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<head><title>normalCone -- the normal cone of a subscheme</title>
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<div><h1>normalCone -- the normal cone of a subscheme</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>normalCone I</tt><br/><tt>normalCone(I,f)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span></span></li>
<li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, optional argument, if given it should be a non-zero divisor in the ideal <tt>I</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, the ring <i>R[It] ⊗R/I</i> of the normal cone of <i>I</i></span></li>
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<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_symmetric__Kernel_lp..._cm_sp__Variable_sp_eq_gt_sp..._rp.html">Variable => ...</a>, -- Choose name for variables in the created ring</span></li>
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<div class="single"><h2>Description</h2>
<div><div>The normal cone of an ideal <i>I⊂R</i> is the ring <i>R/I ⊕I/I<sup>2</sup> ⊕...</i>, also called the associated graded ring of <i>R</i> with respect to <i>I</i>. If <i>S</i> is the Rees algebra of <i>I</i>, then this ring is isomorphic to <i>S/IS</i>, which is how it is computed here.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_rees__Algebra.html" title="compute the defining ideal of the Rees Algebra">reesAlgebra</a> -- compute the defining ideal of the Rees Algebra</span></li>
<li><span><a href="_associated__Graded__Ring.html" title="the associated graded ring of an ideal">associatedGradedRing</a> -- the associated graded ring of an ideal</span></li>
<li><span><a href="_normal__Cone.html" title="the normal cone of a subscheme">normalCone</a> -- the normal cone of a subscheme</span></li>
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<div class="waystouse"><h2>Ways to use <tt>normalCone</tt> :</h2>
<ul><li>normalCone(Ideal)</li>
<li>normalCone(Ideal,RingElement)</li>
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