<?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>Ring _ ZZ -- get a ring variable by index</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Ring_sp__Array.html">next</a> | <a href="___Ring_sp_us_sp__String.html">previous</a> | <a href="___Ring_sp__Array.html">forward</a> | <a href="___Ring_sp_us_sp__String.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>Ring _ ZZ -- get a ring variable by index</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>R_i</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="__us.html" title="a binary operator, used for subscripting and access to elements">_</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> <li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Element.html">ring element</a></span>, the <tt>i</tt>-th generator of the ring <tt>R</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The indexing of generators is based on 0, so <tt>R_0</tt> would be the first one, and so on.<table class="examples"><tr><td><pre>i1 : R = ZZ[a..d] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : R_2 o2 = c o2 : R</pre> </td></tr> </table> <p/> If the coefficient ring is a polynomial ring, then the numbering matches that in the list returned by <a href="_generators.html" title="provide matrix or list of generators">generators</a>.<table class="examples"><tr><td><pre>i3 : S = R[x,y,z] o3 = S o3 : PolynomialRing</pre> </td></tr> <tr><td><pre>i4 : generators(S,CoefficientRing=>ZZ) o4 = {x, y, z, a, b, c, d} o4 : List</pre> </td></tr> <tr><td><pre>i5 : S_2 o5 = z o5 : S</pre> </td></tr> <tr><td><pre>i6 : S_6 o6 = d o6 : S</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_generators.html" title="provide matrix or list of generators">generators</a> -- provide matrix or list of generators</span></li> <li><span><a href="___Ring_sp_us_sp__String.html" title="get a ring variable by name">Ring _ String</a> -- get a ring variable by name</span></li> </ul> </div> </div> </body> </html>