Poset :
allRelations(Poset) -- see allRelations -- computes all relations of a poset
allRelations(Poset,Boolean) -- see allRelations -- computes all relations of a poset
antichains(Poset) -- see antichains -- computes all antichains of a poset
antichains(Poset,ZZ) -- see antichains -- computes all antichains of a poset
areIsomorphic(Poset,Poset) -- see areIsomorphic -- determines if two posets are isomorphic
Poset == Poset -- see areIsomorphic -- determines if two posets are isomorphic
atoms(Poset) -- see atoms -- computes the list of elements covering the minimal elements of a poset
chains(Poset) -- see chains -- computes all chains of a poset
chains(Poset,ZZ) -- see chains -- computes all chains of a poset
characteristicPolynomial(Poset) -- see characteristicPolynomial -- computes the characteristic polynomial of a ranked poset with a unique minimal element
comparabilityGraph(Poset) -- see comparabilityGraph -- produces the comparability graph of a poset
compare(Poset,Thing,Thing) -- see compare -- compares two elements in a poset