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<head><title>RelationMatrix -- the matrix expressing all of the relations between elements in a Poset</title>
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<div><h1>RelationMatrix -- the matrix expressing all of the relations between elements in a Poset</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 = P.RelationMatrix</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>P</tt>, <span>an object of class <a href="___Poset.html" title="a class for partially ordered sets (posets)">Poset</a></span></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>, where the ijth entry indicates whether or not the jth element in the set is less than or equal to the ith element</span></li>
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<div class="single"><h2>Description</h2>
<div><div>Since any poset is in fact a HashTable this symbol denotes the data in the HashTable containing all possible relations between elements.</div>
<table class="examples"><tr><td><pre>i1 : S = QQ[a,b,c,d];</pre>
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<tr><td><pre>i2 : M = monomialIdeal (b^2, b*c, c^2);
o2 : MonomialIdeal of S</pre>
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<tr><td><pre>i3 : L = lcmLattice (M);</pre>
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<tr><td><pre>i4 : L.GroundSet
2 2 2 2 2 2
o4 = {b , b*c, c , b c, b c , b*c }
o4 : List</pre>
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<tr><td><pre>i5 : L.RelationMatrix
o5 = | 1 0 0 1 1 0 |
| 0 1 0 1 1 1 |
| 0 0 1 0 1 1 |
| 0 0 0 1 1 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 1 1 |
6 6
o5 : Matrix ZZ <--- ZZ</pre>
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<div class="single"><h2>See also</h2>
<ul><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="___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="_poset.html" title="creating a poset">poset</a> -- creating a poset</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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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Relation__Matrix.html" title="the matrix expressing all of the relations between elements in a Poset">RelationMatrix</a> is <span>a <a href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p>
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