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      <h1>bertiniSample -- a main method to sample points from an irreducible component of a variety</h1>
      <ul>
        <li>
          <dl class="element">
            <dt>Usage: </dt>
            <dd><code class="language-macaulay2">V = bertiniSample (n, W)</code></dd>
          </dl>
        </li>
        <li>Inputs:          <ul>
            <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>, an integer specifying the number of desired sample points</span></li>
            <li><span><span class="tt">W</span>, <span>a <a title="a witness set" href="../../NAGtypes/html/___Witness__Set.html">witness set</a></span>, a witness set for an irreducible component</span></li>
          </ul>
        </li>
        <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:          <ul>
            <li><span><span class="tt">BertiniInputConfiguration</span> (missing documentation)
<span class="tt"> => </span><span class="tt">...</span>, <span>default value {}</span>, <span></span></span></li>
            <li><span><a title="optional argument to specify whether to use homogeneous coordinates" href="___Is__Projective.html">IsProjective</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value -1</span>, <span>optional argument to specify whether to use homogeneous coordinates</span></span></li>
            <li><span><a title="Option to silence additional output" href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value false</span>, <span>Option to silence additional output</span></span></li>
          </ul>
        </li>
        <li>Outputs:          <ul>
            <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 sample points</span></li>
          </ul>
        </li>
      </ul>
      <div>
        <h2>Description</h2>
        <div>
          <p>Samples points from an irreducible component of a variety using Bertini.  The irreducible component needs to be in its numerical form as a <a title="a witness set" href="../../NAGtypes/html/___Witness__Set.html">WitnessSet</a>.  The method <a title="a main method that is used to produce witness sets" href="_bertini__Pos__Dim__Solve.html">bertiniPosDimSolve</a> can be used to generate a witness set for the component. Bertini (1) writes the witness set to a temporary file, (2) invokes <span class="tt">Bertini</span>'s solver with option <span class="tt">TrackType => 2</span>, and (3 moves the hyperplanes defined in the <a title="a witness set" href="../../NAGtypes/html/___Witness__Set.html">WitnessSet</a> W within the space until the desired points are sampled, (4) stores the output of <span class="tt">Bertini</span> in a temporary file, and finally (5) parses and outputs the solutions.</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i1 : R = CC[x,y,z]

o1 = R

o1 : PolynomialRing</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : F = { (y^2+x^2+z^2-1)*x, (y^2+x^2+z^2-1)*y }

3      2      2       2     3      2
o2 = {x  + x*y  + x*z  - x, x y + y  + y*z  - y}

o2 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : NV = bertiniPosDimSolve(F)

o3 = NV

o3 : NumericalVariety</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i4 : W = NV#1_0 --z-axis

o4 = W

o4 : WitnessSet</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i5 : bertiniSample(4, W)

o5 = {{-3.98895e-21-2.66903e-21*ii, -1.09049e-20+2.39057e-21*ii,
     ------------------------------------------------------------------------
     .335497+.0877674*ii}, {-2.38851e-21+7.43066e-21*ii,
     ------------------------------------------------------------------------
     7.04885e-21-3.31435e-21*ii, .235164+.0679316*ii},
     ------------------------------------------------------------------------
     {-7.16418e-21+3.40793e-21*ii, 8.68665e-21+1.35454e-20*ii,
     ------------------------------------------------------------------------
     .376396+.160188*ii}, {7.24583e-21+2.22616e-21*ii,
     ------------------------------------------------------------------------
     5.24083e-21+5.80899e-21*ii, .330083+.265624*ii}}

o5 : List</code></pre>
            </td>
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      </div>
      <div>
        <div class="waystouse">
          <h2>Ways to use <span class="tt">bertiniSample</span>:</h2>
          <ul>
            <li><kbd>bertiniSample(ZZ,WitnessSet)</kbd></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="a main method to sample points from an irreducible component of a variety" href="_bertini__Sample.html">bertiniSample</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">Bertini.m2:2790:0</span>.</p>
        </div>
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