<?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>exteriorPower(..., Strategy => ...) -- choose between Bareiss and Cofactor algorithms</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_exterior__Power_lp__Z__Z_cm__Coherent__Sheaf_rp.html">next</a> | <a href="_exterior__Power.html">previous</a> | <a href="_exterior__Power_lp__Z__Z_cm__Coherent__Sheaf_rp.html">forward</a> | <a href="_exterior__Power.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>exteriorPower(..., Strategy => ...) -- choose between Bareiss and Cofactor algorithms</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>exteriorPower(M, Strategy => s)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li> <li><span><tt>s</tt>, <span>a <a href="___Symbol.html">symbol</a></span>, either <tt>Bareiss</tt> or <tt>Cofactor</tt></span></li> </ul> </div> </li> <li><div class="single">Consequences:<ul><li>If <tt>s</tt> is <a href="___Bareiss.html" title="">Bareiss</a>, then the Bareiss algorithm is used; if <tt>s</tt> is <a href="___Cofactor.html" title="">Cofactor</a>, then cofactor expansion is used.</li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The <a href="___Ring.html">ring</a> of <tt>M</tt> determines the default strategy. If the ring is a <a href="___Polynomial__Ring.html">polynomial ring</a> or a field (as identified by <a href="_is__Field.html" title="whether something is a field">isField</a>) then the <a href="___Bareiss.html" title="">Bareiss</a> algorithm is used. If the ring is a <a href="___Quotient__Ring.html">quotient ring</a> (which has not been declared a field by <a href="_to__Field_lp__Ring_rp.html" title="declare that a ring is a field">toField</a>), then the <a href="___Cofactor.html" title="">Cofactor</a> algorithm is used.<p/> </div> </div> <h2>Further information</h2> <ul><li><span>Default value: <a href="_null.html" title="the unique member of the empty class">null</a></span></li> <li><span>Function: <span><a href="_exterior__Power.html" title="exterior power">exteriorPower</a> -- exterior power</span></span></li> <li><span>Option name: <span><a href="___Strategy.html" title="name for an optional argument">Strategy</a> -- name for an optional argument</span></span></li> </ul> <div class="single"><h2>Caveat</h2> <div>The <a href="___Bareiss.html" title="">Bareiss</a> algorithm returns a ring element that may differ from the actual determinant by a zero divisor in the ring. Thus, an <em>incorrect</em> answer may be computed if the ring contains zero divisors.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_determinant.html" title="determinant of a matrix">determinant</a> -- determinant of a matrix</span></li> <li><span><a href="_minors_lp__Z__Z_cm__Matrix_rp.html" title="ideal generated by minors">minors</a> -- ideal generated by minors</span></li> </ul> </div> </div> </body> </html>