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___Ring__Map_sp__Chordal__Net.html
<!DOCTYPE html> <html lang="en"> <head> <title>RingMap ChordalNet -- apply ring map to a chordal network</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="exploiting chordal structure in polynomial ideals" href="index.html">Chordal</a> :: <a title="apply ring map to a chordal network" href="___Ring__Map_sp__Chordal__Net.html">RingMap ChordalNet</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_root__Count.html">next</a> | <a href="___Ring__Element_sp_pc_sp__Chordal__Net.html">previous</a> | <a href="_root__Count.html">forward</a> | <a href="___Ring__Element_sp_pc_sp__Chordal__Net.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>RingMap ChordalNet -- apply ring map to a chordal network</h1> <ul> <li><span>Operator: <a title="blank operator; often used for function application, making polynomial rings" href="../../Macaulay2Doc/html/___S__P__A__C__E.html">SPACE</a></span></li> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">f N</code></dd> <dd><code class="language-macaulay2">f tree</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">f</span>, <span>a <a title="the class of all ring maps" href="../../Macaulay2Doc/html/___Ring__Map.html">ring map</a></span>, </span></li> <li><span><span class="tt">N</span>, <span>an instance of the type <a title="a chordal network" href="___Chordal__Net.html">ChordalNet</a></span>, </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="a chordal network" href="___Chordal__Net.html">ChordalNet</a></span>, image of N under the ring map f</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = QQ[x_0..x_3, MonomialOrder=>Lex];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : I = ideal {x_0^3-x_0, x_0*x_2-x_2, x_1-x_2, x_2^2-x_2, x_2*x_3^2-x_3}; o2 : Ideal of R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : N = chordalNet I 3 2 o3 = ChordalNet{ x => {{x - x , x x - x , x - x }} } 0 0 0 0 2 2 2 2 2 x => {{x - x , x - x }} 1 1 2 2 2 2 x => {x x - x } 2 2 3 3 x => { } 3 o3 : ChordalNet</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : S = QQ[y_0..y_3, MonomialOrder=>Lex];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : f = map(S,R,gens S) o5 = map (S, R, {y , y , y , y }) 0 1 2 3 o5 : RingMap S <-- R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : f N 3 2 o6 = ChordalNet{ y => {{y - y , y y - y , y - y }} } 0 0 0 0 2 2 2 2 2 y => {{y - y , y - y }} 1 1 2 2 2 2 y => {y y - y } 2 2 3 3 y => { } 3 o6 : ChordalNet</code></pre> </td> </tr> </table> <pre></pre> </div> <div> <h2>See also</h2> <ul> <li><span><a title="a chordal network" href="___Chordal__Net.html">ChordalNet</a> -- a chordal network</span></li> <li><span><a title="apply a ring map" href="../../Macaulay2Doc/html/___Ring__Map_sp__Ring__Element.html">RingMap RingElement</a> -- apply a ring map</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use this method:</h2> <ul> <li><span><a title="apply ring map to a chordal network" href="___Ring__Map_sp__Chordal__Net.html">RingMap ChordalNet</a> -- apply ring map to a chordal network</span></li> <li><kbd>RingMap ElimTree</kbd></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Chordal/ChordalDoc.m2:889:0</span>.</p> </div> </div> </div> </body> </html>