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<div class="ChapSects"><a href="chap2_mj.html#X7B222197819984A6">2 <span class="Heading">Ring Maps</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7EBF1DD67BD0758F">2.1 <span class="Heading">Ring Maps: Attributes</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X87C00FFB79FA93A8">2.1-1 KernelSubobject</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7C7401BA7E2221CB">2.2 <span class="Heading">Ring Maps: Operations and Functions</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7B7DDDA17837AEF5">2.2-1 SegreMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X78E0B36179C5646C">2.2-2 PlueckerMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X816B9AB287EEF9A5">2.2-3 VeroneseMap</a></span>
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<h3>2 <span class="Heading">Ring Maps</span></h3>

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<h4>2.1 <span class="Heading">Ring Maps: Attributes</span></h4>

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<h5>2.1-1 KernelSubobject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; KernelSubobject</code>( <var class="Arg">phi</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> submodule</p>

<p>The kernel ideal of the ring map <var class="Arg">phi</var>.</p>

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<h4>2.2 <span class="Heading">Ring Maps: Operations and Functions</span></h4>

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<h5>2.2-1 SegreMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SegreMap</code>( <var class="Arg">R</var>, <var class="Arg">s</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> ring map</p>

<p>The ring map corresponding to the Segre embedding of <span class="SimpleMath">\(MultiProj(\textit{R})\)</span> into the projective space according to <span class="SimpleMath">\(P(W_1)\times P(W_2) \to P(W_1\otimes W_2)\)</span>.</p>

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<h5>2.2-2 PlueckerMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; PlueckerMap</code>( <var class="Arg">l</var>, <var class="Arg">n</var>, <var class="Arg">A</var>, <var class="Arg">s</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> ring map</p>

<p>The ring map corresponding to the Plücker embedding of the Grassmannian <span class="SimpleMath">\(G_l(P^{\textit{n}}(\textit{A}))=G_l(P(W))\)</span> into the projective space <span class="SimpleMath">\(P(\bigwedge^l W)\)</span>, where <span class="SimpleMath">\(W=V^*\)</span> is the <span class="SimpleMath">\(\textit{A}\)</span>-dual of the free module <span class="SimpleMath">\(V=A^{\textit{n}+1}\)</span> of rank <span class="SimpleMath">\(\textit{n}+1\)</span>.</p>

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<h5>2.2-3 VeroneseMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; VeroneseMap</code>( <var class="Arg">n</var>, <var class="Arg">d</var>, <var class="Arg">A</var>, <var class="Arg">s</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> ring map</p>

<p>The ring map corresponding to the Veronese embedding of the projective space <span class="SimpleMath">\(P^{\textit{n}}(\textit{A})=P(W)\)</span> into the projective space <span class="SimpleMath">\(P(S^d W)\)</span>, where <span class="SimpleMath">\(W=V^*\)</span> is the <span class="SimpleMath">\(\textit{A}\)</span>-dual of the free module <span class="SimpleMath">\(V=A^{\textit{n}+1}\)</span> of rank <span class="SimpleMath">\(\textit{n}+1\)</span>.</p>


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