<?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>pivots(Matrix) -- list of pivot locations of a matrix</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_plus.html">next</a> | <a href="_pi.html">previous</a> | <a href="_plus.html">forward</a> | <a href="_pi.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>pivots(Matrix) -- list of pivot locations of a matrix</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>pivots f</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_pivots_lp__Matrix_rp.html" title="list of pivot locations of a matrix">pivots</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, of positions (r,c) which are the positions of the non-zero lead terms (in each column)</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : f = matrix{{1,3,0,0,3,5,2,0,0},{0,0,0,1,3,6,7,8,0}} o1 = | 1 3 0 0 3 5 2 0 0 | | 0 0 0 1 3 6 7 8 0 | 2 9 o1 : Matrix ZZ <--- ZZ</pre> </td></tr> <tr><td><pre>i2 : pivots f o2 = {(0, 0), (0, 1), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7)} o2 : List</pre> </td></tr> </table> <p>This function is used in the current implementation of the Smith normal form.</p> </div> </div> <div class="single"><h2>Caveat</h2> <div>Should be implemented in the engine.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_smith__Normal__Form_lp__Matrix_rp.html" title="smith normal form for a matrix over ZZ or a PID">smithNormalForm</a> -- smith normal form for a matrix over ZZ or a PID</span></li> </ul> </div> </div> </body> </html>