<?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 ++ CoherentSheaf -- direct sum of coherent sheaves</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_sl_sp__Coherent__Sheaf.html">next</a> | <a href="___Coherent__Sheaf_sp_st_st_sp__Coherent__Sheaf.html">previous</a> | <a href="___Coherent__Sheaf_sp_sl_sp__Coherent__Sheaf.html">forward</a> | <a href="___Coherent__Sheaf_sp_st_st_sp__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 ++ CoherentSheaf -- direct sum of coherent sheaves</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 ++ G</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="__pl_pl.html" title="a binary operator, usually used for direct sum">++</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></span></li> <li><span><tt>G</tt>, <span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span>, the direct sum of <tt>F</tt> and <tt>G</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : X = Proj(QQ[x,y,z]) o1 = X o1 : ProjectiveVariety</pre> </td></tr> <tr><td><pre>i2 : OO_X(3) ++ OO_X(4) 1 1 o2 = OO (3) ++ OO (4) X X o2 : coherent sheaf on X, free</pre> </td></tr> <tr><td><pre>i3 : module oo 2 o3 = (QQ[x, y, z]) o3 : QQ[x, y, z]-module, free, degrees {-3, -4}</pre> </td></tr> </table> </div> </div> </div> </body> </html>