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<head><title>dim(ProjectiveVariety) -- dimension of the projective variety</title>
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<div><h1>dim(ProjectiveVariety) -- dimension of the projective variety</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>dim V</tt></div>
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<li><span>Function: <a href="_dim.html" title="compute the Krull dimension">dim</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>V</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></span></li>
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<div class="single"><h2>Description</h2>
<div>Computes the dimension of the projective algebraic set from the Krull dimension of its homogeneous coordinate ring.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[x_0..x_4];</pre>
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<tr><td><pre>i2 : M = matrix{{x_0,x_1,x_2,x_3},{x_1,x_2,x_3,x_4}}
o2 = | x_0 x_1 x_2 x_3 |
| x_1 x_2 x_3 x_4 |
2 4
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : V = Proj(R/minors(2,M));</pre>
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<tr><td><pre>i4 : degree V
o4 = 4</pre>
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<tr><td><pre>i5 : dim V
o5 = 1</pre>
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<tr><td><pre>i6 : dim minors(2,M)
o6 = 2</pre>
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<div class="single"><h2>See also</h2>
<ul><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="_dim_lp__Affine__Variety_rp.html" title="dimension of the affine variety">dim(AffineVariety)</a> -- dimension of the affine variety</span></li>
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