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<!DOCTYPE html> <html lang="en"> <head> <title>witnessSet -- construct a WitnessSet</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="Common types used in Numerical Algebraic Geometry" href="index.html">NAGtypes</a> :: <a title="construct a WitnessSet" href="_witness__Set.html">witnessSet</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="___W__Set.html">next</a> | <a href="___Witness__Set.html">previous</a> | <a href="___W__Set.html">forward</a> | <a href="___Witness__Set.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>witnessSet -- construct a WitnessSet</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">w = witnessSet(E,S,P)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">E</span>, <span>an <a title="the class of all ideals" href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span> or <span>a <a title="a polynomial system" href="___Poly__System.html">polynomial system</a></span></span></li> <li><span><span class="tt">S</span>, <span>an <a title="the class of all ideals" href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span> generated by linear polynomials (or <span>a <a title="a polynomial system" href="___Poly__System.html">polynomial system</a></span> of the generators or <span>a <a title="the class of all matrices" href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span> of their coefficients)</span></li> <li><span><span class="tt">P</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, contains witness points (of type <a title="a type used to store a point in complex space" href="___Abstract__Point.html">AbstractPoint</a>)</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">w</span>, <span>a <a title="a witness set" href="___Witness__Set.html">witness set</a></span></span></li> </ul> </li> </ul> <div> <h2>Description</h2> <p>Used to construct a witness set of a component of the variety <span class="tt">V(E)</span>. It is expected that <span class="tt">codim E == dim S</span> and that <span class="tt">P</span> is a subset of the intersection of <span class="tt">V(E)</span> and <span class="tt">V(S)</span>.</p> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = CC[x,y] o1 = R o1 : PolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : w = witnessSet( ideal(x^2+y^2+2), ideal(x-y), {point {{0.999999*ii,0.999999*ii}}, point {{-1.000001*ii,-1.000001*ii}}} ) o2 = w o2 : WitnessSet</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : peek w o3 = WitnessSet{cache => CacheTable{...1...} } Equations => {-2} | x2+y2+2 | Points => {{.999999*ii, .999999*ii}} {{-ii, -ii} } Slice => | 1 -1 0 |</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">witnessSet</span>:</h2> <ul> <li><kbd>witnessSet(Ideal,Ideal,List)</kbd></li> <li><kbd>witnessSet(Ideal,Matrix,List)</kbd></li> <li><kbd>witnessSet(PolySystem,Matrix,List)</kbd></li> <li><kbd>witnessSet(PolySystem,PolySystem,List)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="construct a WitnessSet" href="_witness__Set.html">witnessSet</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">NAGtypes/doc-NAGtypes.m2:614:0</span>.</p> </div> </div> </div> </body> </html>