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<title>GAP (toric) - Chapter 3: Affine toric varieties</title>
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<div class="ChapSects"><a href="chap3.html#X82F418F483E4D0D6">3 <span class="Heading">Affine toric varieties</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7B54D98C7A1AC612">3.1 <span class="Heading">Ideals defining affine toric varieties</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8139AACB7F0F44EE">3.1-1 EmbeddingAffineToricVariety</a></span>
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<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_σ</span>.</p>

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

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<h5>3.1-1 EmbeddingAffineToricVariety</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ 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>


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