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<head><title>integralClosure(..., Limit => ...) -- do a partial integral closure</title>
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<div><h1>integralClosure(..., Limit => ...) -- do a partial integral closure</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, Limit => n)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, how many steps to perform</span></li>
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<div class="single"><h2>Description</h2>
<div><p>The integral closure algorithm proceeds by finding a suitable ideal <i>J</i>, and then computing <i>Hom<sub>R</sub>(J,J)</i>, and repeating these steps. This optional argument limits the number of such steps to perform.</p>
<div>The result is an integral extension, but is not necessarily integrally closed.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4-z^3);</pre>
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<tr><td><pre>i2 : R' = integralClosure(R, Variable => symbol t, Limit => 2)
o2 = R'
o2 : QuotientRing</pre>
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<tr><td><pre>i3 : trim ideal R'
2 2 4 2 2 4 5 2 5 2 2
o3 = ideal (t x - y z - z - z, t y z + t z - x y - x z , t z -
1,1 1,1 1,1 1,1
------------------------------------------------------------------------
4 2 4 3 4 3 3 4 2 3 2 4 3 6 3 2 3 3 3
x y z - x z - x , t - x y z - 2x y z - x z - 2x y z - 2x z - x )
1,1
o3 : Ideal of QQ[t , x, y, z]
1,1</pre>
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<tr><td><pre>i4 : icFractions R
2 2 4
y z + z + z
o4 = {-------------, x, y, z}
x
o4 : List</pre>
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<h2>Further information</h2>
<ul><li><span>Default value: <a href="../../Macaulay2Doc/html/_infinity.html" title="infinity">infinity</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="../../Macaulay2Doc/html/___Limit.html" title="name for an optional argument">Limit</a> -- name for an optional argument</span></span></li>
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