One Hat Cyber Team

One Hat Cyber Team

Your IP : 216.73.216.115

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/Bertini/html/

Edit File: _bertiniComponentMember__Test.html

<!DOCTYPE html>
<html lang="en">
  <head>
    <title>bertiniComponentMemberTest -- a main method to test whether points lie on a given variety</title>
    <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
    <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css">

<link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css">
    <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script>
    <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script>
    <script>
      var macros = {
          "\\break": "\\\\",
          "\\ZZ": "\\mathbb{Z}",
          "\\NN": "\\mathbb{N}",
          "\\QQ": "\\mathbb{Q}",
          "\\RR": "\\mathbb{R}",
          "\\CC": "\\mathbb{C}",
          "\\PP": "\\mathbb{P}"
      }, delimiters = [
          { left: "$$",  right: "$$",  display: true},
          { left: "\\[", right: "\\]", display: true},
          { left: "$",   right: "$",   display: false},
          { left: "\\(", right: "\\)", display: false}
      ], ignoredTags = [
	  "kbd", "var", "samp", "script", "noscript",
	  "style", "textarea", "pre", "code", "option" ];
      document.addEventListener("DOMContentLoaded", function() {
        renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true });
      });
    </script>
    <style>.katex { font-size: 1em; }</style>
    <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script>
    <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script>
    <script src="../../../../Macaulay2/Style/prism.js"></script>
    <script>var current_version = '1.25.06';</script>
    <script src="../../../../Macaulay2/Style/version-select.js"></script>
    <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif">
  </head>
  <body>
    <div id="buttons">
      <div>
<a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="software for numerical algebraic geometry" href="index.html">Bertini</a> :: <a title="a main method to test whether points lie on a given variety" href="_bertini__Component__Member__Test.html">bertiniComponentMemberTest</a></span>      </div>
      <div class="right">
<form method="get" action="https://www.google.com/search">
  <input placeholder="Search" type="text" name="q" value="">
  <input type="hidden" name="q" value="site:macaulay2.com/doc">
</form>
<a href="_bertini__Parameter__Homotopy.html">next</a> | <a href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">previous</a> | <a href="_bertini__Parameter__Homotopy.html">forward</a> | <a href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a>      </div>
    </div>
    <hr>
    <div>
      <h1>bertiniComponentMemberTest -- a main method to test whether points lie on a given variety</h1>
      <ul>
        <li>
          <dl class="element">
            <dt>Usage: </dt>
            <dd><code class="language-macaulay2">L = bertiniComponentMemberTest (pts, NV)</code></dd>
          </dl>
        </li>
        <li>Inputs:          <ul>
            <li><span><span class="tt">pts</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of points to test</span></li>
            <li><span><span class="tt">NV</span>, <span>a <a title="a numerical variety" href="../../NAGtypes/html/___Numerical__Variety.html">numerical variety</a></span>, a numerical variety to test if points lie on a given 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>, entries are lists of witness sets containing the test point</span></li>
          </ul>
        </li>
      </ul>
      <div>
        <h2>Description</h2>
        <div>
          <p>This method checks whether the test points pts lie on NV using <span class="tt">Bertini</span> by (1) writing the witness set information of NV and the test points to temporary files, (2) invokes <span class="tt">Bertini</span>'s solver with option <span class="tt">TRACKTYPE => 3</span>, (3) stores output of <span class="tt">Bertini</span> in temporary file, (4) parses and outputs the solutions.</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i1 : R = CC[x,y,z];</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};</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 : pts = {{0,0,0}} --z-axis

o4 = {{0, 0, 0}}

o4 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i5 : bertiniComponentMemberTest(pts, NV)

o5 = {{(dim=1,deg=1)}}

o5 : List</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p>In the current implementation, at most one witness set is listed for each test point although the point may lie on more than one component.</p>
        </div>
      </div>
      <div>
        <div class="waystouse">
          <h2>Ways to use <span class="tt">bertiniComponentMemberTest</span>:</h2>
          <ul>
            <li><kbd>bertiniComponentMemberTest(List,NumericalVariety)</kbd></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="a main method to test whether points lie on a given variety" href="_bertini__Component__Member__Test.html">bertiniComponentMemberTest</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.m2:2927:0</span>.</p>
        </div>
      </div>
    </div>
  </body>

</html>