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<head><title>isLexIdeal -- determine whether an ideal is a lexicographic ideal</title>
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<div><h1>isLexIdeal -- determine whether an ideal is a lexicographic 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=isLexIdeal 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>, a homogeneous ideal in a polynomial ring or quotient of a polynomial ring by a homogeneous ideal</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 a lexicographic 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 ring <tt>R</tt> that is either a polynomial ring or a quotient of a polynomial ring by a monomial ideal, <tt>isLexIdeal</tt> computes bases of <tt>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 a lexicographic 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 : isLexIdeal lexIdeal(R,{1,3,4,3,1})
o2 = true</pre>
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<tr><td><pre>i3 : isLexIdeal ideal(a^3-a^2*b)
o3 = false</pre>
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<tr><td><pre>i4 : isLexIdeal ideal(a^3,a^2*b)
o4 = true</pre>
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<tr><td><pre>i5 : isLexIdeal ideal(a^3,a^2*b,a^3-a^2*b) --not given as a monomial ideal but still a lex ideal
o5 = true</pre>
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<tr><td><pre>i6 : Q=R/ideal(a^3,b^3,a*c^2);</pre>
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<tr><td><pre>i7 : isLexIdeal ideal(a^2*b,a^2*c)
o7 = true</pre>
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<tr><td><pre>i8 : isLexIdeal ideal(a^2*b,a*b^2)
o8 = false</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_lex__Ideal.html" title="produce a lexicographic ideal">lexIdeal</a> -- produce a lexicographic ideal</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isLexIdeal</tt> :</h2>
<ul><li>isLexIdeal(Ideal)</li>
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