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<head><title>integralClosure(..., Strategy => ...) -- control the algorithm used</title>
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<div><h1>integralClosure(..., Strategy => ...) -- control the algorithm used</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, Strategy=>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>, of a subset of the following: <tt>RadicalCodim1, AllCodimensions</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><p><tt>RadicalCodim1</tt> chooses an alternate, often much faster, sometimes much slower, algorithm for computing the radical of ideals. This will often produce a different presentation for the integral closure.</p>
<div><tt>AllCodimensions</tt> tels the algorithm to bypass the computation of the S2-ification, but in each iteration of the algorithm, use the radical of the extended Jacobian ideal from the previous step, instead of using only the codimension 1 components of that. This is useful when for some reason the S2-ification is hard to compute, or if the probabilistic algorithm for computing it fails. In general though, this option slows down the computation for many examples.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);</pre>
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<tr><td><pre>i2 : time R' = integralClosure(R, Strategy=>{RadicalCodim1})
-- used 0.850871 seconds
o2 = R'
o2 : QuotientRing</pre>
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<tr><td><pre>i3 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);</pre>
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<tr><td><pre>i4 : time R' = integralClosure(R)
-- used 0.669898 seconds
o4 = R'
o4 : QuotientRing</pre>
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<tr><td><pre>i5 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);</pre>
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<tr><td><pre>i6 : time R' = integralClosure(R, Strategy=>{AllCodimensions})
-- used 0.710892 seconds
o6 = R'
o6 : QuotientRing</pre>
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<tr><td><pre>i7 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);</pre>
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<tr><td><pre>i8 : time R' = integralClosure(R, Strategy=>{RadicalCodim1, AllCodimensions})
-- used 0.755885 seconds
o8 = R'
o8 : QuotientRing</pre>
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<h2>Further information</h2>
<ul><li><span>Default value: <tt>{}</tt></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/___Strategy.html" title="name for an optional argument">Strategy</a> -- name for an optional argument</span></span></li>
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