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<!DOCTYPE html> <html lang="en"> <head> <title>evaluate -- evaluate a polynomial system or matrix at a point</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="evaluate a polynomial system or matrix at a point" href="_evaluate.html">evaluate</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="_general__Equations.html">next</a> | <a href="_dual__Space.html">previous</a> | <a href="_general__Equations.html">forward</a> | <a href="_dual__Space.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>evaluate -- evaluate a polynomial system or matrix at a point</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">y = evaluate(f,x)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">f</span>, <span>a <a title="a polynomial system" href="___Poly__System.html">polynomial system</a></span> or <span>a <a title="the class of all matrices" href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li> <li><span><span class="tt">x</span>, <span>a <a title="a type used to store a point in complex space" href="___Abstract__Point.html">point</a></span> or <span>a <a title="the class of all matrices" href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">y</span>, the value <span class="tt">f(x)</span></span></li> </ul> </li> </ul> <div> <h2>Description</h2> <p>Evaluates a <a title="a polynomial system" href="___Poly__System.html">PolySystem</a> or a matrix with polynomial entries at a point.</p> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = CC[x,y]; S = polySystem {x^2+y^2-6, 2*x^2-y};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : p = point {{1.0+3*ii,2.3+ii}};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : evaluate(S,p) o4 = | -9.71+10.6ii | | -18.3+11ii | 2 1 o4 : Matrix CC <-- CC 53 53</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : evaluate(jacobian S, p) o5 = | 2+6ii 4.6+2ii | | 4+12ii -1 | 2 2 o5 : Matrix CC <-- CC 53 53</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="a polynomial system" href="___Poly__System.html">PolySystem</a> -- a polynomial system</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">evaluate</span>:</h2> <ul> <li><kbd>evaluate(Matrix,AbstractPoint)</kbd></li> <li><kbd>evaluate(Matrix,Matrix)</kbd></li> <li><kbd>evaluate(PolySystem,Matrix)</kbd></li> <li><span><kbd>evaluate(System,AbstractPoint)</kbd> -- see <span><a title="a system of functions" href="___System.html">System</a> -- a system of functions</span></span></li> <li><span><kbd>evaluate(System,AbstractPoint,AbstractPoint)</kbd> -- see <span><a title="a system of functions" href="___System.html">System</a> -- a system of functions</span></span></li> <li><span><kbd>evaluate(System,Matrix)</kbd> -- see <span><a title="a system of functions" href="___System.html">System</a> -- a system of functions</span></span></li> <li><span><kbd>evaluate(System,Matrix,Matrix)</kbd> -- see <span><a title="a system of functions" href="___System.html">System</a> -- a system of functions</span></span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="evaluate a polynomial system or matrix at a point" href="_evaluate.html">evaluate</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.m2:415:0</span>.</p> </div> </div> </div> </body> </html>