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<!DOCTYPE html> <html lang="en"> <head> <title>System -- a system of functions</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="a system of functions" href="___System.html">System</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="_to__Affine__Chart_lp__Z__Z_cm__List_rp.html">next</a> | <a href="_substitute_lp__Poly__System_cm__Ring_rp.html">previous</a> | <a href="_to__Affine__Chart_lp__Z__Z_cm__List_rp.html">forward</a> | <a href="_substitute_lp__Poly__System_cm__Ring_rp.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>System -- a system of functions</h1> <div> <h2>Description</h2> <div> <p>A type that inherits from this <b>abstract</b> type should supply methods for evaluating a map that takes <a title="a system of functions" href="___System.html">numVariables</a> (+ <a title="a system of functions" href="___System.html">numParameters</a> if the system is parametric) inputs and produces <a title="a system of functions" href="___System.html">numFunctions</a> outputs and its jacobian.</p> <p>Note for developers: it suffices to override the versions of <a title="evaluate a polynomial system or matrix at a point" href="_evaluate.html">evaluate</a> and <a title="a system of functions" href="___System.html">evaluateJacobian</a> that take <span class="tt">(System,Matrix,Matrix)</span> as arguments.</p> </div> </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>Types of <span class="tt">System</span>:</h2> <ul> <li><span><a title="a polynomial system" href="___Poly__System.html">PolySystem</a> -- a polynomial system</span></li> </ul> <h2>Methods that use an object of class System:</h2> <ul> <li><span><kbd>residual(System,AbstractPoint)</kbd> -- see <span><a title="residual of a polynomial function at a point" href="_residual.html">residual</a> -- residual of a polynomial function at a point</span></span></li> <li><span><kbd>residual(System,Point)</kbd> -- see <span><a title="residual of a polynomial function at a point" href="_residual.html">residual</a> -- residual of a polynomial function at a point</span></span></li> <li><kbd>evaluate(System,AbstractPoint)</kbd></li> <li><kbd>evaluate(System,AbstractPoint,AbstractPoint)</kbd></li> <li><kbd>evaluate(System,Matrix)</kbd></li> <li><kbd>evaluate(System,Matrix,Matrix)</kbd></li> <li><kbd>evaluateJacobian(System,AbstractPoint)</kbd></li> <li><kbd>evaluateJacobian(System,AbstractPoint,AbstractPoint)</kbd></li> <li><kbd>evaluateJacobian(System,Matrix)</kbd></li> <li><kbd>evaluateJacobian(System,Matrix,Matrix)</kbd></li> <li><kbd>numFunctions(System)</kbd></li> <li><kbd>numParameters(System)</kbd></li> <li><kbd>numVariables(System)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="a system of functions" href="___System.html">System</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of all mutable hash tables" href="../../Macaulay2Doc/html/___Mutable__Hash__Table.html">MutableHashTable</a> < <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> < <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">NAGtypes/doc-NAGtypes.m2:1016:0</span>.</p> </div> </div> </div> </body> </html>