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<!DOCTYPE html> <html lang="en"> <head> <title>extension(...,EntryMode=>...) -- use a modular cut or linear subclass</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="a package for computations with matroids" href="index.html">Matroids</a> :: <a title="use a modular cut or linear subclass" href="_extension_lp..._cm__Entry__Mode_eq_gt..._rp.html">extension(...,EntryMode=>...)</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="_flats.html">next</a> | <a href="_extension_lp..._cm__Check__Well__Defined_eq_gt..._rp.html">previous</a> | <a href="_flats.html">forward</a> | <a href="_extension_lp..._cm__Check__Well__Defined_eq_gt..._rp.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>extension(...,EntryMode=>...) -- use a modular cut or linear subclass</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">extension(M, L, Entry => "hyperplanes")</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">M</span>, <span>a <a title="the class of all matroids" href="___Matroid.html">matroid</a></span></span></li> <li><span><span class="tt">L</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of flats or hyperplanes of the matroid forming a modular cut/linear subclass</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>a <a title="the class of all matroids" href="___Matroid.html">matroid</a></span>, the extension of the matroid associated to modular cut/linear subclass</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <p>This option is provided by the package <a title="a package for computations with matroids" href="index.html">Matroids</a>.</p> <p>A single-element extension of a matroid M can be produced from a list of flats forming a modular cut of M or a list of hyperplanes of M forming a linear subclass. By default, it is assumed the specified list is a modular cut, but setting this option to "hyperplanes" allows passing a much shorter list of hyperplanes forming a linear subclass instead.</p> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : A = matrix {{1, 0, 0, 1, 1}, {0, 1, 0, 1, -1}, {0, 0, 1, 0, 0}} o1 = | 1 0 0 1 1 | | 0 1 0 1 -1 | | 0 0 1 0 0 | 3 5 o1 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : M = matroid A o2 = a "matroid" of rank 3 on 5 elements o2 : Matroid</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : H = drop(hyperplanes M, 1) o3 = {set {4, 2}, set {2, 3}, set {1, 2}, set {0, 2}} o3 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : extension(M, H, EntryMode => "hyperplanes") o4 = a "matroid" of rank 3 on 6 elements o4 : Matroid</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="of a matroid relative to a flat or modular cut" href="_extension.html">extension</a> -- of a matroid relative to a flat or modular cut</span></li> </ul> </div> <div> <div> <h2>Functions with optional argument named <span class="tt">EntryMode</span>:</h2> <ul> <li><span><span class="tt">digraph(...,EntryMode=>...)</span> (missing documentation)<!--tag: [digraph, EntryMode]--> </span></li> <li><span><a title="use a modular cut or linear subclass" href="_elementary__Quotient_lp..._cm__Entry__Mode_eq_gt..._rp.html">elementaryQuotient(...,EntryMode=>...)</a> -- use a modular cut or linear subclass</span></li> <li><span><a title="use a modular cut or linear subclass" href="_extension_lp..._cm__Entry__Mode_eq_gt..._rp.html">extension(...,EntryMode=>...)</a> -- use a modular cut or linear subclass</span></li> <li><span><kbd>graph(...,EntryMode=>...)</kbd> -- see <span><a title="Constructs a simple graph" href="../../Graphs/html/_graph.html">graph</a> -- Constructs a simple graph</span></span></li> <li><span><a title="select method of specifying matroid" href="_matroid_lp..._cm__Entry__Mode_eq_gt..._rp.html">matroid(...,EntryMode=>...)</a> -- select method of specifying matroid</span></li> </ul> </div> <div> <h2>Further information</h2> <ul> <li><span>Default value: <span class="tt">modular cut</span></span></li> <li><span>Function: <span><a title="of a matroid relative to a flat or modular cut" href="_extension.html">extension</a> -- of a matroid relative to a flat or modular cut</span></span></li> <li><span>Option key: <span><a title="Constructs a simple graph" href="../../Graphs/html/_graph.html">EntryMode</a> -- Constructs a simple graph</span></span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Matroids/doc-Matroids.m2:3997:0</span>.</p> </div> </div> </div> </body> </html>
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