<?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>irreducibleDecomposition(MonomialIdeal) -- express a monomial ideal as an intersection of irreducible monomial ideals</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_is__Primary.html">next</a> | <a href="_primary__Decomposition_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">previous</a> | <a href="_is__Primary.html">forward</a> | <a href="index.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>irreducibleDecomposition(MonomialIdeal) -- express a monomial ideal as an intersection of irreducible monomial ideals</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>irreducibleDecomposition I</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_irreducible__Decomposition_lp__Monomial__Ideal_rp.html" title="express a monomial ideal as an intersection of irreducible monomial ideals">irreducibleDecomposition</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>a <a href="../../Macaulay2Doc/html/___Monomial__Ideal.html">monomial ideal</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of irreducible monomial ideals whose intersection is <tt>I</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : QQ[x..z];</pre> </td></tr> <tr><td><pre>i2 : I = monomialIdeal (x*y^3, x*y^2*z) 3 2 o2 = monomialIdeal (x*y , x*y z) o2 : MonomialIdeal of QQ[x, y, z]</pre> </td></tr> <tr><td><pre>i3 : w = irreducibleDecomposition I 2 3 o3 = {monomialIdeal(x), monomialIdeal(y ), monomialIdeal (y , z)} o3 : List</pre> </td></tr> <tr><td><pre>i4 : assert( I == intersect w )</pre> </td></tr> </table> </div> </div> </div> </body> </html>