<?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>ZZ ..< ZZ -- sequences of consecutive integers</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Z__Z_sp_co_sp__Thing.html">next</a> | <a href="___Z__Z_sp.._sp__Z__Z.html">previous</a> | <a href="___Z__Z_sp_co_sp__Thing.html">forward</a> | <a href="___Z__Z_sp.._sp__Z__Z.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>ZZ ..< ZZ -- sequences of consecutive integers</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 ..< t</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="_.._lt.html" title="a binary operator, used for sequences of consecutive items, not including the endpoint">..<</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>s</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li> <li><span><tt>t</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="___Sequence.html">sequence</a></span>, the sequence of consecutive integers from <tt>s</tt> to <tt>t</tt>, not including the endpoint</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : 0 ..< 10 o1 = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) o1 : Sequence</pre> </td></tr> </table> <p>The indices valid for a list of length <tt>n</tt> can be obtained with <tt>0 ..< n</tt>.</p> <table class="examples"><tr><td><pre>i2 : x = {a,c,e,f} o2 = {a, c, e, f} o2 : List</pre> </td></tr> <tr><td><pre>i3 : 0 ..< #x o3 = (0, 1, 2, 3) o3 : Sequence</pre> </td></tr> <tr><td><pre>i4 : apply(0 ..< #x, i -> x#i) o4 = (a, c, e, f) o4 : Sequence</pre> </td></tr> </table> </div> </div> </div> </body> </html>