<?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>preImage -- Compute the preimage.</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___P__T1.html">next</a> | <a href="_possible__Denominators.html">previous</a> | <a href="___P__T1.html">forward</a> | <a href="_possible__Denominators.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>preImage -- Compute the preimage.</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>preImage(A,v)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>A</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, of full rank.</span></li> <li><span><tt>v</tt>, <span>a <a href="../../Macaulay2Doc/html/___Vector.html">vector</a></span>, in <a href="../../Macaulay2Doc/html/_target.html" title="target of a map">target</a> A.</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Vector.html">vector</a></span>, in <a href="../../Macaulay2Doc/html/_source.html" title="source of a map">source</a> A.</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p>Computes the preimage of v under A. If v is not in <a href="../../Macaulay2Doc/html/_image.html" title="image of a map">image</a> A then returns false.</p> <div/> <table class="examples"><tr><td><pre>i1 : A=matrix {{1, 0}, {0, 1}, {-1, -1}} o1 = | 1 0 | | 0 1 | | -1 -1 | 3 2 o1 : Matrix ZZ <--- ZZ</pre> </td></tr> <tr><td><pre>i2 : b=vector {-2,2,0} o2 = | -2 | | 2 | | 0 | 3 o2 : ZZ</pre> </td></tr> <tr><td><pre>i3 : v=preImage(A,b) o3 = | -2 | | 2 | 2 o3 : ZZ</pre> </td></tr> <tr><td><pre>i4 : A*v o4 = | -2 | | 2 | | 0 | 3 o4 : ZZ</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>preImage</tt> :</h2> <ul><li>preImage(Matrix,Vector)</li> </ul> </div> </div> </body> </html>