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<head><title>Posets -- A package for working with posets.</title>
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<div><h1>Posets -- A package for working with posets.</h1>
<div class="single"><h2>Description</h2>
<div><div><em>Posets</em> 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.</div>
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<div class="single"><h2>Authors</h2>
<ul><li><div class="single"><a href="http://www.math.columbia.edu/~mapes/">Sonja Mapes</a><span> <<a href="mailto:mapes@math.columbia.edu">mapes@math.columbia.edu</a>></span></div>
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<li><div class="single"><a href="http://www.math.cornell.edu/People/Grads/whieldon.html">Gwyn Whieldon</a><span> <<a href="mailto:whieldon@math.cornell.edu">whieldon@math.cornell.edu</a>></span></div>
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<li><div class="single"><a href="http://www-math.mit.edu/~jyu/">Josephine Yu</a><span> <<a href="mailto:jyu@math.mit.edu">jyu@math.mit.edu</a>></span></div>
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<div class="single"><h2>Version</h2>
This documentation describes version <b>0.1</b> of Posets.</div>
<div class="single"><h2>Source code</h2>
The source code from which this documentation is derived is in the file <a href="../../../../Macaulay2/Posets.m2">Posets.m2</a>.</div>
<div class="single"><h2>Exports</h2>
<ul><li><div class="single">Types<ul><li><span><a href="___Directed__Graph.html" title="a class for directed graphs">DirectedGraph</a> -- a class for directed graphs</span></li>
<li><span><a href="___Poset.html" title="a class for partially ordered sets (posets)">Poset</a> -- a class for partially ordered sets (posets)</span></li>
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<li><div class="single">Functions<ul><li><span><a href="_adjacency__Matrix.html" title="returns adjacency matrix of a directed graph">adjacencyMatrix</a> -- returns adjacency matrix of a directed graph</span></li>
<li><span><a href="_all__Pairs__Shortest__Path.html" title="computes lengths of shortest paths between all pairs in a directed graph">allPairsShortestPath</a> -- computes lengths of shortest paths between all pairs in a directed graph</span></li>
<li><span><a href="_compare.html" title="returns boolean value for whether an element is less than another">compare</a> -- returns boolean value for whether an element is less than another</span></li>
<li><span><a href="_directed__Graph.html" title="creating a directed graph">directedGraph</a> -- creating a directed graph</span></li>
<li><span><a href="_filter.html" title="returns a principal filter generated by the given element">filter</a> -- returns a principal filter generated by the given element</span></li>
<li><span><a href="_is__Lattice.html" title="determines if a poset is a lattice">isLattice</a> -- determines if a poset is a lattice</span></li>
<li><span><a href="_join__Exists.html" title="determines if the join exists">joinExists</a> -- determines if the join exists</span></li>
<li><span><a href="_lcm__Lattice.html" title="returns the LCM lattice of an ideal">lcmLattice</a> -- returns the LCM lattice of an ideal</span></li>
<li><span><a href="_meet__Exists.html" title="determines if the meet exists">meetExists</a> -- determines if the meet exists</span></li>
<li><span><a href="_order__Ideal.html" title="returns a principal order ideal generated by the given element">orderIdeal</a> -- returns a principal order ideal generated by the given element</span></li>
<li><span><a href="_poset.html" title="creating a poset">poset</a> -- creating a poset</span></li>
<li><span><a href="_poset__Join.html" title="returns the join of two elements">posetJoin</a> -- returns the join of two elements</span></li>
<li><span><a href="_poset__Meet.html" title="returns the meet of two elements">posetMeet</a> -- returns the meet of two elements</span></li>
<li><span><a href="_transitive__Closure.html" title="computes the transitive closure of a given set of relations.">transitiveClosure</a> -- computes the transitive closure of a given set of relations.</span></li>
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<li><div class="single">Methods<ul><li><span>compare(Poset,Thing,Thing), see <span><a href="_compare.html" title="returns boolean value for whether an element is less than another">compare</a> -- returns boolean value for whether an element is less than another</span></span></li>
<li><span>filter(Poset,Thing), see <span><a href="_filter.html" title="returns a principal filter generated by the given element">filter</a> -- returns a principal filter generated by the given element</span></span></li>
<li><span>joinExists(Poset,Thing,Thing), see <span><a href="_join__Exists.html" title="determines if the join exists">joinExists</a> -- determines if the join exists</span></span></li>
<li><span>meetExists(Poset,Thing,Thing), see <span><a href="_meet__Exists.html" title="determines if the meet exists">meetExists</a> -- determines if the meet exists</span></span></li>
<li><span>orderIdeal(Poset,Thing), see <span><a href="_order__Ideal.html" title="returns a principal order ideal generated by the given element">orderIdeal</a> -- returns a principal order ideal generated by the given element</span></span></li>
<li><span>posetJoin(Poset,Thing,Thing), see <span><a href="_poset__Join.html" title="returns the join of two elements">posetJoin</a> -- returns the join of two elements</span></span></li>
<li><span>posetMeet(Poset,Thing,Thing), see <span><a href="_poset__Meet.html" title="returns the meet of two elements">posetMeet</a> -- returns the meet of two elements</span></span></li>
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<li><div class="single">Symbols<ul><li><span><a href="___Directed__Edges.html" title="the set of directed edges of a directed graph">DirectedEdges</a> -- the set of directed edges of a directed graph</span></li>
<li><span><a href="___Ground__Set.html" title="underlying set of a poset">GroundSet</a> -- underlying set of a poset</span></li>
<li><span><a href="___Relation__Matrix.html" title="the matrix expressing all of the relations between elements in a Poset">RelationMatrix</a> -- the matrix expressing all of the relations between elements in a Poset</span></li>
<li><span><a href="___Relations.html" title="a set of relations in the poset that generates all other relations">Relations</a> -- a set of relations in the poset that generates all other relations</span></li>
<li><span><a href="___Vertices.html" title="the set of vertices a directed graph">Vertices</a> -- the set of vertices a directed graph</span></li>
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