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<!DOCTYPE html> <html lang="en"> <head> <title>pairs -- list the pairs in a hash table, dictionary, or basic list</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="_hash_sptables.html">hash tables</a> » <a title="list the pairs in a hash table, dictionary, or basic list" href="_pairs.html">pairs</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="_copy.html">next</a> | <a href="_values.html">previous</a> | <a href="_copy.html">forward</a> | <a href="_values.html">backward</a> | <a href="_hash_sptables.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>pairs -- list the pairs in a hash table, dictionary, or basic list</h1> <div> <h2>Description</h2> <div> <h2>Synopsis</h2> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">pairs x</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">x</span>, <span>a <a title="the class of all hash tables" href="___Hash__Table.html">hash table</a></span>, <span>a <a title="the class of all dictionaries" href="___Dictionary.html">dictionary</a></span>, or <span>a <a title="the class of all basic lists" href="___Basic__List.html">basic list</a></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="___List.html">list</a></span>, of all pairs <code>(k, x#k)</code>; </span></li> </ul> </li> </ul> </div> <div> <h2>Synopsis</h2> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">pairs x</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">x</span>, <span>a <a title="the class of all things" href="___Thing.html">thing</a></span>, an instance of a class with an <a title="get an iterator" href="_iterator.html">iterator</a> method installed; </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an <a title="class for iterators" href="___Iterator.html">iterator</a></span>, </span></li> </ul> </li> </ul> </div> <div> <p>If <span class="tt">x</span> is a hash table or dictionary, the pairs consist of each key along with its associated value.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : x = new HashTable from {a => 1, b => 2, c => 3} o1 = HashTable{a => 1} b => 2 c => 3 o1 : HashTable</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : pairs x o2 = {(c, 3), (a, 1), (b, 2)} o2 : List</code></pre> </td> </tr> </table> <div> <p>A dictionary is a special hash table whose keys are strings, and whose values are the corresponding symbols.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i3 : d = new Dictionary o3 = d o3 : GlobalDictionary</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : getGlobalSymbol (d, "foo") o4 = foo o4 : Symbol</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : getGlobalSymbol (d, "bar") o5 = bar o5 : Symbol</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : pairs d o6 = {(bar, bar), (foo, foo)} o6 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : first oo o7 = (bar, bar) o7 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : class \ oo o8 = (String, Symbol) o8 : Sequence</code></pre> </td> </tr> </table> <div> <p>If <span class="tt">x</span> is a basic list, the pairs consist of each index along with the element at that index in the list.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i9 : L = {3, 5, 7};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i10 : pairs L o10 = {(0, 3), (1, 5), (2, 7)} o10 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i11 : pairs {apple, banana, carrot} o11 = {(0, apple), (1, banana), (2, carrot)} o11 : List</code></pre> </td> </tr> </table> <div> <p>If <code>x</code> belongs to any other class, then <a title="get an iterator" href="_iterator.html">iterator</a> is called on it, and if successful, an <a title="class for iterators" href="___Iterator.html">Iterator</a> object is returned.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i12 : pairs "foo" o12 = iterator "foo" o12 : Iterator</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i13 : toList oo o13 = {(0, f), (1, o), (2, o)} o13 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i14 : i = pairs Iterator(() -> 5) o14 = i o14 : Iterator</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i15 : next i o15 = (0, 5) o15 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i16 : next i o16 = (1, 5) o16 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i17 : next i o17 = (2, 5) o17 : Sequence</code></pre> </td> </tr> </table> </div> <div> <h2>Caveat</h2> <div> <p>As the first example illustrates, pairs are not necessarily listed in any particular order.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a href="_hash_sptables.html">hash tables</a></span></li> <li><span><a title="apply a function to each pair in a hash table" href="_apply__Pairs.html">applyPairs</a> -- apply a function to each pair in a hash table</span></li> <li><span><a title="keys used in a hash table, dictionary, or database" href="_keys.html">keys</a> -- keys used in a hash table, dictionary, or database</span></li> <li><span><a title="apply a function to the pairs in a hash table" href="_scan__Pairs.html">scanPairs</a> -- apply a function to the pairs in a hash table</span></li> <li><span><a title="values in a hash table" href="_values.html">values</a> -- values in a hash table</span></li> <li><span><a title="length or access to elements" href="__sh.html">#</a> -- length or access to elements</span></li> <li><span><a title="check existence of value in a list, hash table, database, or string" href="__sh_qu.html">#?</a> -- check existence of value in a list, hash table, database, or string</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">pairs</span>:</h2> <ul> <li><kbd>pairs(BasicList)</kbd></li> <li><kbd>pairs(Dictionary)</kbd></li> <li><kbd>pairs(HashTable)</kbd></li> <li><kbd>pairs(Thing)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="list the pairs in a hash table, dictionary, or basic list" href="_pairs.html">pairs</a> is <span>a <a title="the class of all compiled functions" href="___Compiled__Function.html">compiled function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Macaulay2Doc/ov_hashtables.m2:482:0</span>.</p> </div> </div> </div> </body> </html>