<?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>Ideal * Ideal -- product of ideals</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Ideal_sp_pl_sp__Ideal.html">next</a> | <a href="_ideal.html">previous</a> | <a href="___Ideal_sp_pl_sp__Ideal.html">forward</a> | <a href="_ideal.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>Ideal * Ideal -- product of 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>I * J</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="__st.html" title="a binary operator, usually used for multiplication">*</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="___Ideal.html">ideal</a></span></span></li> <li><span><tt>J</tt>, <span>an <a href="___Ideal.html">ideal</a></span>, in the same ring as <tt>I</tt></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>an <a href="___Ideal.html">ideal</a></span>, the product of the two ideals <tt>I</tt> and <tt>J</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = QQ[t][a..d];</pre> </td></tr> <tr><td><pre>i2 : I = ideal(a,(t+1)*c) * ideal(a^2,b^2) 3 2 2 2 o2 = ideal (a , a*b , (t + 1)a c, (t + 1)b c) o2 : Ideal of R</pre> </td></tr> </table> The generators produced are not generally minimal. Use <a href="_trim_lp__Ideal_rp.html" title="">trim(Ideal)</a> or <a href="_mingens_lp__Module_rp.html" title="minimal generator matrix">mingens(Ideal)</a> to find a smaller generating set.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_ideals.html" title="">ideals</a></span></li> </ul> </div> </div> </body> </html>