<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>ideal(Variety) -- returns the defining ideal</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_identity.html">next</a> | <a href="_ideal_lp__Ring__Element_rp.html">previous</a> | <a href="_identity.html">forward</a> | <a href="_ideal_lp__Ring__Element_rp.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<hr/>
<div><h1>ideal(Variety) -- returns the defining 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>ideal X</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_ideal.html" title="make an ideal">ideal</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>X</tt>, <span>a <a href="___Variety.html">variety</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Ideal.html">ideal</a></span>, which is the defining ideal of <tt>X</tt></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>A <a href="___Variety.html">variety</a> is defined by a <a href="___Ring.html">ring</a>. This function returns the defining ideal of the ring of <tt>X</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[w,x,y,z];</pre>
</td></tr>
<tr><td><pre>i2 : X = Spec(R/(y^2-x*z,x^2*y-z^2,x^3-y*z))
o2 = X
o2 : AffineVariety</pre>
</td></tr>
<tr><td><pre>i3 : ideal X
2 2 2 3
o3 = ideal (y - x*z, x y - z , x - y*z)
o3 : Ideal of R</pre>
</td></tr>
<tr><td><pre>i4 : ring X
R
o4 = ------------------------------
2 2 2 3
(y - x*z, x y - z , x - y*z)
o4 : QuotientRing</pre>
</td></tr>
<tr><td><pre>i5 : Y = Proj(R/(x^2-w*y, x*y-w*z, x*z-y^2))
o5 = Y
o5 : ProjectiveVariety</pre>
</td></tr>
<tr><td><pre>i6 : ideal Y
2 2
o6 = ideal (x - w*y, x*y - w*z, - y + x*z)
o6 : Ideal of R</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_ring.html" title="get the associated ring of an object">ring</a> -- get the associated ring of an object</span></li>
<li><span><a href="_ideal_lp__Ring_rp.html" title="returns the defining ideal">ideal(Ring)</a> -- returns the defining ideal</span></li>
<li><span><a href="___Spec_lp__Ring_rp.html" title="make an affine variety">Spec</a> -- make an affine variety</span></li>
<li><span><a href="___Affine__Variety.html" title="the class of all affine varieties">AffineVariety</a> -- the class of all affine varieties</span></li>
<li><span><a href="___Proj_lp__Ring_rp.html" title="make a projective variety">Proj</a> -- make a projective variety</span></li>
<li><span><a href="___Projective__Variety.html" title="the class of all projective varieties">ProjectiveVariety</a> -- the class of all projective varieties</span></li>
</ul>
</div>
</div>
</body>
</html>
