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<head><title>isLPP -- determine whether an ideal is an LPP ideal</title>
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<div><h1>isLPP -- determine whether an ideal is an LPP ideal</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>B=isLPP I</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, an ideal in a polynomial ring</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>B</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <tt>true</tt> if <tt>I</tt> is an LPP ideal in <tt>ring I</tt> and <tt>false</tt> otherwise</span></li>
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<div class="single"><h2>Description</h2>
<div><div>Given an ideal <tt>I</tt> in a polynomial ring <tt>R</tt>, <tt>isLPP</tt> checks that <tt>I</tt> is Artinian and that the power sequence is weakly increasing. Then <tt>isLPP</tt> computes bases of <tt>R/I</tt> in each degree up through the maximum degree of a minimal generator of <tt>I</tt> to determine whether <tt>I</tt> is an LPP ideal in <tt>R</tt>.</div>
<table class="examples"><tr><td><pre>i1 : R=ZZ/32003[a..c];</pre>
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<tr><td><pre>i2 : isLPP LPP(R,{1,3,4,3,2},{2,2,4})
o2 = true</pre>
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<tr><td><pre>i3 : isLPP ideal(a^3,b^3,c^3,a^2*b,a^2*c,a*b^2*c^2)
o3 = true</pre>
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<tr><td><pre>i4 : isLPP ideal(a^3,b^4) --not Artinian since no power of c
o4 = false</pre>
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<tr><td><pre>i5 : isLPP ideal(a^3,b^4,c^3) --powers not weakly increasing
o5 = false</pre>
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<tr><td><pre>i6 : isLPP ideal(a^3,b^3,c^3,a^2*b,a*b^2)
o6 = false</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_is__Lex__Ideal.html" title="determine whether an ideal is a lexicographic ideal">isLexIdeal</a> -- determine whether an ideal is a lexicographic ideal</span></li>
<li><span><a href="___L__P__P.html" title="return the lex-plus-powers (LPP) ideal corresponding to a given Hilbert function and power sequence">LPP</a> -- return the lex-plus-powers (LPP) ideal corresponding to a given Hilbert function and power sequence</span></li>
<li><span><a href="_generate__L__P__Ps.html" title="return all LPP ideals corresponding to a given Hilbert function">generateLPPs</a> -- return all LPP ideals corresponding to a given Hilbert function</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isLPP</tt> :</h2>
<ul><li>isLPP(Ideal)</li>
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