<?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>isSkewCommutative -- whether a ring has skew commuting variables</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_is__Sorted_lp__Visible__List_rp.html">next</a> | <a href="_is__Ring.html">previous</a> | <a href="_is__Sorted_lp__Visible__List_rp.html">forward</a> | <a href="_is__Ring.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>isSkewCommutative -- whether a ring has skew commuting variables</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>isSkewCommutative R</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="___Ring.html">ring</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Boolean.html">Boolean value</a></span>, <a href="_true.html" title="">true</a> if <tt>R</tt> has skew commuting variables and <a href="_false.html" title="">false</a> otherwise</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : A = ZZ/3[a,b,c];</pre> </td></tr> <tr><td><pre>i2 : isSkewCommutative A o2 = false</pre> </td></tr> <tr><td><pre>i3 : B = QQ[a..d,SkewCommutative=>{a,b}] o3 = B o3 : PolynomialRing</pre> </td></tr> <tr><td><pre>i4 : isSkewCommutative B o4 = true</pre> </td></tr> <tr><td><pre>i5 : C = B[x,y] o5 = C o5 : PolynomialRing</pre> </td></tr> <tr><td><pre>i6 : isSkewCommutative C o6 = true</pre> </td></tr> <tr><td><pre>i7 : b_C * a_C o7 = -a*b o7 : C</pre> </td></tr> <tr><td><pre>i8 : D = B/(a*d-b*c) o8 = D o8 : QuotientRing</pre> </td></tr> <tr><td><pre>i9 : isSkewCommutative D o9 = true</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_exterior_spalgebras.html" title="">exterior algebras</a></span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>isSkewCommutative</tt> :</h2> <ul><li>isSkewCommutative(PolynomialRing)</li> <li>isSkewCommutative(QuotientRing)</li> <li>isSkewCommutative(Ring)</li> </ul> </div> </div> </body> </html>