<?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>dim(AffineVariety) -- dimension of the affine variety</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_dim_lp__Ideal_rp.html">next</a> | <a href="_dim.html">previous</a> | <a href="_dim_lp__Ideal_rp.html">forward</a> | <a href="_dim.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>dim(AffineVariety) -- dimension of the affine variety</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>dim V</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_dim.html" title="compute the Krull dimension">dim</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>V</tt>, <span>an <a href="___Affine__Variety.html">affine variety</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>Computes the dimension of the affine algebraic set <tt>V</tt> as the Krull dimension of its affine coordinate ring.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y];</pre> </td></tr> <tr><td><pre>i2 : point = ideal(x,y); o2 : Ideal of R</pre> </td></tr> <tr><td><pre>i3 : line = ideal(2*x+3*y-1); o3 : Ideal of R</pre> </td></tr> <tr><td><pre>i4 : V=Spec(R/intersect(point,line)) o4 = V o4 : AffineVariety</pre> </td></tr> <tr><td><pre>i5 : dim V o5 = 1</pre> </td></tr> <tr><td><pre>i6 : Z=Spec(R/(point+line)) o6 = Z o6 : AffineVariety</pre> </td></tr> <tr><td><pre>i7 : dim Z o7 = -infinity o7 : InfiniteNumber</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="___Spec_lp__Ring_rp.html" title="make an affine variety">Spec</a> -- make an affine variety</span></li> <li><span><a href="_dim_lp__Projective__Variety_rp.html" title="dimension of the projective variety">dim(ProjectiveVariety)</a> -- dimension of the projective variety</span></li> </ul> </div> </div> </body> </html>