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<div class="ChapSects"><a href="chap2.html#X7B222197819984A6">2 <span class="Heading">Ring Maps</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.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.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.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.html#X7B7DDDA17837AEF5">2.2-1 SegreMap</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X78E0B36179C5646C">2.2-2 PlueckerMap</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X816B9AB287EEF9A5">2.2-3 VeroneseMap</a></span>
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<h3>2 <span class="Heading">Ring Maps</span></h3>
<p><a id="X7EBF1DD67BD0758F" name="X7EBF1DD67BD0758F"></a></p>
<h4>2.1 <span class="Heading">Ring Maps: Attributes</span></h4>
<p><a id="X87C00FFB79FA93A8" name="X87C00FFB79FA93A8"></a></p>
<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>
<p><a id="X7C7401BA7E2221CB" name="X7C7401BA7E2221CB"></a></p>
<h4>2.2 <span class="Heading">Ring Maps: Operations and Functions</span></h4>
<p><a id="X7B7DDDA17837AEF5" name="X7B7DDDA17837AEF5"></a></p>
<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(<var class="Arg">R</var>)</span> into the projective space according to <span class="SimpleMath">P(W_1)× P(W_2) -> P(W_1⊗ W_2)</span>.</p>
<p><a id="X78E0B36179C5646C" name="X78E0B36179C5646C"></a></p>
<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^<var class="Arg">n</var>(<var class="Arg">A</var>))=G_l(P(W))</span> into the projective space <span class="SimpleMath">P(⋀^l W)</span>, where <span class="SimpleMath">W=V^*</span> is the <span class="SimpleMath"><var class="Arg">A</var></span>-dual of the free module <span class="SimpleMath">V=A^<var class="Arg">n</var>+1</span> of rank <span class="SimpleMath"><var class="Arg">n</var>+1</span>.</p>
<p><a id="X816B9AB287EEF9A5" name="X816B9AB287EEF9A5"></a></p>
<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^<var class="Arg">n</var>(<var class="Arg">A</var>)=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"><var class="Arg">A</var></span>-dual of the free module <span class="SimpleMath">V=A^<var class="Arg">n</var>+1</span> of rank <span class="SimpleMath"><var class="Arg">n</var>+1</span>.</p>
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