<?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>GeneralOrderedMonoid -- the class of all ordered free commutative monoids</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_generate__Assertions.html">next</a> | <a href="_genera_lp__Ring_rp.html">previous</a> | <a href="_generate__Assertions.html">forward</a> | <a href="_genera_lp__Ring_rp.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>GeneralOrderedMonoid -- the class of all ordered free commutative monoids</h1> <div class="single"><h2>Description</h2> <div>This is the class of free monoids that can be handled by the <a href="_engine.html" title="">engine</a>. Elements of such monoids are implemented as instances of <a href="___Monoid__Element.html" title="the class of all monoid elements">MonoidElement</a>.<p/> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_monoid.html" title="make or retrieve a monoid">monoid</a> -- make or retrieve a monoid</span></li> </ul> </div> <div class="waystouse"><h2>Functions and methods returning a general ordered monoid :</h2> <ul><li><span><a href="_monoid.html" title="make or retrieve a monoid">monoid</a> -- make or retrieve a monoid</span></li> </ul> <h2>Methods that use a general ordered monoid :</h2> <ul><li><span>degreeLength(GeneralOrderedMonoid), see <span><a href="_degree__Length.html" title="the number of degrees">degreeLength</a> -- the number of degrees</span></span></li> <li><span>degrees(GeneralOrderedMonoid), see <span><a href="_degrees_lp__Ring_rp.html" title="degrees of generators">degrees(Ring)</a> -- degrees of generators</span></span></li> <li><span>degreesMonoid(GeneralOrderedMonoid), see <span><a href="_degrees__Monoid.html" title="get the monoid of degrees">degreesMonoid</a> -- get the monoid of degrees</span></span></li> <li><span>degreesRing(GeneralOrderedMonoid), see <span><a href="_degrees__Ring_lp__Ring_rp.html" title="the ring of degrees">degreesRing(Ring)</a> -- the ring of degrees</span></span></li> <li><span>describe(GeneralOrderedMonoid), see <span><a href="_describe.html" title="real description">describe</a> -- real description</span></span></li> <li><span><tt>GeneralOrderedMonoid _*</tt> (missing documentation<!-- tag: (_*,GeneralOrderedMonoid) -->)</span></li> <li><span><a href="_generators_lp__General__Ordered__Monoid_rp.html" title="list of generators">generators(GeneralOrderedMonoid)</a> -- list of generators</span></li> <li><span><a href="_numgens_lp__General__Ordered__Monoid_rp.html" title="number of generators of a monoid">numgens(GeneralOrderedMonoid)</a> -- number of generators of a monoid</span></li> <li><span>options(GeneralOrderedMonoid), see <span><a href="_options_lp__Monoid_rp.html" title="get values used for optional arguments">options(Monoid)</a> -- get values used for optional arguments</span></span></li> <li><span><a href="_vars_lp__General__Ordered__Monoid_rp.html" title="row matrix of the variables">vars(GeneralOrderedMonoid)</a> -- row matrix of the variables</span></li> </ul> </div> <div class="waystouse"><h2>For the programmer</h2> <p>The object <a href="___General__Ordered__Monoid.html" title="the class of all ordered free commutative monoids">GeneralOrderedMonoid</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Ordered__Monoid.html" title="the class of all ordered monoids">OrderedMonoid</a> < <a href="___Monoid.html" title="the class of all monoids">Monoid</a> < <a href="___Type.html" title="the class of all types">Type</a> < <a href="___Mutable__Hash__Table.html" title="the class of all mutable hash tables">MutableHashTable</a> < <a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p> </div> </div> </body> </html>