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<head><title>transitiveClosure -- computes the transitive closure of a given set of relations.</title>
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<div><h1>transitiveClosure -- computes the transitive closure of a given set of relations.</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>M = transitiveClosure(I,R)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, ground set</span></li>
<li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of pairs of elements in the ground set I.</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, whose (i,j) entry is 1 if (i,j) is a relation and 0 otherwise.</span></li>
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<div class="single"><h2>Description</h2>
<div><div>This function uses allPairsShortestPath method is used by the poset constructor to compute RelationMatrix from Relations in a Poset.</div>
<table class="examples"><tr><td><pre>i1 : I = {a,b,c,d,e}; -- the ground set</pre>
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<tr><td><pre>i2 : R = {(a,b),(b,c),(a,c),(a,d),(d,e)}; -- relations</pre>
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<tr><td><pre>i3 : transitiveClosure(I,R)
o3 = | 1 1 1 1 1 |
| 0 1 1 0 0 |
| 0 0 1 0 0 |
| 0 0 0 1 1 |
| 0 0 0 0 1 |
5 5
o3 : Matrix RR <--- RR
53 53</pre>
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<div class="single"><h2>Caveat</h2>
<div><div>Output matrix is over RR.</div>
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<div class="single"><h2>See also</h2>
<ul><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>
<li><span><a href="_poset.html" title="creating a poset">poset</a> -- creating 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="___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="_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>
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<div class="waystouse"><h2>Ways to use <tt>transitiveClosure</tt> :</h2>
<ul><li>transitiveClosure(List,List)</li>
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