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<head><title>integralClosure(..., Keep => ...) -- list ring generators which should not be simplified away</title>
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<div><h1>integralClosure(..., Keep => ...) -- list ring generators which should not be simplified away</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>integralClosure(R, Keep=>L)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of variables in the ring R, or <tt>null</tt> (the default).</span></li>
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<li><div class="single">Consequences:<ul><li><div>The given list of variables (or all of the outer generators, if L is null) will be generators of the integral closure</div>
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<div class="single"><h2>Description</h2>
<div><div>Consider the cuspidal cubic, and three different possibilities for <tt>Keep</tt>.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[x,y]/ideal(x^3-y^2);</pre>
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<tr><td><pre>i2 : R' = integralClosure(R, Variable => symbol t)
o2 = R'
o2 : QuotientRing</pre>
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<tr><td><pre>i3 : trim ideal R'
2 2
o3 = ideal (t y - x , t x - y, t - x)
0,0 0,0 0,0
o3 : Ideal of QQ[t , x, y]
0,0</pre>
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<table class="examples"><tr><td><pre>i4 : R = QQ[x,y]/ideal(x^3-y^2);</pre>
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<tr><td><pre>i5 : R' = integralClosure(R, Variable => symbol t, Keep => {x})
o5 = R'
o5 : QuotientRing</pre>
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<tr><td><pre>i6 : trim ideal R'
2
o6 = ideal(t - x)
0,0
o6 : Ideal of QQ[t , x]
0,0</pre>
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<table class="examples"><tr><td><pre>i7 : R = QQ[x,y]/ideal(x^3-y^2);</pre>
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<tr><td><pre>i8 : integralClosure(R, Variable => symbol t, Keep => {})
o8 = QQ[t ]
0,0
o8 : PolynomialRing</pre>
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<h2>Further information</h2>
<ul><li><span>Default value: <a href="../../Macaulay2Doc/html/_null.html" title="the unique member of the empty class">null</a></span></li>
<li><span>Function: <span><a href="_integral__Closure.html" title="integral closure of an ideal or a domain">integralClosure</a> -- integral closure of an ideal or a domain</span></span></li>
<li><span>Option name: <span><a href="___Keep.html" title="an optional argument for various functions">Keep</a> -- an optional argument for various functions</span></span></li>
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