<?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>numerator -- numerator of a fraction</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_numeric.html">next</a> | <a href="_num__Columns_lp__Matrix_rp.html">previous</a> | <a href="_numeric.html">forward</a> | <a href="_num__Columns_lp__Matrix_rp.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>numerator -- numerator of a fraction</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>numerator x</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>x</tt>, a fraction</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span>the numerator of <tt>x</tt></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : numerator (4/6)
o1 = 2</pre>
</td></tr>
</table>
<p/>
<table class="examples"><tr><td><pre>i2 : R = frac(ZZ[x,y]);</pre>
</td></tr>
<tr><td><pre>i3 : numerator((x+2*y-3)/(x-y))
o3 = x + 2y - 3
o3 : ZZ[x, y]</pre>
</td></tr>
</table>
<p/>
<tt>numerator</tt> also works with Hilbert series.<table class="examples"><tr><td><pre>i4 : R = QQ[a..d]/(a^2,b^2,c^3);</pre>
</td></tr>
<tr><td><pre>i5 : hf = hilbertSeries R
2 3 4 5 7
1 - 2T - T + T + 2T - T
o5 = ----------------------------
4
(1 - T)
o5 : Expression of class Divide</pre>
</td></tr>
<tr><td><pre>i6 : numerator hf
2 3 4 5 7
o6 = 1 - 2T - T + T + 2T - T
o6 : ZZ[T]</pre>
</td></tr>
</table>
<p>For a Laurent polynomial in a ring with inverses of variables, it gives the result after clearing all the denominators in each of the terms by multiplying by a suitable monomial.</p>
<table class="examples"><tr><td><pre>i7 : R = QQ[x,y,z,Inverses => true, MonomialOrder => Lex]
o7 = R
o7 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i8 : numerator (x*y^-1+y*z^-2+1+y^-1*z^-1)
2 2 2
o8 = x*z + y + y*z + z
o8 : R</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_denominator.html" title="denominator of a fraction">denominator</a> -- denominator of a fraction</span></li>
<li><span><a href="_fraction_spfields.html" title="">fraction fields</a></span></li>
<li><span><a href="_hilbert__Series.html" title="compute the Hilbert series">hilbertSeries</a> -- compute the Hilbert series</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>numerator</tt> :</h2>
<ul><li>numerator(Divide)</li>
</ul>
</div>
</div>
</body>
</html>
