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<head><title>icPIdeal -- compute the integral closure in prime characteristic of a principal ideal</title>
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<div><h1>icPIdeal -- compute the integral closure in prime characteristic of a principal 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>icPIdeal (a, D, N)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>a</tt>, an element in <tt>R</tt></span></li>
<li><span><tt>D</tt>, a non-zerodivisor of <tt>R</tt> that is in the conductor</span></li>
<li><span><tt>N</tt>, the number of steps in <a href="_ic__Frac__P.html" title="compute the integral closure in prime characteristic">icFracP</a> to compute the integral closure of <tt>R</tt>, by using the conductor element <tt>D</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span>the integral closure of the ideal <tt>(a)</tt>.</span></li>
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<div class="single"><h2>Description</h2>
<div>The main input is an element <tt>a</tt> which generates a principal ideal whose integral closure we are seeking. The other two input elements, a non-zerodivisor conductor element <tt>D</tt> and the number of steps <tt>N</tt> are the pieces of information obtained from <tt>icFracP(R, Verbosity => true)</tt>. (See the Singh--Swanson paper, An algorithm for computing the integral closure, Remark 1.4.)<table class="examples"><tr><td><pre>i1 : R=ZZ/3[u,v,x,y]/ideal(u*x^2-v*y^2);</pre>
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<tr><td><pre>i2 : icFracP(R, Verbosity => 1)
Number of steps: 3, Conductor Element: x^2
u*x
o2 = {1, ---}
y
o2 : List</pre>
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<tr><td><pre>i3 : icPIdeal(x, x^2, 3)
o3 = ideal (x, v*y)
o3 : Ideal of R</pre>
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<div class="single"><h2>Caveat</h2>
<div>The interface to this algorithm will likely change in Macaulay2 1.4</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_ic__Frac__P.html" title="compute the integral closure in prime characteristic">icFracP</a> -- compute the integral closure in prime characteristic</span></li>
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<div class="waystouse"><h2>Ways to use <tt>icPIdeal</tt> :</h2>
<ul><li>icPIdeal(RingElement,RingElement,ZZ)</li>
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