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<head><title>isNormal -- determine if a reduced ring is normal</title>
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<div><h1>isNormal -- determine if a reduced ring is normal</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>isNormal R</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, a reduced equidimensional ring</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, whether <tt>R</tt> is normal, that is, whether it satisfies Serre’s conditions S2 and R1</span></li>
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<div class="single"><h2>Description</h2>
<div><div>This function computes the jacobian of the ring which can be costly for larger rings. Therefore it checks the less costly S2 condition first and if true, then tests the R1 condition using the jacobian of <tt>R</tt>.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4);</pre>
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<tr><td><pre>i2 : isNormal R
o2 = false</pre>
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<tr><td><pre>i3 : isNormal(integralClosure R)
o3 = true</pre>
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<div class="single"><h2>Caveat</h2>
<div><div>The ring <tt>R</tt> must be an equidimensional ring. If <tt>R</tt> is a domain, then sometimes computing the integral closure of <tt>R</tt> can be faster than this test.</div>
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<div class="single"><h2>See also</h2>
<ul><li><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></li>
<li><span><a href="_make__S2.html" title="compute the S2ification of a reduced ring">makeS2</a> -- compute the S2ification of a reduced ring</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isNormal</tt> :</h2>
<ul><li>isNormal(Ring)</li>
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