<?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>Symbol _ Thing -- index variable</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Symbol_sp_us_sp__Thing_sp_eq_sp__Thing.html">next</a> | <a href="___Symbol_sp_us_sp__Ring.html">previous</a> | <a href="___Symbol_sp_us_sp__Thing_sp_eq_sp__Thing.html">forward</a> | <a href="___Symbol_sp_us_sp__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>Symbol _ Thing -- index variable</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>s_v</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>s</tt>, <span>a <a href="___Symbol.html">symbol</a></span></span></li> <li><span><tt>v</tt>, <span>a <a href="___Thing.html">thing</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>an <a href="___Indexed__Variable.html">indexed variable</a></span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The subscript can be anything, even a mutable object. Often, the subscripts are numbers or sequences. Sequences usually print nicer than lists.<table class="examples"><tr><td><pre>i1 : x_(1,3) o1 = x 1,3 o1 : IndexedVariable</pre> </td></tr> <tr><td><pre>i2 : x_{1,3} o2 = x {1, 3} o2 : IndexedVariable</pre> </td></tr> </table> Indexed variables can be used for ring variables.<table class="examples"><tr><td><pre>i3 : R = ZZ[x_(1,1)..x_(2,3),y_a..y_f] o3 = R o3 : PolynomialRing</pre> </td></tr> <tr><td><pre>i4 : gens R o4 = {x , x , x , x , x , x , y , y , y , y , y , y } 1,1 1,2 1,3 2,1 2,2 2,3 a b c d e f o4 : List</pre> </td></tr> </table> </div> </div> </div> </body> </html>