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