One Hat Cyber Team

Your IP : 216.73.216.14

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/Brackets/html/

Edit File: ___Bracket.html

<!DOCTYPE html>
<html lang="en">
  <head>
    <title>Bracket</title>
    <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
    <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css">

o1 = B
      5,3

o1 : BracketRing</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : [1 2 3]_B

o2 = [123]

o2 : Bracket</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : X = matrix B

o3 = {-1} | x_(1,1) x_(1,2) x_(1,3) |
     {-1} | x_(2,1) x_(2,2) x_(2,3) |
     {-1} | x_(3,1) x_(3,2) x_(3,3) |
     {-1} | x_(4,1) x_(4,2) x_(4,3) |
     {-1} | x_(5,1) x_(5,2) x_(5,3) |

5                                                                                                     3
o3 : Matrix (QQ[x   ..x   , y     , y     , y     , y     , y     , y     , y     , y     , y     , y     ])  &lt;-- (QQ[x   ..x   , y     , y     , y     , y     , y     , y     , y     , y     , y     , y     ])
                 1,1   5,3   [345]   [245]   [235]   [234]   [145]   [135]   [134]   [125]   [124]   [123]             1,1   5,3   [345]   [245]   [235]   [234]   [145]   [135]   [134]   [125]   [124]   [123]</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i4 : toBracketPolynomial(det X^{0,1,2},B)

o4 = [123]

o4 : GCExpression</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p>See also <a href="___Bracket__Ring.html">BracketRing</a> and <a title="Represent an invariant polynomial as a polynomial in brackets" href="_to__Bracket__Polynomial.html">toBracketPolynomial</a>.</p>
          <p></p>
        </div>
      </div>
      <div>
        <div class="waystouse">
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a href="___Bracket.html">Bracket</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a href="___G__C__Expression.html">GCExpression</a> &lt; <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</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">Brackets.m2:518:0</span>.</p>
        </div>
      </div>
    </div>
  </body>

</html>