One Hat Cyber Team

One Hat Cyber Team

Your IP : 216.73.216.80

Server IP : 194.44.31.54

Server : Linux zen.imath.kiev.ua 4.18.0-553.77.1.el8_10.x86_64 #1 SMP Fri Oct 3 14:30:23 UTC 2025 x86_64

Server Software : Apache/2.4.37 (Rocky Linux) OpenSSL/1.1.1k

PHP Version : 5.6.40

Buat File | Buat Folder

Dir : ~/usr/share/doc/Macaulay2/Triplets/html/

Edit File: ___Triplet.html

<!DOCTYPE html>
<html lang="en">
  <head>
    <title>Triplet -- triplet</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="Betti diagrams and hypercohomology tables associated to triplets of degree sequences" href="index.html">Triplets</a> :: <a title="triplet" href="___Triplet.html">Triplet</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="_triplet_lp__List_cm__List_cm__List_rp.html">next</a> | <a href="_to__Homology_lp__Triplet_rp.html">previous</a> | <a href="_triplet_lp__List_cm__List_cm__List_rp.html">forward</a> | <a href="_to__Homology_lp__Triplet_rp.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a>      </div>
    </div>
    <hr>
    <div>
      <h1>Triplet -- triplet</h1>
      <div>
        <h2>Description</h2>
A Triplet is a list consisting of three degree sequences, each  of which is a list of increasing integers. These three degree sequences fulfill certain compatibility conditions. There are two different but equivalent versions:        <p></p>
1. A degree triplet, see Definition 2.9 in math.AC/1207.2071 &quot;Triplets of pure free squarefree complexes&quot;         <p></p>
2. A homology triplet, see Definition 5.4 in math.AC/1212.3675 &quot;Zipping Tate resolutions and exterior coalgebras&quot;         <p></p>
The routines <a title="checks if it is a degree triplet" href="_is__Degree__Triplet_lp__Triplet_rp.html">isDegreeTriplet</a> and <a title="checks if it is a homology triplet" href="_is__Homology__Triplet_lp__Triplet_rp.html">isHomologyTriplet</a> checks if a triplet fulfills the compatibility conditions for degree and homology triplets, respectively.  The routine <a title="from degree triplet to homology triplet" href="_to__Homology_lp__Triplet_rp.html">toHomology</a> converts from a degree triplet to a homology triplet, and the routine <a title="from homology triplet to degree triplet" href="_to__Degree_lp__Triplet_rp.html">toDegree</a> converts from a homology triplet to a degree triplet.      </div>
      <div>
        <div class="waystouse">
          <h2>Functions and methods returning an object of class Triplet:</h2>
          <ul>
            <li><span><kbd>rotBack</kbd> -- see <span><a title="backward cyclic permutation" href="_rot__Back_lp__Triplet_rp.html">rotBack(Triplet)</a> -- backward cyclic permutation</span></span></li>
            <li><span><kbd>rotForw</kbd> -- see <span><a title="forward cyclic permutation" href="_rot__Forw_lp__Triplet_rp.html">rotForw(Triplet)</a> -- forward cyclic permutation</span></span></li>
            <li><span><kbd>toDegree</kbd> -- see <span><a title="from homology triplet to degree triplet" href="_to__Degree_lp__Triplet_rp.html">toDegree(Triplet)</a> -- from homology triplet to degree triplet</span></span></li>
            <li><span><kbd>toHomology</kbd> -- see <span><a title="from degree triplet to homology triplet" href="_to__Homology_lp__Triplet_rp.html">toHomology(Triplet)</a> -- from degree triplet to homology triplet</span></span></li>
            <li><span><kbd>triplet</kbd> -- see <span><a title="make a triplet" href="_triplet_lp__List_cm__List_cm__List_rp.html">triplet(List,List,List)</a> -- make a triplet</span></span></li>
            <li><span><a title="make a triplet" href="_triplet_lp__List_cm__List_cm__List_rp.html">triplet(List,List,List)</a> -- make a triplet</span></li>
          </ul>
          <h2>Methods that use an object of class Triplet:</h2>
          <ul>
            <li><span><a title="Betti numbers of first pure complex" href="___Betti1_lp__Triplet_rp.html">Betti1(Triplet)</a> -- Betti numbers of first pure complex</span></li>
            <li><span><a title="Betti numbers of the three pure complexes" href="___Betti3_lp__Triplet_rp.html">Betti3(Triplet)</a> -- Betti numbers of the three pure complexes</span></li>
            <li><span><a title="Betti diagram of first pure complex " href="___Betti__Diagram1_lp__Triplet_rp.html">BettiDiagram1(Triplet)</a> -- Betti diagram of first pure complex </span></li>
            <li><span><a title="Betti diagrams of the three pure complexes" href="___Betti__Diagram3_lp__Triplet_rp.html">BettiDiagram3(Triplet)</a> -- Betti diagrams of the three pure complexes</span></li>
            <li><span><a title="cohomology table in matrix form" href="_coh__Matrix_lp__Z__Z_cm__Z__Z_cm__Triplet_rp.html">cohMatrix(ZZ,ZZ,Triplet)</a> -- cohomology table in matrix form</span></li>
            <li><span><a title="cohomology table" href="_coh__Table_lp__Z__Z_cm__Z__Z_cm__Triplet_rp.html">cohTable(ZZ,ZZ,Triplet)</a> -- cohomology table</span></li>
            <li><span><a title="the dual homology triplet" href="_dual__Hom__Triplet_lp__Triplet_rp.html">dualHomTriplet(Triplet)</a> -- the dual homology triplet</span></li>
            <li><span><a title="coefficients of Hilbert polynomial" href="_hilb__Coeff_lp__Triplet_rp.html">hilbCoeff(Triplet)</a> -- coefficients of Hilbert polynomial</span></li>
            <li><span><a title="checks if it is a degree triplet" href="_is__Degree__Triplet_lp__Triplet_rp.html">isDegreeTriplet(Triplet)</a> -- checks if it is a degree triplet</span></li>
            <li><span><a title="checks if it is a homology triplet" href="_is__Homology__Triplet_lp__Triplet_rp.html">isHomologyTriplet(Triplet)</a> -- checks if it is a homology triplet</span></li>
            <li><span><a title="backward cyclic permutation" href="_rot__Back_lp__Triplet_rp.html">rotBack(Triplet)</a> -- backward cyclic permutation</span></li>
            <li><span><a title="forward cyclic permutation" href="_rot__Forw_lp__Triplet_rp.html">rotForw(Triplet)</a> -- forward cyclic permutation</span></li>
            <li><span><a title="from homology triplet to degree triplet" href="_to__Degree_lp__Triplet_rp.html">toDegree(Triplet)</a> -- from homology triplet to degree triplet</span></li>
            <li><span><a title="from degree triplet to homology triplet" href="_to__Homology_lp__Triplet_rp.html">toHomology(Triplet)</a> -- from degree triplet to homology triplet</span></li>
            <li><span><a title="number of variables" href="_type_lp__Triplet_rp.html">type(Triplet)</a> -- number of variables</span></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="triplet" href="___Triplet.html">Triplet</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">List</a> &lt; <a title="the class of all visible lists" href="../../Macaulay2Doc/html/___Visible__List.html">VisibleList</a> &lt; <a title="the class of all basic lists" href="../../Macaulay2Doc/html/___Basic__List.html">BasicList</a> &lt; <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p>
        </div>
        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Triplets.m2:725:0</span>.</p>
        </div>
      </div>
    </div>
  </body>

</html>