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<head><title>degree(ProjectiveVariety)</title>
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<div><h1>degree(ProjectiveVariety)</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>degree X</tt></div>
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<li><span>Function: <a href="_degree.html" title="">degree</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>X</tt>, <span>a <a href="___Projective__Variety.html">projective variety</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span>, the degree of <tt>X</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : S = ZZ/32003[x,y,z];</pre>
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<tr><td><pre>i2 : I = ideal(x^4-4*x*y*z^2-z^4-y^4);
o2 : Ideal of S</pre>
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<tr><td><pre>i3 : R = S/I;</pre>
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<tr><td><pre>i4 : X = variety I
o4 = X
o4 : ProjectiveVariety</pre>
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<tr><td><pre>i5 : degree X
o5 = 4</pre>
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The degree of a projective variety <tt>X = V(I) = Proj R</tt> is the degree of the homogeneous coordinate ring <tt>R = S/I</tt> of <tt>X</tt>.<table class="examples"><tr><td><pre>i6 : degree X == degree I
o6 = true</pre>
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<tr><td><pre>i7 : degree X == degree R
o7 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_degree_lp__Ideal_rp.html" title="">degree(Ideal)</a></span></li>
<li><span><a href="_variety.html" title="get the variety">variety</a> -- get the variety</span></li>
<li><span><a href="_varieties.html" title="">varieties</a></span></li>
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