<?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>simplexRing(FirstOrderDeformation) -- The underlying polynomial ring of a deformation or face.</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_source_lp__First__Order__Deformation_rp.html">next</a> | <a href="_simplex__Ring_lp__Face_rp.html">previous</a> | <a href="_source_lp__First__Order__Deformation_rp.html">forward</a> | <a href="_simplex__Ring_lp__Face_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>simplexRing(FirstOrderDeformation) -- The underlying polynomial ring of a deformation or face.</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>simplexRing(f)</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_simplex__Ring.html" title="The underlying polynomial ring of a deformation or face or complex.">simplexRing</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___First__Order__Deformation.html">first order deformation</a></span></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></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><p>Returns the underlying <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html" title="the class of all ordered monoid rings">PolynomialRing</a> of f.</p>
<div/>
<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4];</pre>
</td></tr>
<tr><td><pre>i2 : addCokerGrading(R);
5 4
o2 : Matrix ZZ <--- ZZ</pre>
</td></tr>
<tr><td><pre>i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o3 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o3 : Ideal of R</pre>
</td></tr>
<tr><td><pre>i4 : mg=mingens I;
1 5
o4 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i5 : f=firstOrderDeformation(mg, vector {-1,-1,0,2,0})
2
x
3
o5 = ----
x x
0 1
o5 : first order deformation space of dimension 1</pre>
</td></tr>
<tr><td><pre>i6 : simplexRing f
o6 = R
o6 : PolynomialRing</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="___First__Order__Deformation.html" title="The class of all first order deformations of monomial ideals.">FirstOrderDeformation</a> -- The class of all first order deformations of monomial ideals.</span></li>
<li><span><a href="_first__Order__Deformation.html" title="Makes a first order deformation.">firstOrderDeformation</a> -- Makes a first order deformation.</span></li>
<li><span><a href="_add__Coker__Grading.html" title="Stores a cokernel grading in a polynomial ring.">addCokerGrading</a> -- Stores a cokernel grading in a polynomial ring.</span></li>
</ul>
</div>
</div>
</body>
</html>
