<?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>min(GradedModule) -- minimum of elements of a list</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_min__Exponent.html">next</a> | <a href="_min.html">previous</a> | <a href="_min__Exponent.html">forward</a> | <a href="_min.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>min(GradedModule) -- minimum of elements of a list</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>max C</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_min.html" title="minimum of elements of a list">min</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>a <a href="___Graded__Module.html">graded module</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span>, the minimum index of a component, possibly zero, of the graded module <tt>C</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = QQ[a..e] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : C = res coker vars R 1 5 10 10 5 1 o2 = R <-- R <-- R <-- R <-- R <-- R <-- 0 0 1 2 3 4 5 6 o2 : ChainComplex</pre> </td></tr> <tr><td><pre>i3 : min C o3 = 0</pre> </td></tr> <tr><td><pre>i4 : dual C 1 5 10 10 5 1 o4 = R <-- R <-- R <-- R <-- R <-- R -5 -4 -3 -2 -1 0 o4 : ChainComplex</pre> </td></tr> <tr><td><pre>i5 : min dual C o5 = -5</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_max_lp__Graded__Module_rp.html" title="maximum of elements of a list">max(GradedModule)</a> -- maximum of elements of a list</span></li> </ul> </div> </div> </body> </html>