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<!DOCTYPE html> <html lang="en"> <head> <title>Poset -- a class for partially ordered sets (posets)</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="a package for working with partially ordered sets" href="index.html">Posets</a> :: <a title="a class for partially ordered sets (posets)" href="___Poset.html">Poset</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_poset.html">next</a> | <a href="_poincare__Polynomial.html">previous</a> | <a href="_poset.html">forward</a> | <a href="_poincare__Polynomial.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>Poset -- a class for partially ordered sets (posets)</h1> <div> <h2>Description</h2> <div> <p>This class is a type of <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> 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.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : G = {1,2,3,4}; -- the ground set</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : R = {{1,2},{1,3},{2,4},{3,4}}; -- a list of cover relations</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : P = poset(G, R) -- the poset with its relations matrix computed o3 = P o3 : Poset</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="creates a new Poset object" href="_poset.html">poset</a> -- creates a new Poset object</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Functions and methods returning an object of class Poset:</h2> <ul> <li><span><kbd>adjoinMax(Poset)</kbd> -- see <span><a title="computes the poset with a new maximum element" href="_adjoin__Max.html">adjoinMax</a> -- computes the poset with a new maximum element</span></span></li> <li><span><kbd>adjoinMax(Poset,Thing)</kbd> -- see <span><a title="computes the poset with a new maximum element" href="_adjoin__Max.html">adjoinMax</a> -- computes the poset with a new maximum element</span></span></li> <li><span><kbd>adjoinMin(Poset)</kbd> -- see <span><a title="computes the poset with a new minimum element" href="_adjoin__Min.html">adjoinMin</a> -- computes the poset with a new minimum element</span></span></li> <li><span><kbd>adjoinMin(Poset,Thing)</kbd> -- see <span><a title="computes the poset with a new minimum element" href="_adjoin__Min.html">adjoinMin</a> -- computes the poset with a new minimum element</span></span></li> <li><span><kbd>augmentPoset(Poset)</kbd> -- see <span><a title="computes the poset with an adjoined minimum and maximum" href="_augment__Poset.html">augmentPoset</a> -- computes the poset with an adjoined minimum and maximum</span></span></li> <li><span><kbd>augmentPoset(Poset,Thing,Thing)</kbd> -- see <span><a title="computes the poset with an adjoined minimum and maximum" href="_augment__Poset.html">augmentPoset</a> -- computes the poset with an adjoined minimum and maximum</span></span></li> <li><span><kbd>booleanLattice(ZZ)</kbd> -- see <span><a title="generates the boolean lattice on $n$ elements" href="_boolean__Lattice.html">booleanLattice</a> -- generates the boolean lattice on $n$ elements</span></span></li> <li><span><kbd>chain(ZZ)</kbd> -- see <span><a title="generates the chain poset on $n$ elements" href="_chain.html">chain</a> -- generates the chain poset on $n$ elements</span></span></li> <li><span><kbd>closedInterval(Poset,Thing,Thing)</kbd> -- see <span><a title="computes the subposet contained between two points" href="_closed__Interval.html">closedInterval</a> -- computes the subposet contained between two points</span></span></li> <li><span><kbd>diamondProduct(Poset,Poset)</kbd> -- see <span><a title="computes the diamond product of two ranked posets" href="_diamond__Product.html">diamondProduct</a> -- computes the diamond product of two ranked posets</span></span></li> <li><span><kbd>dilworthLattice(Poset)</kbd> -- see <span><a title="computes the Dilworth lattice of a poset" href="_dilworth__Lattice.html">dilworthLattice</a> -- computes the Dilworth lattice of a poset</span></span></li> <li><span><kbd>distributiveLattice(Poset)</kbd> -- see <span><a title="computes the lattice of order ideals of a poset" href="_distributive__Lattice.html">distributiveLattice</a> -- computes the lattice of order ideals of a poset</span></span></li> <li><span><kbd>divisorPoset(ZZ)</kbd> -- see <span><a title="generates the poset of divisors" href="_divisor__Poset.html">divisorPoset</a> -- generates the poset of divisors</span></span></li> <li><span><a title="generates the poset of divisors" href="_divisor__Poset_lp__List_cm__List_cm__Polynomial__Ring_rp.html">divisorPoset(List,List,PolynomialRing)</a> -- generates the poset of divisors</span></li> <li><span><a title="generates the poset of divisors" href="_divisor__Poset_lp__Ring__Element_rp.html">divisorPoset(RingElement)</a> -- generates the poset of divisors</span></li> <li><span><a title="generates the poset of divisors with a lower and upper bound" href="_divisor__Poset_lp__Ring__Element_cm__Ring__Element_rp.html">divisorPoset(RingElement,RingElement)</a> -- generates the poset of divisors with a lower and upper bound</span></li> <li><span><kbd>dominanceLattice(ZZ)</kbd> -- see <span><a title="generates the dominance lattice of partitions of $n$" href="_dominance__Lattice.html">dominanceLattice</a> -- generates the dominance lattice of partitions of $n$</span></span></li> <li><span><kbd>dropElements(Poset,Function)</kbd> -- see <span><a title="computes the induced subposet of a poset given a list of elements to remove" href="_drop__Elements.html">dropElements</a> -- computes the induced subposet of a poset given a list of elements to remove</span></span></li> <li><span><kbd>dropElements(Poset,List)</kbd> -- see <span><a title="computes the induced subposet of a poset given a list of elements to remove" href="_drop__Elements.html">dropElements</a> -- computes the induced subposet of a poset given a list of elements to remove</span></span></li> <li><span><a title="produces the derived poset with relations reversed" href="_dual_lp__Poset_rp.html">dual(Poset)</a> -- produces the derived poset with relations reversed</span></li> <li><span><kbd>facePoset(SimplicialComplex)</kbd> -- see <span><a title="generates the face poset of a simplicial complex" href="_face__Poset.html">facePoset</a> -- generates the face poset of a simplicial complex</span></span></li> <li><span><kbd>flagPoset(Poset,List)</kbd> -- see <span><a title="computes the subposet of specified ranks of a ranked poset" href="_flag__Poset.html">flagPoset</a> -- computes the subposet of specified ranks of a ranked poset</span></span></li> <li><span><kbd>gapConvertPoset(Array)</kbd> -- see <span><a title="converts between Macaulay2's Posets and GAP's Posets" href="_gap__Convert__Poset.html">gapConvertPoset</a> -- converts between Macaulay2's Posets and GAP's Posets</span></span></li> <li><span><kbd>gapConvertPoset(String)</kbd> -- see <span><a title="converts between Macaulay2's Posets and GAP's Posets" href="_gap__Convert__Poset.html">gapConvertPoset</a> -- converts between Macaulay2's Posets and GAP's Posets</span></span></li> <li><span><kbd>indexLabeling(Poset)</kbd> -- see <span><a title="relabels a poset with the labeling based on the indices of the vertices" href="_index__Labeling.html">indexLabeling</a> -- relabels a poset with the labeling based on the indices of the vertices</span></span></li> <li><span><kbd>intersectionLattice(List,Ring)</kbd> -- see <span><a title="generates the intersection lattice of a hyperplane arrangement" href="_intersection__Lattice.html">intersectionLattice</a> -- generates the intersection lattice of a hyperplane arrangement</span></span></li> <li><span><kbd>labelPoset(Poset,HashTable)</kbd> -- see <span><a title="relabels a poset with the specified labeling" href="_label__Poset.html">labelPoset</a> -- relabels a poset with the specified labeling</span></span></li> <li><span><kbd>lcmLattice(Ideal)</kbd> -- see <span><a title="generates the lattice of lcms in an ideal" href="_lcm__Lattice.html">lcmLattice</a> -- generates the lattice of lcms in an ideal</span></span></li> <li><span><kbd>naturalLabeling(Poset)</kbd> -- see <span><a title="relabels a poset with a natural labeling" href="_natural__Labeling.html">naturalLabeling</a> -- relabels a poset with a natural labeling</span></span></li> <li><span><kbd>naturalLabeling(Poset,ZZ)</kbd> -- see <span><a title="relabels a poset with a natural labeling" href="_natural__Labeling.html">naturalLabeling</a> -- relabels a poset with a natural labeling</span></span></li> <li><span><kbd>ncpLattice(ZZ)</kbd> -- see <span><a title="computes the non-crossing partition lattice of set-partitions of size $n$" href="_ncp__Lattice.html">ncpLattice</a> -- computes the non-crossing partition lattice of set-partitions of size $n$</span></span></li> <li><span><kbd>openInterval(Poset,Thing,Thing)</kbd> -- see <span><a title="computes the subposet contained strictly between two points" href="_open__Interval.html">openInterval</a> -- computes the subposet contained strictly between two points</span></span></li> <li><span><kbd>partitionLattice(ZZ)</kbd> -- see <span><a title="computes the lattice of set-partitions of size $n$" href="_partition__Lattice.html">partitionLattice</a> -- computes the lattice of set-partitions of size $n$</span></span></li> <li><span><kbd>plueckerPoset(ZZ)</kbd> -- see <span><a title="computes a poset associated to the Plücker relations" href="_pluecker__Poset.html">plueckerPoset</a> -- computes a poset associated to the Plücker relations</span></span></li> <li><span><kbd>poset(List)</kbd> -- see <span><a title="creates a new Poset object" href="_poset.html">poset</a> -- creates a new Poset object</span></span></li> <li><span><kbd>poset(List,Function)</kbd> -- see <span><a title="creates a new Poset object" href="_poset.html">poset</a> -- creates a new Poset object</span></span></li> <li><span><kbd>poset(List,List)</kbd> -- see <span><a title="creates a new Poset object" href="_poset.html">poset</a> -- creates a new Poset object</span></span></li> <li><span><kbd>poset(List,List,Matrix)</kbd> -- see <span><a title="creates a new Poset object" href="_poset.html">poset</a> -- creates a new Poset object</span></span></li> <li><span><a title="computes the product of two posets" href="_product_lp__Poset_cm__Poset_rp.html">product(Poset,Poset)</a> -- computes the product of two posets</span></li> <li><span><kbd>projectivizeArrangement(List,Ring)</kbd> -- see <span><a title="computes the intersection poset of a projectivized hyperplane arrangement" href="_projectivize__Arrangement.html">projectivizeArrangement</a> -- computes the intersection poset of a projectivized hyperplane arrangement</span></span></li> <li><span><kbd>randomPoset(List)</kbd> -- see <span><a title="generates a random poset with a given relation probability" href="_random__Poset.html">randomPoset</a> -- generates a random poset with a given relation probability</span></span></li> <li><span><kbd>randomPoset(ZZ)</kbd> -- see <span><a title="generates a random poset with a given relation probability" href="_random__Poset.html">randomPoset</a> -- generates a random poset with a given relation probability</span></span></li> <li><span><kbd>resolutionPoset(Complex)</kbd> -- see <span><a title="generates a poset from a resolution" href="_resolution__Poset.html">resolutionPoset</a> -- generates a poset from a resolution</span></span></li> <li><span><kbd>resolutionPoset(Ideal)</kbd> -- see <span><a title="generates a poset from a resolution" href="_resolution__Poset.html">resolutionPoset</a> -- generates a poset from a resolution</span></span></li> <li><span><kbd>resolutionPoset(MonomialIdeal)</kbd> -- see <span><a title="generates a poset from a resolution" href="_resolution__Poset.html">resolutionPoset</a> -- generates a poset from a resolution</span></span></li> <li><span><kbd>standardMonomialPoset(MonomialIdeal)</kbd> -- see <span><a title="generates the poset of divisibility in the monomial basis of an ideal" href="_standard__Monomial__Poset.html">standardMonomialPoset</a> -- generates the poset of divisibility in the monomial basis of an ideal</span></span></li> <li><span><kbd>standardMonomialPoset(MonomialIdeal,ZZ,ZZ)</kbd> -- see <span><a title="generates the poset of divisibility in the monomial basis of an ideal" href="_standard__Monomial__Poset.html">standardMonomialPoset</a> -- generates the poset of divisibility in the monomial basis of an ideal</span></span></li> <li><span><kbd>subposet(Poset,List)</kbd> -- see <span><a title="computes the induced subposet of a poset given a list of elements" href="_subposet.html">subposet</a> -- computes the induced subposet of a poset given a list of elements</span></span></li> <li><span><kbd>transitiveOrientation(Graph)</kbd> -- see <span><a title="generates a poset whose comparability graph is the given graph" href="_transitive__Orientation.html">transitiveOrientation</a> -- generates a poset whose comparability graph is the given graph</span></span></li> <li><span><kbd>Poset + Poset</kbd> -- see <span><a title="computes the union of two posets" href="_union_lp__Poset_cm__Poset_rp.html">union(Poset,Poset)</a> -- computes the union of two posets</span></span></li> <li><span><a title="computes the union of two posets" href="_union_lp__Poset_cm__Poset_rp.html">union(Poset,Poset)</a> -- computes the union of two posets</span></li> <li><span><kbd>youngSubposet(List)</kbd> -- see <span><a title="generates a subposet of Young's lattice" href="_young__Subposet.html">youngSubposet</a> -- generates a subposet of Young's lattice</span></span></li> <li><span><kbd>youngSubposet(List,List)</kbd> -- see <span><a title="generates a subposet of Young's lattice" href="_young__Subposet.html">youngSubposet</a> -- generates a subposet of Young's lattice</span></span></li> <li><span><kbd>youngSubposet(ZZ)</kbd> -- see <span><a title="generates a subposet of Young's lattice" href="_young__Subposet.html">youngSubposet</a> -- generates a subposet of Young's lattice</span></span></li> </ul> <h2>Methods that use an object of class Poset:</h2> <ul> <li><span><kbd>allRelations(Poset)</kbd> -- see <span><a title="computes all relations of a poset" href="_all__Relations.html">allRelations</a> -- computes all relations of a poset</span></span></li> <li><span><kbd>allRelations(Poset,Boolean)</kbd> -- see <span><a title="computes all relations of a poset" href="_all__Relations.html">allRelations</a> -- computes all relations of a poset</span></span></li> <li><span><kbd>antichains(Poset)</kbd> -- see <span><a title="computes all antichains of a poset" href="_antichains.html">antichains</a> -- computes all antichains of a poset</span></span></li> <li><span><kbd>antichains(Poset,ZZ)</kbd> -- see <span><a title="computes all antichains of a poset" href="_antichains.html">antichains</a> -- computes all antichains of a poset</span></span></li> <li><span><kbd>areIsomorphic(Poset,Poset)</kbd> -- see <span><a title="determines if two posets are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines if two posets are isomorphic</span></span></li> <li><span><kbd>Poset == Poset</kbd> -- see <span><a title="determines if two posets are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines if two posets are isomorphic</span></span></li> <li><span><kbd>atoms(Poset)</kbd> -- see <span><a title="computes the list of elements covering the minimal elements of a poset" href="_atoms.html">atoms</a> -- computes the list of elements covering the minimal elements of a poset</span></span></li> <li><span><kbd>chains(Poset)</kbd> -- see <span><a title="computes all chains of a poset" href="_chains.html">chains</a> -- computes all chains of a poset</span></span></li> <li><span><kbd>chains(Poset,ZZ)</kbd> -- see <span><a title="computes all chains of a poset" href="_chains.html">chains</a> -- computes all chains of a poset</span></span></li> <li><span><kbd>characteristicPolynomial(Poset)</kbd> -- see <span><a title="computes the characteristic polynomial of a ranked poset with a unique minimal element" href="_characteristic__Polynomial.html">characteristicPolynomial</a> -- computes the characteristic polynomial of a ranked poset with a unique minimal element</span></span></li> <li><span><kbd>comparabilityGraph(Poset)</kbd> -- see <span><a title="produces the comparability graph of a poset" href="_comparability__Graph.html">comparabilityGraph</a> -- produces the comparability graph of a poset</span></span></li> <li><span><kbd>compare(Poset,Thing,Thing)</kbd> -- see <span><a title="compares two elements in a poset" href="_compare.html">compare</a> -- compares two elements in a poset</span></span></li> <li><span><a title="generates a list of connected components of a poset" href="_connected__Components_lp__Poset_rp.html">connectedComponents(Poset)</a> -- generates a list of connected components of a poset</span></li> <li><span><kbd>coveringRelations(Poset)</kbd> -- see <span><a title="computes the minimal list of generating relations of a poset" href="_covering__Relations.html">coveringRelations</a> -- computes the minimal list of generating relations of a poset</span></span></li> <li><span><kbd>coxeterPolynomial(Poset)</kbd> -- see <span><a title="computes the Coxeter polynomial of a poset" href="_coxeter__Polynomial.html">coxeterPolynomial</a> -- computes the Coxeter polynomial of a poset</span></span></li> <li><span><kbd>degreePolynomial(Poset)</kbd> -- see <span><a title="computes the degree polynomial of a poset" href="_degree__Polynomial.html">degreePolynomial</a> -- computes the degree polynomial of a poset</span></span></li> <li><span><kbd>dilworthNumber(Poset)</kbd> -- see <span><a title="computes the Dilworth number of a poset" href="_dilworth__Number.html">dilworthNumber</a> -- computes the Dilworth number of a poset</span></span></li> <li><span><kbd>displayPoset(Poset)</kbd> -- see <span><a title="generates a PDF representation of a poset and attempts to display it" href="_display__Poset.html">displayPoset</a> -- generates a PDF representation of a poset and attempts to display it</span></span></li> <li><span><kbd>Poset - List</kbd> -- see <span><a title="computes the induced subposet of a poset given a list of elements to remove" href="_drop__Elements.html">dropElements</a> -- computes the induced subposet of a poset given a list of elements to remove</span></span></li> <li><span><kbd>filter(Poset,List)</kbd> -- see <span><a title="computes the elements above given elements in a poset" href="_filter.html">filter</a> -- computes the elements above given elements in a poset</span></span></li> <li><span><kbd>filtration(Poset)</kbd> -- see <span><a title="generates the filtration of a poset" href="_filtration.html">filtration</a> -- generates the filtration of a poset</span></span></li> <li><span><kbd>flagChains(Poset,List)</kbd> -- see <span><a title="computes the maximal chains in a list of flags of a ranked poset" href="_flag__Chains.html">flagChains</a> -- computes the maximal chains in a list of flags of a ranked poset</span></span></li> <li><span><kbd>flagfPolynomial(Poset)</kbd> -- see <span><a title="computes the flag-f polynomial of a ranked poset" href="_flagf__Polynomial.html">flagfPolynomial</a> -- computes the flag-f polynomial of a ranked poset</span></span></li> <li><span><kbd>flaghPolynomial(Poset)</kbd> -- see <span><a title="computes the flag-h polynomial of a ranked poset" href="_flagh__Polynomial.html">flaghPolynomial</a> -- computes the flag-h polynomial of a ranked poset</span></span></li> <li><span><kbd>fPolynomial(Poset)</kbd> -- see <span><a title="computes the f-polynomial of a poset" href="_f__Polynomial.html">fPolynomial</a> -- computes the f-polynomial of a poset</span></span></li> <li><span><kbd>gapConvertPoset(Poset)</kbd> -- see <span><a title="converts between Macaulay2's Posets and GAP's Posets" href="_gap__Convert__Poset.html">gapConvertPoset</a> -- converts between Macaulay2's Posets and GAP's Posets</span></span></li> <li><span><kbd>greeneKleitmanPartition(Poset)</kbd> -- see <span><a title="computes the Greene-Kleitman partition of a poset" href="_greene__Kleitman__Partition.html">greeneKleitmanPartition</a> -- computes the Greene-Kleitman partition of a poset</span></span></li> <li><span><kbd>hasseDiagram(Poset)</kbd> -- see <span><a title="produces the Hasse diagram of a poset" href="_hasse__Diagram.html">hasseDiagram</a> -- produces the Hasse diagram of a poset</span></span></li> <li><span><a title="computes the height of a poset" href="_height_lp__Poset_rp.html">height(Poset)</a> -- computes the height of a poset</span></li> <li><span><kbd>hibiIdeal(Poset)</kbd> -- see <span><a title="produces the Hibi ideal of a poset" href="_hibi__Ideal.html">hibiIdeal</a> -- produces the Hibi ideal of a poset</span></span></li> <li><span><kbd>hibiRing(Poset)</kbd> -- see <span><a title="produces the Hibi ring of a poset" href="_hibi__Ring.html">hibiRing</a> -- produces the Hibi ring of a poset</span></span></li> <li><span><kbd>hPolynomial(Poset)</kbd> -- see <span><a title="computes the h-polynomial of a poset" href="_h__Polynomial.html">hPolynomial</a> -- computes the h-polynomial of a poset</span></span></li> <li><span><kbd>incomparabilityGraph(Poset)</kbd> -- see <span><a title="produces the incomparability graph of a poset" href="_incomparability__Graph.html">incomparabilityGraph</a> -- produces the incomparability graph of a poset</span></span></li> <li><span><kbd>isAntichain(Poset,List)</kbd> -- see <span><a title="determines if a given list of vertices is an antichain of a poset" href="_is__Antichain.html">isAntichain</a> -- determines if a given list of vertices is an antichain of a poset</span></span></li> <li><span><kbd>isAtomic(Poset)</kbd> -- see <span><a title="determines if a lattice is atomic" href="_is__Atomic.html">isAtomic</a> -- determines if a lattice is atomic</span></span></li> <li><span><kbd>isBounded(Poset)</kbd> -- see <span><a title="determines if a poset is bounded" href="_is__Bounded.html">isBounded</a> -- determines if a poset is bounded</span></span></li> <li><span><a title="determines if a poset is connected" href="_is__Connected_lp__Poset_rp.html">isConnected(Poset)</a> -- determines if a poset is connected</span></li> <li><span><kbd>isDistributive(Poset)</kbd> -- see <span><a title="determines if a lattice is distributive" href="_is__Distributive.html">isDistributive</a> -- determines if a lattice is distributive</span></span></li> <li><span><a title="determines if a ranked poset is Eulerian" href="_is__Eulerian_lp__Poset_rp.html">isEulerian(Poset)</a> -- determines if a ranked poset is Eulerian</span></li> <li><span><kbd>isGeometric(Poset)</kbd> -- see <span><a title="determines if a lattice is geometric" href="_is__Geometric.html">isGeometric</a> -- determines if a lattice is geometric</span></span></li> <li><span><kbd>isGraded(Poset)</kbd> -- see <span><a title="determines if a poset is graded" href="_is__Graded.html">isGraded</a> -- determines if a poset is graded</span></span></li> <li><span><kbd>isLattice(Poset)</kbd> -- see <span><a title="determines if a poset is a lattice" href="_is__Lattice.html">isLattice</a> -- determines if a poset is a lattice</span></span></li> <li><span><kbd>isLowerSemilattice(Poset)</kbd> -- see <span><a title="determines if a poset is a lower (or meet) semilattice" href="_is__Lower__Semilattice.html">isLowerSemilattice</a> -- determines if a poset is a lower (or meet) semilattice</span></span></li> <li><span><kbd>isLowerSemimodular(Poset)</kbd> -- see <span><a title="determines if a ranked lattice is lower semimodular" href="_is__Lower__Semimodular.html">isLowerSemimodular</a> -- determines if a ranked lattice is lower semimodular</span></span></li> <li><span><kbd>isModular(Poset)</kbd> -- see <span><a title="determines if a lattice is modular" href="_is__Modular.html">isModular</a> -- determines if a lattice is modular</span></span></li> <li><span><a title="computes an isomorphism between isomorphic posets" href="_isomorphism_lp__Poset_cm__Poset_rp.html">isomorphism(Poset,Poset)</a> -- computes an isomorphism between isomorphic posets</span></li> <li><span><kbd>isRanked(Poset)</kbd> -- see <span><a title="determines if a poset is ranked" href="_is__Ranked.html">isRanked</a> -- determines if a poset is ranked</span></span></li> <li><span><kbd>isSperner(Poset)</kbd> -- see <span><a title="determines if a ranked poset has the Sperner property" href="_is__Sperner.html">isSperner</a> -- determines if a ranked poset has the Sperner property</span></span></li> <li><span><kbd>isStrictSperner(Poset)</kbd> -- see <span><a title="determines if a ranked poset has the strict Sperner property" href="_is__Strict__Sperner.html">isStrictSperner</a> -- determines if a ranked poset has the strict Sperner property</span></span></li> <li><span><kbd>isUpperSemilattice(Poset)</kbd> -- see <span><a title="determines if a poset is an upper (or join) semilattice" href="_is__Upper__Semilattice.html">isUpperSemilattice</a> -- determines if a poset is an upper (or join) semilattice</span></span></li> <li><span><kbd>isUpperSemimodular(Poset)</kbd> -- see <span><a title="determines if a lattice is upper semimodular" href="_is__Upper__Semimodular.html">isUpperSemimodular</a> -- determines if a lattice is upper semimodular</span></span></li> <li><span><kbd>joinExists(Poset,Thing,Thing)</kbd> -- see <span><a title="determines if the join exists for two elements of a poset" href="_join__Exists.html">joinExists</a> -- determines if the join exists for two elements of a poset</span></span></li> <li><span><kbd>joinIrreducibles(Poset)</kbd> -- see <span><a title="determines the join irreducible elements of a poset" href="_join__Irreducibles.html">joinIrreducibles</a> -- determines the join irreducible elements of a poset</span></span></li> <li><span><kbd>linearExtensions(Poset)</kbd> -- see <span><a title="computes all linear extensions of a poset" href="_linear__Extensions.html">linearExtensions</a> -- computes all linear extensions of a poset</span></span></li> <li><span><kbd>magnitude(Poset)</kbd> -- see <span><a title="computes the magnitude of a poset" href="_magnitude.html">magnitude</a> -- computes the magnitude of a poset</span></span></li> <li><span><kbd>maximalAntichains(Poset)</kbd> -- see <span><a title="computes all maximal antichains of a poset" href="_maximal__Antichains.html">maximalAntichains</a> -- computes all maximal antichains of a poset</span></span></li> <li><span><kbd>maximalChains(Poset)</kbd> -- see <span><a title="computes all maximal chains of a poset" href="_maximal__Chains.html">maximalChains</a> -- computes all maximal chains of a poset</span></span></li> <li><span><kbd>maximalElements(Poset)</kbd> -- see <span><a title="determines the maximal elements of a poset" href="_maximal__Elements.html">maximalElements</a> -- determines the maximal elements of a poset</span></span></li> <li><span><kbd>meetExists(Poset,Thing,Thing)</kbd> -- see <span><a title="determines if the meet exists for two elements of a poset" href="_meet__Exists.html">meetExists</a> -- determines if the meet exists for two elements of a poset</span></span></li> <li><span><kbd>meetIrreducibles(Poset)</kbd> -- see <span><a title="determines the meet irreducible elements of a poset" href="_meet__Irreducibles.html">meetIrreducibles</a> -- determines the meet irreducible elements of a poset</span></span></li> <li><span><kbd>minimalElements(Poset)</kbd> -- see <span><a title="determines the minimal elements of a poset" href="_minimal__Elements.html">minimalElements</a> -- determines the minimal elements of a poset</span></span></li> <li><span><kbd>moebiusFunction(Poset)</kbd> -- see <span><a title="computes the Moebius function at every pair of elements of a poset" href="_moebius__Function.html">moebiusFunction</a> -- computes the Moebius function at every pair of elements of a poset</span></span></li> <li><span><kbd>orderComplex(Poset)</kbd> -- see <span><a title="produces the order complex of a poset" href="_order__Complex.html">orderComplex</a> -- produces the order complex of a poset</span></span></li> <li><span><kbd>orderIdeal(Poset,List)</kbd> -- see <span><a title="computes the elements below given elements in a poset" href="_order__Ideal.html">orderIdeal</a> -- computes the elements below given elements in a poset</span></span></li> <li><span><kbd>outputTexPoset(Poset,String)</kbd> -- see <span><a title="writes a LaTeX file with a TikZ-representation of a poset" href="_output__Tex__Poset.html">outputTexPoset</a> -- writes a LaTeX file with a TikZ-representation of a poset</span></span></li> <li><span><kbd>poincare(Poset)</kbd> -- see <span><a title="computes the Poincaré polynomial of a ranked poset with a unique minimal element" href="_poincare__Polynomial.html">poincarePolynomial</a> -- computes the Poincaré polynomial of a ranked poset with a unique minimal element</span></span></li> <li><span><kbd>poincarePolynomial(Poset)</kbd> -- see <span><a title="computes the Poincaré polynomial of a ranked poset with a unique minimal element" href="_poincare__Polynomial.html">poincarePolynomial</a> -- computes the Poincaré polynomial of a ranked poset with a unique minimal element</span></span></li> <li><span><a title="returns elements of the ground set" href="___Poset_sp_us_sp__List.html">Poset _ List</a> -- returns elements of the ground set</span></li> <li><span><a title="returns an element of the ground set" href="___Poset_sp_us_sp__Z__Z.html">Poset _ ZZ</a> -- returns an element of the ground set</span></li> <li><span><a title="returns the ground set of a poset" href="___Poset_sp_us_st.html">Poset _*</a> -- returns the ground set of a poset</span></li> <li><span><kbd>vertices(Poset)</kbd> -- see <span><a title="returns the ground set of a poset" href="___Poset_sp_us_st.html">Poset _*</a> -- returns the ground set of a poset</span></span></li> <li><span><kbd>posetJoin(Poset,Thing,Thing)</kbd> -- see <span><a title="determines the join for two elements of a poset" href="_poset__Join.html">posetJoin</a> -- determines the join for two elements of a poset</span></span></li> <li><span><kbd>posetMeet(Poset,Thing,Thing)</kbd> -- see <span><a title="determines the meet for two elements of a poset" href="_poset__Meet.html">posetMeet</a> -- determines the meet for two elements of a poset</span></span></li> <li><span><kbd>pPartitionRing(Poset)</kbd> -- see <span><a title="produces the p-partition ring of a poset" href="_p__Partition__Ring.html">pPartitionRing</a> -- produces the p-partition ring of a poset</span></span></li> <li><span><kbd>principalFilter(Poset,Thing)</kbd> -- see <span><a title="computes the elements above a given element in a poset" href="_principal__Filter.html">principalFilter</a> -- computes the elements above a given element in a poset</span></span></li> <li><span><kbd>principalOrderIdeal(Poset,Thing)</kbd> -- see <span><a title="computes the elements below a given element in a poset" href="_principal__Order__Ideal.html">principalOrderIdeal</a> -- computes the elements below a given element in a poset</span></span></li> <li><span><kbd>Poset * Poset</kbd> -- see <span><a title="computes the product of two posets" href="_product_lp__Poset_cm__Poset_rp.html">product(Poset,Poset)</a> -- computes the product of two posets</span></span></li> <li><span><kbd>rankFunction(Poset)</kbd> -- see <span><a title="computes the rank function of a ranked poset" href="_rank__Function.html">rankFunction</a> -- computes the rank function of a ranked poset</span></span></li> <li><span><kbd>rankGeneratingFunction(Poset)</kbd> -- see <span><a title="computes the rank generating function of a ranked poset" href="_rank__Generating__Function.html">rankGeneratingFunction</a> -- computes the rank generating function of a ranked poset</span></span></li> <li><span><kbd>rank(Poset)</kbd> -- see <span><a title="generates a list of lists representing the ranks of a ranked poset" href="_rank__Poset.html">rankPoset</a> -- generates a list of lists representing the ranks of a ranked poset</span></span></li> <li><span><kbd>rankPoset(Poset)</kbd> -- see <span><a title="generates a list of lists representing the ranks of a ranked poset" href="_rank__Poset.html">rankPoset</a> -- generates a list of lists representing the ranks of a ranked poset</span></span></li> <li><span><kbd>tex(Poset)</kbd> -- see <span><a title="generates a string containing a TikZ-figure of a poset" href="_tex__Poset.html">texPoset</a> -- generates a string containing a TikZ-figure of a poset</span></span></li> <li><span><kbd>texPoset(Poset)</kbd> -- see <span><a title="generates a string containing a TikZ-figure of a poset" href="_tex__Poset.html">texPoset</a> -- generates a string containing a TikZ-figure of a poset</span></span></li> <li><span><kbd>tuttePolynomial(Poset)</kbd> -- see <span><a title="computes the Tutte polynomial of a poset" href="_tutte__Polynomial.html">tuttePolynomial</a> -- computes the Tutte polynomial of a poset</span></span></li> <li><span><span class="tt">vertexSet(Poset)</span> (missing documentation)<!--tag: (vertexSet,Poset)--> </span></li> <li><span><kbd>zetaPolynomial(Poset)</kbd> -- see <span><a title="computes the zeta polynomial of a poset" href="_zeta__Polynomial.html">zetaPolynomial</a> -- computes the zeta polynomial of a poset</span></span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="a class for partially ordered sets (posets)" href="___Poset.html">Poset</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> < <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Posets.m2:1959:0</span>.</p> </div> </div> </div> </body> </html>