<?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(Ring,Ring,List) -- make a ring map</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">next</a> | <a href="_map_lp__Ring_cm__Ring_rp.html">previous</a> | <a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">forward</a> | <a href="_map_lp__Ring_cm__Ring_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__Ring_cm__Ring_cm__List_rp.html" title="make a ring map">map(Ring,Ring,List)</a></div> <hr/> <div><h1>map(Ring,Ring,List) -- make a ring map</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(R,S,m)</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>R</tt>, <span>a <a href="___Ring.html">ring</a></span>, the target ring</span></li> <li><span><tt>S</tt>, <span>a <a href="___Ring.html">ring</a></span>, the source ring</span></li> <li><span><tt>m</tt>, <span>a <a href="___List.html">list</a></span>, of <tt>n</tt> elements of <tt>R</tt>, where <tt>n</tt> is the number of variables in the polynomial ring <tt>S</tt>, or a list of pairs <tt>x => r</tt>, where <tt>x</tt> is a generator of <tt>S</tt> and <tt>r</tt> is an element of <tt>R</tt>, specifying that <tt>x</tt> is to be sent to <tt>r</tt>.</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Map.html">ring map</a></span>, the ring homomorphism from <tt>S</tt> to <tt>R</tt> which sends the <tt>i</tt>-th variable of <tt>S</tt> to the <tt>i</tt>-th entry in <tt>m</tt>, or in the second case, performs the indicated substitutions.</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><table class="examples"><tr><td><pre>i1 : R = ZZ[x,y];</pre> </td></tr> <tr><td><pre>i2 : S = ZZ[a,b,c];</pre> </td></tr> <tr><td><pre>i3 : f = map(R,S,{x^2,x*y,y^2}) 2 2 o3 = map(R,S,{x , x*y, y }) o3 : RingMap R <--- S</pre> </td></tr> <tr><td><pre>i4 : f(a+b+c^2) 4 2 o4 = y + x + x*y o4 : R</pre> </td></tr> <tr><td><pre>i5 : g = map(R,S,{a=>x^2,b=>x*y,c=>y^2}) 2 2 o5 = map(R,S,{x , x*y, y }) o5 : RingMap R <--- S</pre> </td></tr> <tr><td><pre>i6 : g(a+b+c^2) 4 2 o6 = y + x + x*y o6 : R</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_substitution_spand_spmaps_spbetween_springs.html" title="">substitution and maps between rings</a></span></li> <li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html" title="make a ring map">map(Ring,Ring,Matrix)</a> -- make a ring map</span></li> </ul> </div> </div> </body> </html>