<?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>leadTerm(Ideal) -- get the ideal of greatest terms</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_lead__Term_lp__Matrix_rp.html">next</a> | <a href="_lead__Term.html">previous</a> | <a href="_lead__Term_lp__Matrix_rp.html">forward</a> | <a href="_lead__Term.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>leadTerm(Ideal) -- get the ideal of greatest terms</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>leadTerm I</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_lead__Term.html" title="get the greatest term">leadTerm</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> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, The ideal of all possible lead terms of <tt>I</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>Compute a <a href="___Gröbner_spbases.html">Gröbner basis</a> and return the ideal generated by the lead terms of the Gröbner basis elements.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre> </td></tr> <tr><td><pre>i2 : I = ideal(a*b-c*d, a*c-b*d) o2 = ideal (a*b - c*d, a*c - b*d) o2 : Ideal of R</pre> </td></tr> <tr><td><pre>i3 : leadTerm I o3 = | ac ab b2d | 1 3 o3 : Matrix R <--- R</pre> </td></tr> </table> <table class="examples"><tr><td><pre>i4 : R = ZZ[a..d][x,y,z];</pre> </td></tr> <tr><td><pre>i5 : I = ideal(a*x-b*y, x^3, y^3, z^3) 3 3 3 o5 = ideal (a*x - b*y, x , y , z ) o5 : Ideal of R</pre> </td></tr> <tr><td><pre>i6 : leadTerm I o6 = | xa z3 y3 xy2b2 x2yb x3 | 1 6 o6 : Matrix R <--- R</pre> </td></tr> </table> </div> </div> </div> </body> </html>