<?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>createDpairs(PolynomialRing) -- pairs up the variables in Weyl algebra </title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Cycles.html">next</a> | <a href="___Cohomology__Groups.html">previous</a> | <a href="___Cycles.html">forward</a> | <a href="___Cohomology__Groups.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>createDpairs(PolynomialRing) -- pairs up the variables in Weyl 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>createDpairs A</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_create__Dpairs_lp__Polynomial__Ring_rp.html" title="pairs up the variables in Weyl algebra ">createDpairs</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>A</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, the Weyl algebra</span></li> </ul> </div> </li> <li><div class="single">Consequences:<ul><li>attaches to <tt>A</tt> a pair of keys to help distinguish the coordinate variables from the derivation variables.</li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>Since the Weyl algebra has commutation rules, this routine attaches to the Weyl algebra two keys to organize the variables. The first key 'dpairVars' contains 3 lists: a list of the coordinate variables, a list of the derivative variables, and a list of the central variables. The second key 'dpairInds' also contains 3 lists of the corresponding indices to 'dpairVars'.<table class="examples"><tr><td><pre>i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}] o1 = W o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : createDpairs W </pre> </td></tr> <tr><td><pre>i3 : W.dpairVars o3 = {{x, y}, {Dx, Dy}, {}} o3 : List</pre> </td></tr> <tr><td><pre>i4 : W.dpairInds o4 = {{0, 1}, {2, 3}, {}} o4 : List</pre> </td></tr> </table> </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>