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<head><title>hilbertSeries -- compute the Hilbert series</title>
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<div><h1>hilbertSeries -- compute the Hilbert series</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__Series_lp..._cm_sp__Order_sp_eq_gt_sp..._rp.html">Order => ...</a>, -- display the truncated power series expansion</span></li>
<li><span><a href="_hilbert__Series_lp..._cm_sp__Reduce_sp_eq_gt_sp..._rp.html">Reduce => ...</a>, -- reduce the Hilbert series</span></li>
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<div class="single"><h2>Description</h2>
<div>The Hilbert series is the formal power series in the variables of the degrees ring whose coefficients are the dimensions of the corresponding graded component.Note that the series is provided as a type of expression called a <a href="___Divide.html" title="the class of all divide expressions">Divide</a>.</div>
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<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__Polynomial.html" title="compute the Hilbert polynomial">hilbertPolynomial</a> -- compute the Hilbert polynomial</span></li>
<li><span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></li>
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<div class="waystouse"><h2>Ways to use <tt>hilbertSeries</tt> :</h2>
<ul><li><span>hilbertSeries(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__Series_lp__Ideal_rp.html" title="compute the Hilbert series of the quotient of the ambient ring by the ideal">hilbertSeries(Ideal)</a> -- compute the Hilbert series of the quotient of the ambient ring by the ideal</span></li>
<li><span><a href="_hilbert__Series_lp__Module_rp.html" title="compute the Hilbert series of the module">hilbertSeries(Module)</a> -- compute the Hilbert series of the module</span></li>
<li><span><a href="_hilbert__Series_lp__Polynomial__Ring_rp.html" title="compute the Hilbert series of a ring">hilbertSeries(PolynomialRing)</a> -- compute the Hilbert series of a ring</span></li>
<li><span>hilbertSeries(QuotientRing), see <span><a href="_hilbert__Series_lp__Polynomial__Ring_rp.html" title="compute the Hilbert series of a ring">hilbertSeries(PolynomialRing)</a> -- compute the Hilbert series of a ring</span></span></li>
<li><span><a href="_hilbert__Series_lp__Projective__Hilbert__Polynomial_rp.html" title="compute the Hilbert series of a projective Hilbert polynomial">hilbertSeries(ProjectiveHilbertPolynomial)</a> -- compute the Hilbert series of a projective Hilbert polynomial</span></li>
<li><span><a href="_hilbert__Series_lp__Projective__Variety_rp.html" title="compute the Hilbert series of a projective variety">hilbertSeries(ProjectiveVariety)</a> -- compute the Hilbert series of a projective variety</span></li>
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