<?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>monomial orderings</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_examples_spof_spspecifying_spalternate_spmonomial_sporders.html">next</a> | <a href="_monoid.html">previous</a> | <a href="_graded_spand_spmultigraded_sppolynomial_springs.html">forward</a> | <a href="_monoid.html">backward</a> | <a href="_rings.html">up</a> | <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>
<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_rings.html" title="">rings</a> > <a href="_monomial_sporderings.html" title="">monomial orderings</a></div>
<hr/>
<div><h1>monomial orderings</h1>
<div>Every polynomial ring in Macaulay2 comes equipped with an ordering on the monomials. See below for the definitions of all implemented orderings. The default ordering is GRevLex, the graded reverse lexicographic order.<p/>
Polynomials are displayed by ordering the monomials in decreasing order. The choice of monomial order can make a difference in the time and space required for various computations, especially Gröbner basis computations.<p/>
</div>
<div><h3>Menu</h3>
<ul><li><span><a href="_examples_spof_spspecifying_spalternate_spmonomial_sporders.html" title="">examples of specifying alternate monomial orders</a></span></li>
<li><span><a href="_monomial_sporders_spfor_spfree_spmodules.html" title="">monomial orders for free modules</a></span></li>
<li><span><a href="_packing_spmonomials_spfor_spefficiency.html" title="">packing monomials for efficiency</a></span></li>
</ul>
<h4>Definitions of the specific monomial orders</h4>
<ul><li><span><a href="___G__Rev__Lex.html" title="graded reverse lexicographical monomial order.">GRevLex</a> -- graded reverse lexicographical monomial order.</span></li>
<li><span><a href="___Lex.html" title="lexicographical monomial order.">Lex</a> -- lexicographical monomial order.</span></li>
<li><span><a href="___G__Lex.html" title="graded lexicographic ordering">GLex</a> -- graded lexicographic ordering</span></li>
<li><span><a href="___Weights.html" title="assigning weights to the variables">Weights</a> -- assigning weights to the variables</span></li>
<li><span><a href="___Eliminate.html" title="elimination order">Eliminate</a> -- elimination order</span></li>
<li><span><a href="___Group__Lex.html" title="defines a ring where some variables are inverted">GroupLex</a> -- defines a ring where some variables are inverted</span></li>
<li><span><a href="___Group__Rev__Lex.html" title="">GroupRevLex</a></span></li>
<li><span><a href="_definition_spof_spproduct_sp_lpblock_rp_sporders.html" title="">definition of product (block) orders</a></span></li>
<li><span><a href="___Rev__Lex.html" title="reverse lexicographic ordering">RevLex</a> -- reverse lexicographic ordering</span></li>
<li><span><a href="___N__C__Lex.html" title="Non-commutative lexicographical order.">NCLex</a> -- Non-commutative lexicographical order.</span></li>
</ul>
<h4>A succinct summary</h4>
<ul><li><span><a href="___Monomial__Order.html" title="monomial ordering">MonomialOrder</a> -- monomial ordering</span></li>
</ul>
<h4>Developers' corner</h4>
<ul><li><span><a href="_obtaining_spthe_spmonomial_sporder_spof_spa_spring.html" title="">obtaining the monomial order of a ring</a></span></li>
</ul>
</div>
</div>
</body>
</html>
