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<!DOCTYPE html> <html lang="en"> <head> <title>-> -- make a function</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="index.html">Documentation </a> <br><a href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="Macaulay2 documentation" href="index.html">Macaulay2Doc</a> » <a href="___The_sp__Macaulay2_splanguage.html">The Macaulay2 language</a> » <a href="_operators.html">operators</a> » <a title="make a function" href="_-_gt.html">-></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="__at_at.html">next</a> | <a href="___S__P__A__C__E.html">previous</a> | <a href="_options_lp__Function_rp.html">forward</a> | <a href="___S__P__A__C__E.html">backward</a> | <a href="_operators.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>-> -- make a function</h1> <div> <h2>Description</h2> <span class="tt">x -> e</span> -- denotes a function. When the function is called, the initial value of the variable x is the argument if there is just one, or else is the sequence of arguments.<br><span class="tt">(x) -> e</span> -- denotes a function of one argument. When the function is applied to an expression w three things may happen: <ul> <li>if w is not a sequence, then the initial value of x is w;</li> <li>if w is a sequence of length one, then the initial value of x is the unique element of w; or</li> <li>if w is a sequence of length other than one, then it is an error.</li> </ul> <br><span class="tt">(x,y) -> e</span> -- denotes a function of two arguments. <p></p> Similarly for more arguments. <p></p> These operations create what is usually called a <i>closure</i>, which signifies that the function remembers the values of local variables in effect at the time of its creation, can change those values, and share the changes with other functions created at the same time. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : f = x -> 2*x+1 o1 = f o1 : FunctionClosure</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : f 100 o2 = 201</code></pre> </td> </tr> </table> The class of all functions is <a title="the class of all functions" href="___Function.html">Function</a>. </div> <div> <h3>Menu</h3> <ul> <li><span><a title="get the optional arguments and default values of a function or method" href="_options_lp__Function_rp.html">options(Function)</a> -- get the optional arguments and default values of a function or method</span></li> </ul> </div> <div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="make a function" href="_-_gt.html">-></a> is <span>a <a title="the class of all keywords" href="___Keyword.html">keyword</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Macaulay2Doc/ov_methods.m2:318:0</span>.</p> </div> </div> </div> </body> </html>
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