<?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>makeWeylAlgebra(PolynomialRing) -- Weyl algebra corresponding to a polynomial ring</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___None.html">next</a> | <a href="_make__Cyclic_lp__Matrix_rp.html">previous</a> | <a href="___None.html">forward</a> | <a href="_make__Cyclic_lp__Matrix_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>makeWeylAlgebra(PolynomialRing) -- Weyl algebra corresponding to a polynomial ring</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>makeWeylAlgebra R</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_make__Weyl__Algebra_lp__Polynomial__Ring_rp.html" title="Weyl algebra corresponding to a polynomial ring">makeWeylAlgebra</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, a (commutative) ring of polynomials</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, the (non-commutative) Weyl algebra</span></li> </ul> </div> </li> <li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>SetVariables => </tt><span><span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <span>default value true</span>, whether to set variables of the created algebra to be global</span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>Given a polynomial ring <em>R</em> with variables <em>x_1,..,x_n</em>, this routine returns a Weyl algebra with variables <em>x_1,..,x_n</em> and <em>dx_1,..,dx_n</em>.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : W = makeWeylAlgebra R o2 = W o2 : PolynomialRing</pre> </td></tr> </table> Abbreviations :<ul><li>makeWA</li> </ul> </div> </div> <div class="single"><h2>Caveat</h2> <div>The polynomial ring R must be commutative.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="../../Macaulay2Doc/html/___Weyl__Algebra.html" title="name for an optional argument">WeylAlgebra</a> -- name for an optional argument</span></li> </ul> </div> </div> </body> </html>