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<!DOCTYPE html> <html lang="en"> <head> <title>MonoidElement -- the class of all monoid elements</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="index.html">Documentation </a> <br><a href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="Macaulay2 documentation" href="index.html">Macaulay2Doc</a> » <a href="___The_sp__Macaulay2_splanguage.html">The Macaulay2 language</a> » <a title="the class of all mutable types" href="___Type.html">Type</a> » <a title="the class of all monoids" href="___Monoid.html">Monoid</a> » <a title="the class of all monoid elements" href="___Monoid__Element.html">MonoidElement</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_generators_lp__Monoid_rp.html">next</a> | <a href="___General__Ordered__Monoid.html">previous</a> | <a href="_generators_lp__Monoid_rp.html">forward</a> | <a href="___General__Ordered__Monoid.html">backward</a> | <a href="___Monoid.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>MonoidElement -- the class of all monoid elements</h1> <div> <!--empty documentation body--> </div> <div> <h2>See also</h2> <ul> <li><span><a title="make or retrieve a monoid" href="_monoid.html">monoid</a> -- make or retrieve a monoid</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Functions and methods returning a monoid element:</h2> <ul> <li><span><kbd>Monoid _ ZZ</kbd> -- see <span><a title="get a ring variable by index" href="_get_spa_spring_spvariable_spby_spindex.html">get a ring variable by index</a> -- get a ring variable by index</span></span></li> <li><span><kbd>String _ Monoid</kbd> -- see <span><a title="get a ring variable by name" href="_get_spa_spring_spvariable_spby_spname.html">get a ring variable by name</a> -- get a ring variable by name</span></span></li> </ul> <h2>Methods that use a monoid element:</h2> <ul> <li><span><kbd>baseName(MonoidElement)</kbd> -- see <span><a title="the base name of a generator" href="_base__Name.html">baseName</a> -- the base name of a generator</span></span></li> <li><span><span class="tt">degree(MonoidElement)</span> (missing documentation)<!--tag: (degree,MonoidElement)--> </span></li> <li><span><kbd>exponents(MonoidElement)</kbd> -- see <span><a title="the exponents of a polynomial" href="_exponents.html">exponents</a> -- the exponents of a polynomial</span></span></li> <li><span><kbd>listForm(MonoidElement)</kbd> -- see <span><a title="convert to list form" href="_list__Form.html">listForm</a> -- convert to list form</span></span></li> <li><span><span class="tt">MonoidElement : MonoidElement</span> (missing documentation)<!--tag: (:,MonoidElement,MonoidElement)--> </span></li> <li><span><span class="tt">MonoidElement Array</span> (missing documentation)<!--tag: (SPACE,MonoidElement,Array)--> </span></li> <li><span><kbd>MonoidElement ^ ZZ</kbd> -- see <span><a title="power" href="___Ring__Element_sp%5E_sp__Z__Z.html">RingElement ^ ZZ</a> -- power</span></span></li> <li><span><kbd>standardForm(MonoidElement)</kbd> -- see <span><a title="convert to standard form" href="_standard__Form.html">standardForm</a> -- convert to standard form</span></span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="the class of all monoid elements" href="___Monoid__Element.html">MonoidElement</a> is <span>a <a title="the class of all mutable types" href="___Type.html">type</a></span>, with ancestor classes <a title="the class of all hash tables" href="___Hash__Table.html">HashTable</a> < <a title="the class of all things" href="___Thing.html">Thing</a>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Macaulay2Doc/doc_rings.m2:64:0</span>.</p> </div> </div> </div> </body> </html>