<?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>buildSymmetricGB -- Groebner basis of elementary symmetric polynomials algebra</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_build__Symmetric__G__B_lp__Polynomial__Ring_rp.html">next</a> | <a href="index.html">previous</a> | <a href="_build__Symmetric__G__B_lp__Polynomial__Ring_rp.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>buildSymmetricGB -- Groebner basis of elementary symmetric polynomials algebra</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>buildSymmetricGB R</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>R</tt>, a<a href="../../Macaulay2Doc/html/___Ring.html" title="the class of all rings">Ring</a></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span>the Groebner basis of the elementary symmetric algebra</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : n=5;</pre> </td></tr> <tr><td><pre>i2 : R=QQ[x_1..x_n];</pre> </td></tr> <tr><td><pre>i3 : buildSymmetricGB R 5 4 3 2 4 3 3 2 2 2 o3 = {- x + x e - x e + x e - x e + e , x + x x - x e + x x - x x e 5 5 1 5 2 5 3 5 4 5 4 4 5 4 1 4 5 4 5 1 ------------------------------------------------------------------------ 2 3 2 4 3 2 + x e + x x - x x e + x x e - x e + x - x e + x e - x e + e , - 4 2 4 5 4 5 1 4 5 2 4 3 5 5 1 5 2 5 3 4 ------------------------------------------------------------------------ 3 2 2 2 2 2 x - x x - x x + x e - x x - x x x + x x e - x x + x x e - x e 3 3 4 3 5 3 1 3 4 3 4 5 3 4 1 3 5 3 5 1 3 2 ------------------------------------------------------------------------ 3 2 2 2 3 2 2 - x - x x + x e - x x + x x e - x e - x + x e - x e + e , x + 4 4 5 4 1 4 5 4 5 1 4 2 5 5 1 5 2 3 2 ------------------------------------------------------------------------ 2 2 x x + x x + x x - x e + x + x x + x x - x e + x + x x - x e + 2 3 2 4 2 5 2 1 3 3 4 3 5 3 1 4 4 5 4 1 ------------------------------------------------------------------------ 2 x - x e + e , - x - x - x - x - x + e } 5 5 1 2 1 2 3 4 5 1 o3 : List</pre> </td></tr> </table> <p>This function should work up to a size of 15 variables in the base ring</p> <p>This function is part of the package SymmetricPolynomials.</p> </div> </div> <div class="waystouse"><h2>Ways to use <tt>buildSymmetricGB</tt> :</h2> <ul><li><span><a href="_build__Symmetric__G__B_lp__Polynomial__Ring_rp.html" title="Groebner basis of elementary symmetric polynomials algebra">buildSymmetricGB(PolynomialRing)</a> -- Groebner basis of elementary symmetric polynomials algebra</span></li> </ul> </div> </div> </body> </html>