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<head><title>filter -- returns a principal filter generated by the given element</title>
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<div><h1>filter -- returns a principal filter generated by the given element</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>F = filter (P,a)</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>
<li><span><tt>a</tt>, <span>a <a href="../../Macaulay2Doc/html/___Thing.html">thing</a></span>, a is an element of P</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>F</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of all elements in P that are less than or equal to a</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : G = {a,b,c,d};</pre>
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<tr><td><pre>i2 : R = {(a,b), (a,c), (c,d)};</pre>
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<tr><td><pre>i3 : P = poset (G,R);</pre>
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<tr><td><pre>i4 : F = filter (P,d)
o4 = {a, c, d}
o4 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><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>
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<div class="waystouse"><h2>Ways to use <tt>filter</tt> :</h2>
<ul><li>filter(Poset,Thing)</li>
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