<?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>map(Module,Module,Matrix) -- create the matrix induced on generators by a given matrix</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_map_lp__Module_cm__Z__Z_cm__Function_rp.html">next</a> | <a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html">previous</a> | <a href="_map_lp__Module_cm__Z__Z_cm__Function_rp.html">forward</a> | <a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html">backward</a> | <a href="_map.html">up</a> | <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> <div><a href="_map.html" title="make a map">map</a> > <a href="_map_lp__Module_cm__Module_cm__Matrix_rp.html" title="create the matrix induced on generators by a given matrix">map(Module,Module,Matrix)</a></div> <hr/> <div><h1>map(Module,Module,Matrix) -- create the matrix induced on generators by a given 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>map(M,N,p)</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_map.html" title="make a map">map</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li> <li><span><tt>N</tt>, <span>a <a href="___Module.html">module</a></span></span></li> <li><span><tt>p</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="___Matrix.html">matrix</a></span>, A matrix with the same entries as <tt>p</tt>, but whose target is <tt>M</tt> and source is <tt>N</tt></span></li> </ul> </div> </li> <li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_map_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html">Degree => ...</a>, -- set the degree of a map</span></li> <li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">DegreeLift => ...</a>, -- make a ring map</span></li> <li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">DegreeMap => ...</a>, -- make a ring map</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><tt>M</tt> and <tt>N</tt> should be modules over the same ring, and have the same number of generators as <tt>target p</tt> and <tt>source p</tt>, respectively.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre> </td></tr> <tr><td><pre>i2 : p = matrix {{x,y,z}} o2 = | x y z | 1 3 o2 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i3 : q = map(R^1,R^3,p) o3 = | x y z | 1 3 o3 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i4 : degrees source p o4 = {{1}, {1}, {1}} o4 : List</pre> </td></tr> <tr><td><pre>i5 : degrees source q o5 = {{0}, {0}, {0}} o5 : List</pre> </td></tr> </table> </div> </div> <div class="single"><h2>Caveat</h2> <div>If <tt>M</tt> or <tt>N</tt> is not free, then we don't check that the the result is a well defined homomorphism.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_induced__Map.html" title="compute an induced map">inducedMap</a> -- compute an induced map</span></li> </ul> </div> </div> </body> </html>