<?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 / Function -- apply a function to generators of an ideal</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Ideal_sp_sl_sp__Ideal.html">next</a> | <a href="___Ideal_sp_pl_sp__Ideal.html">previous</a> | <a href="___Ideal_sp_sl_sp__Ideal.html">forward</a> | <a href="___Ideal_sp_pl_sp__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 / Function -- apply a function to generators of an ideal</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/f</tt><br/><tt>f\I</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="__sl.html" title="a binary operator, usually used for division">/</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>f</tt>, <span>a <a href="___Function.html">function</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, obtained by applying the function <tt>f</tt> to each generator of <tt>I</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p>The operator <a href="__sl.html" title="a binary operator, usually used for division">/</a> is left associative, which means that <tt>w / f / g</tt> is interpreted as <tt>(w / f) / g</tt>. The operator <a href="__bs.html" title="a binary operator">\</a> is right associative, so <tt>g \ f \ w</tt> is interpreted as <tt>g \ (f \ w)</tt>. Both operators have parsing precedence lower than that of <a href="__at_at.html" title="a binary operator">@@</a>, which means that the previous two expressions are equivalent to <tt>w / g @@ f</tt> and <tt>g @@ f \ w</tt>, respectively. See <a href="_precedence_spof_spoperators.html" title="">precedence of operators</a>.</p> <table class="examples"><tr><td><pre>i1 : R = ZZ[a..d];</pre> </td></tr> <tr><td><pre>i2 : I = ideal"abc-d3,ab-d-1,a2+b2+c3-14d-3" 3 3 2 2 o2 = ideal (a*b*c - d , a*b - d - 1, c + a + b - 14d - 3) o2 : Ideal of R</pre> </td></tr> <tr><td><pre>i3 : I/size o3 = {2, 3, 5} o3 : List</pre> </td></tr> <tr><td><pre>i4 : (f->f+a*b-1)\I 3 3 2 2 o4 = {a*b*c - d + a*b - 1, 2a*b - d - 2, c + a + a*b + b - 14d - 4} o4 : List</pre> </td></tr> <tr><td><pre>i5 : I/leadTerm/support/set//sum o5 = set {a, b, c} o5 : Set</pre> </td></tr> </table> </div> </div> </div> </body> </html>