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      <h1>incOrbit -- the increasing map orbit of an element</h1>
      <ul>
        <li>
          <dl class="element">
            <dt>Usage: </dt>
            <dd><code class="language-macaulay2">O = incOrbit(f,n)</code></dd>
            <dd><code class="language-macaulay2">O = incOrbit(F,n)</code></dd>
          </dl>
        </li>
        <li>Inputs:          <ul>
            <li><span><span class="tt">f</span>, <span>a <a title="the class of all ring elements handled by the engine" href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, an element of a ring created by <a title="creates a ring to be used with other functions in the EquivariantGB package" href="_build__E__Ring.html">buildERing</a></span></li>
            <li><span><span class="tt">F</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of ring elements</span></li>
            <li><span><span class="tt">n</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the index bound</span></li>
          </ul>
        </li>
        <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:          <ul>
            <li><span><span class="tt">Symmetrize</span><span class="tt"> => </span><span class="tt">...</span>, <span>default value false</span></span></li>
          </ul>
        </li>
        <li>Outputs:          <ul>
            <li><span><span class="tt">O</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of all elements in the orbit of <span class="tt">f</span> or <span class="tt">F</span></span></li>
          </ul>
        </li>
      </ul>
      <div>
        <h2>Description</h2>
        <div>
          <p>If <span class="tt">F</span> is an equivariant Gröbner basis for invariant ideal <span class="tt">I</span> with respect to a width order then this method produces a traditional Gröbner basis for the <span class="tt">n</span>th truncation of <span class="tt">I</span>.</p>
          <p>If the optional argument <span class="tt">Symmetrize</span> is set to true, then the full S_n orbit is produced.</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i1 : R = buildERing({symbol x}, {1}, QQ, 2);</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : O = incOrbit(x_0^2, 4)

2   2   2   2
o2 = {x , x , x , x }
       0   1   2   3

o2 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : P = incOrbit(x_0 + x_1^2, 3, Symmetrize=>true)

2             2   2             2   2             2
o3 = {x  + x , x  + x , x  + x , x  + x , x  + x , x  + x }
       1    0   1    0   2    0   2    0   2    1   2    1

o3 : List</code></pre>
            </td>
          </tr>
        </table>
      </div>
      <div>
        <h2>Caveat</h2>
        <div>
          <p>The output is not necessarily in the same ring as the input.  The width bound of the ring of the output will always be <span class="tt">n</span>.</p>
        </div>
      </div>
      <div>
        <div class="waystouse">
          <h2>Ways to use <span class="tt">incOrbit</span>:</h2>
          <ul>
            <li><kbd>incOrbit(List,ZZ)</kbd></li>
            <li><kbd>incOrbit(RingElement,ZZ)</kbd></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="the increasing map orbit of an element" href="_inc__Orbit.html">incOrbit</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">EquivariantGB.m2:1383:0</span>.</p>
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