<?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>pureAll -- Vector of first betti number of our three specific exact complexes</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_pure__Betti_lp__List_rp.html">next</a> | <a href="_matrix_lp__Betti__Tally_cm__Z__Z_cm__Z__Z_rp.html">previous</a> | <a href="_pure__Betti_lp__List_rp.html">forward</a> | <a href="_matrix_lp__Betti__Tally_cm__Z__Z_cm__Z__Z_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>pureAll -- Vector of first betti number of our three specific exact complexes</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>pureAll</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a strictly increasing sequence of degrees</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, The vector of zero-th betti numbers of the three corresponding pure resolution construction.</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><a href="_pure__All.html" title="Vector of first betti number of our three specific exact complexes">pureAll</a> returns all three numbers at one time.<table class="examples"><tr><td><pre>i1 : L = {0,2,3,9}
o1 = {0, 2, 3, 9}
o1 : List</pre>
</td></tr>
<tr><td><pre>i2 : B = pureBettiDiagram L
0 1 2 3
o2 = total: 7 27 21 1
0: 7 . . .
1: . 27 21 .
2: . . . .
3: . . . .
4: . . . .
5: . . . .
6: . . . 1
o2 : BettiTally</pre>
</td></tr>
<tr><td><pre>i3 : pureCharFree L
o3 = 56</pre>
</td></tr>
<tr><td><pre>i4 : pureTwoInvariant L
o4 = 196</pre>
</td></tr>
<tr><td><pre>i5 : pureWeyman L
o5 = 21</pre>
</td></tr>
<tr><td><pre>i6 : pureAll L
o6 = (56, 196, 21)
o6 : Sequence</pre>
</td></tr>
<tr><td><pre>i7 : gcd pureAll L
o7 = 7</pre>
</td></tr>
</table>
Thus, for large enough multiples m, m*B occurs as the Betti diagram of a module.<p/>
However, B itself occurs:<table class="examples"><tr><td><pre>i8 : betti res randomSocleModule(L,1)
0 1 2 3
o8 = total: 7 27 21 1
0: 7 . . .
1: . 27 21 .
2: . . . .
3: . . . .
4: . . . .
5: . . . .
6: . . . 1
o8 : BettiTally</pre>
</td></tr>
<tr><td><pre>i9 : betti res randomModule(L,1)
0 1 2 3
o9 = total: 7 27 35 15
0: 7 . . .
1: . 27 11 .
2: . . 24 15
o9 : BettiTally</pre>
</td></tr>
<tr><td><pre>i10 : betti res randomModule({0,6,7,9},1)
0 1 2 3
o10 = total: 1 21 27 7
0: 1 . . .
1: . . . .
2: . . . .
3: . . . .
4: . . . .
5: . 21 27 .
6: . . . 7
o10 : BettiTally</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_pure__Weyman.html" title="first betti number of specific exact complex">pureWeyman</a> -- first betti number of specific exact complex</span></li>
<li><span><a href="_pure__Two__Invariant.html" title="first betti number of specific exact complex">pureTwoInvariant</a> -- first betti number of specific exact complex</span></li>
<li><span><a href="_pure__Char__Free.html" title="first betti number of specific exact complex">pureCharFree</a> -- first betti number of specific exact complex</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>pureAll</tt> :</h2>
<ul><li>pureAll(List)</li>
</ul>
</div>
</div>
</body>
</html>
