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<head><title>variety(Ideal) -- the closed projective subvariety defined by an ideal</title>
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<div><h1>variety(Ideal) -- the closed projective subvariety defined by an 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>variety I</tt></div>
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<li><span>Function: <a href="_variety.html" title="get the variety">variety</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="___Ideal.html">ideal</a></span>, a homogeneous ideal</span></li>
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<li><div class="single">Outputs:<ul><li><span>the closed subvariety defined by an ideal</span></li>
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<div class="single"><h2>Description</h2>
<div>In the example, we compute the dimension of a line in the projective plane.<table class="examples"><tr><td><pre>i1 : R = QQ[x..z]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : variety ideal x
R
o2 = Proj(-)
x
o2 : ProjectiveVariety</pre>
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<tr><td><pre>i3 : dim oo
o3 = 1</pre>
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<div class="single"><h2>Caveat</h2>
<div>An alternative task for this function would be to define the affine subvariety, so if something like this eventually becomes useful, we may have to redesign it. Suggestions welcome.</div>
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