<?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>degreesRing(Ring) -- the ring of degrees</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_demark.html">next</a> | <a href="_degrees__Ring_lp__List_rp.html">previous</a> | <a href="_demark.html">forward</a> | <a href="_degrees__Ring_lp__List_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>degreesRing(Ring) -- the ring of degrees</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>degreesRing R</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_degrees__Ring.html" title="the ring of degrees">degreesRing</a></span></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="___Polynomial__Ring.html">polynomial ring</a></span>, actually Laurent polynomial ring</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>This function produces a Laurent polynomial ring in n variables<tt>T_0, ... , T_{n-1}</tt> whose monomials are the degrees of elements of the given ring. If n=1, then the variable has no subscript.<table class="examples"><tr><td><pre>i1 : R = ZZ [x, y];</pre> </td></tr> <tr><td><pre>i2 : degreesRing R o2 = ZZ[T] o2 : PolynomialRing</pre> </td></tr> <tr><td><pre>i3 : S = ZZ[x,y, Degrees=>{{1,1},{1,1}}];</pre> </td></tr> <tr><td><pre>i4 : degreesRing S o4 = ZZ[T , T ] 0 1 o4 : PolynomialRing</pre> </td></tr> </table> </div> </div> </div> </body> </html>