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<head><title>lcm(MonomialIdeal) -- least common multiple of all minimal generators</title>
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<div><h1>lcm(MonomialIdeal) -- least common multiple of all minimal generators</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 = lcm I</tt></div>
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<li><span>Function: <a href="_lcm.html" title="least common multiple">lcm</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>a <a href="___Monomial__Ideal.html">monomial ideal</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>m</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><div>This function is implemented in the engine, as it is used in many algorithms involving monomial ideals.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : I = monomialIdeal "a4,a3b6,a2b8c2,c4d5"
4 3 6 2 8 2 4 5
o2 = monomialIdeal (a , a b , a b c , c d )
o2 : MonomialIdeal of R</pre>
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<tr><td><pre>i3 : lcm I
4 8 4 5
o3 = a b c d
o3 : R</pre>
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<tr><td><pre>i4 : first exponents lcm I
o4 = {4, 8, 4, 5}
o4 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_dual_lp__Monomial__Ideal_rp.html" title="the Alexander dual of a monomial ideal">dual(MonomialIdeal)</a> -- the Alexander dual of a monomial ideal</span></li>
<li><span><a href="../../PrimaryDecomposition/html/_irreducible__Decomposition_lp__Monomial__Ideal_rp.html" title="express a monomial ideal as an intersection of irreducible monomial ideals">irreducibleDecomposition(MonomialIdeal)</a> -- express a monomial ideal as an intersection of irreducible monomial ideals</span></li>
<li><span><a href="../../PrimaryDecomposition/html/_primary__Decomposition.html" title="irredundant primary decomposition of an ideal">primaryDecomposition(MonomialIdeal)</a> -- irredundant primary decomposition of an ideal</span></li>
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