<?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>ambient(Ring) -- ambient polynomial ring</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_ancestors.html">next</a> | <a href="_ambient_lp__Projective__Variety_rp.html">previous</a> | <a href="_ancestors.html">forward</a> | <a href="_ambient_lp__Projective__Variety_rp.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>ambient(Ring) -- ambient polynomial ring</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>ambient R</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_ambient.html" title="ambient free module of a subquotient, or ambient ring">ambient</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="___Ring.html">ring</a></span>, a polynomial ring or a quotient of a polynomial ring</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring.html">ring</a></span>, the polynomial ring of which this ring is a quotient</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : A = ZZ[a..d];</pre> </td></tr> <tr><td><pre>i2 : B = A/(3*a^2-1);</pre> </td></tr> <tr><td><pre>i3 : C = B/(a*b-3);</pre> </td></tr> <tr><td><pre>i4 : describe C A ------- 2 3a - 1 o4 = --------- a*b - 3</pre> </td></tr> <tr><td><pre>i5 : ambient C o5 = B o5 : QuotientRing</pre> </td></tr> </table> If R is not a quotient of a polynomial ring, an error is given.</div> </div> <div class="single"><h2>Caveat</h2> <div>If the ring is a <a href="___Galois__Field.html" title="the class of all Galois fields">GaloisField</a>, then the meaning is different. See <a href="_ambient_lp__Galois__Field_rp.html" title="corresponding quotient ring">ambient(GaloisField)</a>.</div> </div> </div> </body> </html>