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      <h1>bertiniRefineSols -- sharpen solutions to a prescribed number of digits</h1>
      <ul>
        <li>
          <dl class="element">
            <dt>Usage: </dt>
            <dd><code class="language-macaulay2">S = bertiniRefineSols(IFD, d, W, OFD)</code></dd>
            <dd><code class="language-macaulay2">S = bertiniRefineSols(d, W, OFD)</code></dd>
            <dd><code class="language-macaulay2">S = bertiniRefineSols(d, W)</code></dd>
          </dl>
        </li>
        <li>Inputs:          <ul>
            <li><span><span class="tt">IFD</span>, <span>a <a title="the class of all strings" href="../../Macaulay2Doc/html/___String.html">string</a></span>, a directory where the input file of a bertiniZeroDim solve is stored along with that runs output files</span></li>
            <li><span><span class="tt">d</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 digits of precision</span></li>
            <li><span><span class="tt">W</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of points to be sharpened</span></li>
            <li><span><span class="tt">OFD</span>, <span>a <a title="the class of all strings" href="../../Macaulay2Doc/html/___String.html">string</a></span>, a directory where the output files of the refinement are stored</span></li>
          </ul>
        </li>
        <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:          <ul>
            <li><span><span class="tt">AdditionalFiles</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><span class="tt">NameB'InputFile</span> (missing documentation)
<span class="tt"> => </span><span class="tt">...</span>, <span>default value &quot;input&quot;</span>, <span></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">S</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of solutions of type Point</span></li>
          </ul>
        </li>
      </ul>
      <div>
        <h2>Description</h2>
        <div>
          <p>This method takes the list W of solutions from a bertiniZeroDimSolve and sharpens them to d digits using the sharpening module of <span class="tt">Bertini</span>. When IFD is omitted the information is pulled from the cache of the first point in W. When OFD is omitted a temporary directory is created.</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i1 : R = CC[x,y];</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : F = {x^2-2,y^2-2};</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : W = bertiniZeroDimSolve (F)

o3 = {{1.41421, 1.41421}, {1.41421, -1.41421}, {-1.41421, 1.41421},
     ------------------------------------------------------------------------
     {-1.41421, -1.41421}}

o3 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i4 : S = bertiniRefineSols (100,W)

o4 = {{1.41421, 1.41421}, {1.41421, -1.41421}, {-1.41421, 1.41421},
     ------------------------------------------------------------------------
     {-1.41421, -1.41421}}

o4 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i5 : coords = coordinates S_0

o5 = {1.41421, 1.41421}

o5 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i6 : coords_0

o6 = 1.4142135623730950488016887242096980785696718753769480731766797379907324
     78462107038850387534327641573

o6 : CC (of precision 333)</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p><a title="sharpen solutions to a prescribed number of digits" href="_bertini__Refine__Sols.html">bertiniRefineSols</a> will only refine non-singular solutions and does not currently work for homogeneous systems.</p>
        </div>
      </div>
      <div>
        <div class="waystouse">
          <h2>Ways to use <span class="tt">bertiniRefineSols</span>:</h2>
          <ul>
            <li><kbd>bertiniRefineSols(String,ZZ,List,String)</kbd></li>
            <li><kbd>bertiniRefineSols(ZZ,List)</kbd></li>
            <li><kbd>bertiniRefineSols(ZZ,List,String)</kbd></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="sharpen solutions to a prescribed number of digits" href="_bertini__Refine__Sols.html">bertiniRefineSols</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.m2:2965:0</span>.</p>
        </div>
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