<?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>integralClosure(..., Variable => ...) -- set the base letter for the indexed variables introduced while computing the integral closure</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_integral__Closure_lp..._cm_sp__Verbosity_sp_eq_gt_sp..._rp.html">next</a> | <a href="_integral__Closure_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">previous</a> | <a href="_integral__Closure_lp..._cm_sp__Verbosity_sp_eq_gt_sp..._rp.html">forward</a> | <a href="_integral__Closure_lp..._cm_sp__Strategy_sp_eq_gt_sp..._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>integralClosure(..., Variable => ...) -- set the base letter for the indexed variables introduced while computing the integral closure</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>integralClosure(R, Variable=>x)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>x</tt>, <span>a <a href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span></span></li> </ul> </div> </li> <li><div class="single">Consequences:<ul><li><div>The new variables will be subscripted using <tt>x</tt>.</div> </li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4-z^3);</pre> </td></tr> <tr><td><pre>i2 : R' = integralClosure(R, Variable => symbol t) o2 = R' o2 : QuotientRing</pre> </td></tr> <tr><td><pre>i3 : trim ideal R' 2 3 2 3 o3 = ideal (t z - x , t - y z - z - 1) 3,0 3,0 o3 : Ideal of QQ[t , x, y, z] 3,0</pre> </td></tr> </table> <div>The algorithm works in stages, each time adding new fractions to the ring. A variable <tt>t<sub>(</sub>3,0)</tt> represents the first (zero-th) variables added at stage 3. In the future, the variables added will likely just be <tt>t<sub>1</sub>, t<sub>2</sub>, ...</tt>.</div> </div> </div> <h2>Further information</h2> <ul><li><span>Default value: <tt>w</tt> (missing documentation<!-- tag: w -->)</span></li> <li><span>Function: <span><a href="_integral__Closure.html" title="integral closure of an ideal or a domain">integralClosure</a> -- integral closure of an ideal or a domain</span></span></li> <li><span>Option name: <span><a href="../../Macaulay2Doc/html/___Variable.html" title="specify a name for a variable">Variable</a> -- specify a name for a variable</span></span></li> </ul> <div class="single"><h2>Caveat</h2> <div><div>The base name should be a symbol</div> </div> </div> </div> </body> </html>