<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<script type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (toric) - Chapter 3: Affine toric varieties</title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap3"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap2_mj.html">[Previous Chapter]</a>    <a href="chap4_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap3.html">[MathJax off]</a></p>
<p><a id="X82F418F483E4D0D6" name="X82F418F483E4D0D6"></a></p>
<div class="ChapSects"><a href="chap3_mj.html#X82F418F483E4D0D6">3 <span class="Heading">Affine toric varieties</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7B54D98C7A1AC612">3.1 <span class="Heading">Ideals defining affine toric varieties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8139AACB7F0F44EE">3.1-1 EmbeddingAffineToricVariety</a></span>
</div></div>
</div>

<h3>3 <span class="Heading">Affine toric varieties</span></h3>

<p>This chapter concerns <strong class="pkg">toric</strong> commands which deal with the coordinate rings of affine toric varieties <span class="SimpleMath">\(U_\sigma\)</span>.</p>

<p><a id="X7B54D98C7A1AC612" name="X7B54D98C7A1AC612"></a></p>

<h4>3.1 <span class="Heading">Ideals defining affine toric varieties</span></h4>

<p><a id="X8139AACB7F0F44EE" name="X8139AACB7F0F44EE"></a></p>

<h5>3.1-1 EmbeddingAffineToricVariety</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; EmbeddingAffineToricVariety</code>( <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><em>Input</em>: <var class="Arg">L</var> is a list generating a cone (as in <code class="code">DualSemigroupGenerators</code>). <br /> <em>Output</em>: the toroidal embedding of <span class="SimpleMath">\(X=Spec(I)\)</span>, where I is the ideal of the affine toric variety (given as a list of multinomials).</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">phi:=EmbeddingAffineToricVariety([[1,0],[3,4]]);</span>
[ x_2, x_1, x_1^2/x_4, x_1^3/x_4^2, x_1^4/x_4^3 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">L:=[[1,0,0],[1,1,0],[1,1,1],[1,0,1]];;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">phi:=EmbeddingAffineToricVariety(L);</span>
[ x_3, x_2, x_1/x_5, x_1/x_6 ]
</pre></div>


<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap2_mj.html">[Previous Chapter]</a>    <a href="chap4_mj.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>