<?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>hilbertPolynomial -- compute the Hilbert polynomial</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_hilbert__Polynomial_lp..._cm_sp__Projective_sp_eq_gt_sp..._rp.html">next</a> | <a href="_hilbert__Function.html">previous</a> | <a href="_hilbert__Polynomial_lp..._cm_sp__Projective_sp_eq_gt_sp..._rp.html">forward</a> | <a href="_hilbert__Function.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>hilbertPolynomial -- compute the Hilbert polynomial</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_hilbert__Polynomial_lp..._cm_sp__Projective_sp_eq_gt_sp..._rp.html">Projective => ...</a>, -- choose how to display the Hilbert polynomial</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>In a singly graded ambient ring, the <a href="_hilbert__Function.html">Hilbert function</a> eventually is a polynomial called the Hilbert polynomial. By default this polynomal is written in terms of the Hilbert polynomials of projective spaces because it is a good form for extracting geometric information from the polynomial. The Hilbert polynomial of <tt>P^i</tt> is <tt>z |--> binomial(z + i, i).</tt></div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_degrees__Ring.html" title="the ring of degrees">degreesRing</a> -- the ring of degrees</span></li>
<li><span><a href="_reduce__Hilbert.html" title="reduce a Hilbert series expression">reduceHilbert</a> -- reduce a Hilbert series expression</span></li>
<li><span><a href="_poincare.html" title="assemble degrees into polynomial">poincare</a> -- assemble degrees into polynomial</span></li>
<li><span><a href="_poincare__N.html" title="assemble degrees into polynomial">poincareN</a> -- assemble degrees into polynomial</span></li>
<li><span><a href="_hilbert__Series.html" title="compute the Hilbert series">hilbertSeries</a> -- compute the Hilbert series</span></li>
<li><span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>hilbertPolynomial</tt> :</h2>
<ul><li><span>hilbertPolynomial(ZZ,BettiTally), see <span><a href="___Betti__Tally.html" title="the class of all Betti tallies">BettiTally</a> -- the class of all Betti tallies</span></span></li>
<li><span><a href="_hilbert__Polynomial_lp__Coherent__Sheaf_rp.html" title="compute the Hilbert polynomial of the coherent sheaf">hilbertPolynomial(CoherentSheaf)</a> -- compute the Hilbert polynomial of the coherent sheaf</span></li>
<li><span><a href="_hilbert__Polynomial_lp__Ideal_rp.html" title="compute the Hilbert polynomial of the quotient of the ambient ring by the ideal">hilbertPolynomial(Ideal)</a> -- compute the Hilbert polynomial of the quotient of the ambient ring by the ideal</span></li>
<li><span><a href="_hilbert__Polynomial_lp__Module_rp.html" title="compute the Hilbert polynomial of the module">hilbertPolynomial(Module)</a> -- compute the Hilbert polynomial of the module</span></li>
<li><span><a href="_hilbert__Polynomial_lp__Projective__Variety_rp.html" title="compute the Hilbert polynomial of the projective variety">hilbertPolynomial(ProjectiveVariety)</a> -- compute the Hilbert polynomial of the projective variety</span></li>
<li><span><a href="_hilbert__Polynomial_lp__Ring_rp.html" title="compute the Hilbert polynomial of the ring">hilbertPolynomial(Ring)</a> -- compute the Hilbert polynomial of the ring</span></li>
</ul>
</div>
</div>
</body>
</html>
