One Hat Cyber Team

Edit File: _pminors.html

<!DOCTYPE html>
<html lang="en">
  <head>
    <title>pminors -- Return ideal generated by pminors of a specified size</title>
    <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
    <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css">

o1 = R

o1 : PolynomialRing</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : M = genericMatrix(R,a,3,3)

o2 = | a d g |
     | b e h |
     | c f i |

3      3
o2 : Matrix R  &lt;-- R</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : I = pminors(2,M)

o3 = ideal (b*d + a*e, b*g + a*h, e*g + d*h, c*d + a*f, c*g + a*i, f*g + d*i,
     ------------------------------------------------------------------------
     c*e + b*f, c*h + b*i, f*h + e*i)

o3 : Ideal of R</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p>Here is the ideal generated by the $2\times 2$ permanent minors of a $2\times 3$ matrix using the two different strategies.</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i4 : M=matrix{{1,2,3},{4,5,6}}

o4 = | 1 2 3 |
     | 4 5 6 |

2       3
o4 : Matrix ZZ  &lt;-- ZZ</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i5 : pminors(2,M,Strategy=>glynn)

o5 = ideal (13, 18, 27)

o5 : Ideal of ZZ</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i6 : pminors(2,M,Strategy=>ryser)

o6 = ideal (13, 18, 27)

o6 : Ideal of ZZ</code></pre>
            </td>
          </tr>
        </table>
      </div>
      <div>
        <h2>Caveat</h2>
        <div>
          <p></p>
          <p></p>
        </div>
      </div>
      <div>
        <h2>See also</h2>
        <ul>
          <li><span><a title="ideal generated by square permanents of a matrix" href="../../Macaulay2Doc/html/_permanents.html">permanents</a> -- ideal generated by square permanents of a matrix</span></li>
        </ul>
      </div>
      <div>
        <div class="waystouse">
          <h2>Ways to use <span class="tt">pminors</span>:</h2>
          <ul>
            <li><kbd>pminors(ZZ,Matrix)</kbd></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="Return ideal generated by pminors of a specified size" href="_pminors.html">pminors</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p>
        </div>
        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Permanents.m2:570:0</span>.</p>
        </div>
      </div>
    </div>
  </body>

</html>