<?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>GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Graded__Module_sp__Array.html">next</a> | <a href="___Graded__Module_sp_st_st_sp__Graded__Module.html">previous</a> | <a href="___Graded__Module_sp__Array.html">forward</a> | <a href="___Graded__Module_sp_st_st_sp__Graded__Module.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>GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product</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>C ** M</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="__st_st.html" title="a binary operator, usually used for tensor product or Cartesian product">**</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>a <a href="___Graded__Module.html">graded module</a></span></span></li> <li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Graded__Module.html">graded module</a></span>, the tensor product of <tt>C</tt> with <tt>M</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : C = gradedModule(ZZ^1,ZZ^6,ZZ^2) 1 o1 = 0 : ZZ 6 1 : ZZ 2 2 : ZZ o1 : GradedModule</pre> </td></tr> <tr><td><pre>i2 : C ** ZZ^3 3 o2 = 0 : ZZ 18 1 : ZZ 6 2 : ZZ o2 : GradedModule</pre> </td></tr> <tr><td><pre>i3 : betti oo 0 1 2 o3 = total: 3 18 6 -2: . . 6 -1: . 18 . 0: 3 . . o3 : BettiTally</pre> </td></tr> </table> <p>It also works the other way around.</p> <table class="examples"><tr><td><pre>i4 : ZZ^3 ** C 3 o4 = 0 : ZZ 18 1 : ZZ 6 2 : ZZ o4 : GradedModule</pre> </td></tr> </table> </div> </div> </div> </body> </html>