<?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>rank -- compute the rank</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_read.html">next</a> | <a href="_random__Mutable__Matrix_lp__Z__Z_cm__Z__Z_cm__R__R_cm__Z__Z_rp.html">previous</a> | <a href="_read.html">forward</a> | <a href="_random__Mutable__Matrix_lp__Z__Z_cm__Z__Z_cm__R__R_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>rank -- compute the rank</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>rank M</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span>, <span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span>, <span>a <a href="___Graded__Module.html">graded module</a></span>, <span>a <a href="___Chain__Complex.html">chain complex</a></span>, or <span>a <a href="___Matrix.html">matrix</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span>the rank of <tt>M</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y,z] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : p = vars R; 1 3 o2 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i3 : rank kernel p o3 = 2</pre> </td></tr> <tr><td><pre>i4 : rank cokernel p o4 = 0</pre> </td></tr> <tr><td><pre>i5 : C = res cokernel p 1 3 3 1 o5 = R <-- R <-- R <-- R <-- 0 0 1 2 3 4 o5 : ChainComplex</pre> </td></tr> <tr><td><pre>i6 : rank C o6 = 0</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>rank</tt> :</h2> <ul><li>rank(CoherentSheaf)</li> <li>rank(GradedModule)</li> <li>rank(Matrix)</li> <li>rank(Module)</li> </ul> </div> </div> </body> </html>