<?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>CoherentSheaf (*) -- sum of twists</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="___Coherent__Sheaf_sp_st_st_sp__Coherent__Sheaf.html">next</a> | <a href="___Coherent__Sheaf.html">previous</a> | <a href="___Coherent__Sheaf_sp_st_st_sp__Coherent__Sheaf.html">forward</a> | <a href="___Coherent__Sheaf.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>CoherentSheaf (*) -- sum of twists</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>F(*)</tt></div>
</dd></dl>
</div>
</li>
<li><span>Operator: <a href="__lp_st_rp.html" title="a unary postfix operator, used for indicating a graded object">(*)</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span>, or a <span>a <a href="___Sheaf__Of__Rings.html">sheaf of rings</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span>a symbolic representation of the graded object consisting of the twists <tt>F(n)</tt>, for all integers <tt>n</tt></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre>
</td></tr>
<tr><td><pre>i2 : X = Proj R
o2 = X
o2 : ProjectiveVariety</pre>
</td></tr>
<tr><td><pre>i3 : Ext^0(OO_X^1, OO_X^1)
1
o3 = QQ
o3 : QQ-module, free</pre>
</td></tr>
<tr><td><pre>i4 : Ext^0(OO_X^1, OO_X^1(*))
1
o4 = R
o4 : R-module, free</pre>
</td></tr>
<tr><td><pre>i5 : Ext^0(OO_X^1, OO_X(*))
1
o5 = R
o5 : R-module, free</pre>
</td></tr>
</table>
</div>
</div>
</div>
</body>
</html>
