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<head><title>hilbertPolynomial(..., Projective => ...) -- choose how to display the Hilbert polynomial</title>
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<div><h1>hilbertPolynomial(..., Projective => ...) -- choose how to display 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>hilbertPolynomial(...,Projective => b</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>b</tt>, <span>a <a href="___Boolean.html">Boolean value</a></span>, either true or false</span></li>
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<div class="single"><h2>Description</h2>
<div><tt>Projective => true</tt> is an option to <a href="_hilbert__Polynomial.html" title="compute the Hilbert polynomial">hilbertPolynomial</a> which specifies that the Hilbert polynomial produced should be expressed in terms of the Hilbert polynomials of projective spaces. This is the default.<p/>
<tt>Projective => false</tt> is an option to <a href="_hilbert__Polynomial.html" title="compute the Hilbert polynomial">hilbertPolynomial</a> which specifies that the Hilbert polynomial produced should be expressed as a polynomial in the variable <tt>i</tt>.<p/>
We compute the <a href="_hilbert__Polynomial.html">Hilbert polynomial</a> of a coordinate ring of the rational quartic curve in <tt>P^3.</tt><table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d];</pre>
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<tr><td><pre>i2 : S = coimage map(R, R, {a^4, a^3*b, a*b^3, b^4});</pre>
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<tr><td><pre>i3 : hilbertPolynomial S
o3 = - 3*P + 4*P
0 1
o3 : ProjectiveHilbertPolynomial</pre>
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<tr><td><pre>i4 : hilbertPolynomial(S, Projective=>false)
o4 = 4i + 1
o4 : QQ[i]</pre>
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When the option Projective is false, the variable <tt>i</tt> is a local variable. The command <tt>use ring</tt>will make <tt>i</tt>into a global variable.</div>
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<h2>Further information</h2>
<ul><li><span>Default value: <a href="_true.html" title="">true</a></span></li>
<li><span>Function: <span><a href="_hilbert__Polynomial.html" title="compute the Hilbert polynomial">hilbertPolynomial</a> -- compute the Hilbert polynomial</span></span></li>
<li><span>Option name: <span><a href="___Projective.html" title="whether to produce a projective Hilbert polynomial">Projective</a> -- whether to produce a projective Hilbert polynomial</span></span></li>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Projective__Hilbert__Polynomial.html" title="the class of all Hilbert polynomials">ProjectiveHilbertPolynomial</a> -- the class of all Hilbert polynomials</span></li>
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