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<head><title>dim(ProjectiveHilbertPolynomial) -- the degree of the Hilbert polynomial</title>
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<div><h1>dim(ProjectiveHilbertPolynomial) -- the degree of the Hilbert polynomial</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 P</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>P</tt>, <span>a <a href="___Projective__Hilbert__Polynomial.html">projective Hilbert polynomial</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>ZZ</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div>The command <a href="_dim.html" title="compute the Krull dimension">dim</a>is designed so that the result is the dimension of the projective scheme that may have been used to produce the given Hilbert polynomial.<table class="examples"><tr><td><pre>i1 : V = Proj(QQ[x_0..x_5]/(x_0^3+x_5^3))
o1 = V
o1 : ProjectiveVariety</pre>
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<tr><td><pre>i2 : P = hilbertPolynomial V
o2 = P - 3*P + 3*P
2 3 4
o2 : ProjectiveHilbertPolynomial</pre>
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<tr><td><pre>i3 : dim P
o3 = 4</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_hilbert__Polynomial.html" title="compute the Hilbert polynomial">hilbertPolynomial</a> -- compute the Hilbert polynomial</span></li>
<li><span><a href="_degree_lp__Projective__Hilbert__Polynomial_rp.html" title="">degree(ProjectiveHilbertPolynomial)</a></span></li>
<li><span><a href="_euler_lp__Projective__Hilbert__Polynomial_rp.html" title="constant term of the Hilbert polynomial">euler(ProjectiveHilbertPolynomial)</a> -- constant term of the Hilbert polynomial</span></li>
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