<?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>coefficientRing -- get the coefficient ring</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_coefficients.html">next</a> | <a href="___Coefficient__Ring.html">previous</a> | <a href="_coefficients.html">forward</a> | <a href="___Coefficient__Ring.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>coefficientRing -- get the coefficient 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>coefficientRing R</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="___Ring.html">ring</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring.html">ring</a></span>, the coefficient ring of <tt>R</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>If <tt>R</tt> is a polynomial ring, then the coefficient ring is the base ring from which the coefficients are drawn. If <tt>R</tt> is constructed from a polynomial ring as a quotient ring or a fraction ring or a sequence of such operations, then the original coefficient ring is returned.<table class="examples"><tr><td><pre>i1 : coefficientRing(ZZ/101[a][b]) ZZ o1 = ---[a] 101 o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : ultimate(coefficientRing,ZZ/101[a][b]) ZZ o2 = --- 101 o2 : QuotientRing</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_ultimate.html" title="ultimate value for an iteration">ultimate</a> -- ultimate value for an iteration</span></li> <li><span><a href="_base__Rings.html" title="store the list of base rings of a ring">baseRings</a> -- store the list of base rings of a ring</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>coefficientRing</tt> :</h2> <ul><li>coefficientRing(Ring)</li> <li><span>coefficientRing(SchurRing), see <span><a href="../../SchurRings/html/___Schur__Ring.html" title="the class of all Schur rings">SchurRing</a> -- the class of all Schur rings</span></span></li> </ul> </div> </div> </body> </html>