<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>4. Built-in Types — Python v3.2.2 documentation</title>
<link rel="stylesheet" href="../_static/default.css" type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: '../',
VERSION: '3.2.2',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true
};
</script>
<script type="text/javascript" src="../_static/jquery.js"></script>
<script type="text/javascript" src="../_static/underscore.js"></script>
<script type="text/javascript" src="../_static/doctools.js"></script>
<script type="text/javascript" src="../_static/sidebar.js"></script>
<link rel="search" type="application/opensearchdescription+xml"
title="Search within Python v3.2.2 documentation"
href="../_static/opensearch.xml"/>
<link rel="author" title="About these documents" href="../about.html" />
<link rel="copyright" title="Copyright" href="../copyright.html" />
<link rel="top" title="Python v3.2.2 documentation" href="../index.html" />
<link rel="up" title="The Python Standard Library" href="index.html" />
<link rel="next" title="5. Built-in Exceptions" href="exceptions.html" />
<link rel="prev" title="3. Built-in Constants" href="constants.html" />
<link rel="shortcut icon" type="image/png" href="../_static/py.png" />
</head>
<body>
<div class="related">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="../py-modindex.html" title="Python Module Index"
>modules</a> |</li>
<li class="right" >
<a href="exceptions.html" title="5. Built-in Exceptions"
accesskey="N">next</a> |</li>
<li class="right" >
<a href="constants.html" title="3. Built-in Constants"
accesskey="P">previous</a> |</li>
<li><img src="../_static/py.png" alt=""
style="vertical-align: middle; margin-top: -1px"/></li>
<li><a href="../index.html">Python v3.2.2 documentation</a> »</li>
<li><a href="index.html" accesskey="U">The Python Standard Library</a> »</li>
</ul>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body">
<div class="section" id="built-in-types">
<span id="bltin-types"></span><h1>4. Built-in Types<a class="headerlink" href="#built-in-types" title="Permalink to this headline">¶</a></h1>
<p>The following sections describe the standard types that are built into the
interpreter.</p>
<p id="index-0">The principal built-in types are numerics, sequences, mappings, classes,
instances and exceptions.</p>
<p>Some operations are supported by several object types; in particular,
practically all objects can be compared, tested for truth value, and converted
to a string (with the <a class="reference internal" href="functions.html#repr" title="repr"><tt class="xref py py-func docutils literal"><span class="pre">repr()</span></tt></a> function or the slightly different
<a class="reference internal" href="functions.html#str" title="str"><tt class="xref py py-func docutils literal"><span class="pre">str()</span></tt></a> function). The latter function is implicitly used when an object is
written by the <a class="reference internal" href="functions.html#print" title="print"><tt class="xref py py-func docutils literal"><span class="pre">print()</span></tt></a> function.</p>
<div class="section" id="truth-value-testing">
<span id="truth"></span><h2>4.1. Truth Value Testing<a class="headerlink" href="#truth-value-testing" title="Permalink to this headline">¶</a></h2>
<p id="index-1">Any object can be tested for truth value, for use in an <a class="reference internal" href="../reference/compound_stmts.html#if"><tt class="xref std std-keyword docutils literal"><span class="pre">if</span></tt></a> or
<a class="reference internal" href="../reference/compound_stmts.html#while"><tt class="xref std std-keyword docutils literal"><span class="pre">while</span></tt></a> condition or as operand of the Boolean operations below. The
following values are considered false:</p>
<blockquote>
<div></div></blockquote>
<ul id="index-2">
<li><p class="first"><tt class="xref docutils literal"><span class="pre">None</span></tt></p>
</li>
<li id="index-3"><p class="first"><tt class="xref docutils literal"><span class="pre">False</span></tt></p>
</li>
<li><p class="first">zero of any numeric type, for example, <tt class="docutils literal"><span class="pre">0</span></tt>, <tt class="docutils literal"><span class="pre">0.0</span></tt>, <tt class="docutils literal"><span class="pre">0j</span></tt>.</p>
</li>
<li><p class="first">any empty sequence, for example, <tt class="docutils literal"><span class="pre">''</span></tt>, <tt class="docutils literal"><span class="pre">()</span></tt>, <tt class="docutils literal"><span class="pre">[]</span></tt>.</p>
</li>
<li><p class="first">any empty mapping, for example, <tt class="docutils literal"><span class="pre">{}</span></tt>.</p>
</li>
<li><p class="first">instances of user-defined classes, if the class defines a <a class="reference internal" href="../reference/datamodel.html#object.__bool__" title="object.__bool__"><tt class="xref py py-meth docutils literal"><span class="pre">__bool__()</span></tt></a> or
<a class="reference internal" href="../reference/datamodel.html#object.__len__" title="object.__len__"><tt class="xref py py-meth docutils literal"><span class="pre">__len__()</span></tt></a> method, when that method returns the integer zero or
<a class="reference internal" href="functions.html#bool" title="bool"><tt class="xref py py-class docutils literal"><span class="pre">bool</span></tt></a> value <tt class="xref docutils literal"><span class="pre">False</span></tt>. <a class="footnote-reference" href="#id11" id="id1">[1]</a></p>
</li>
</ul>
<p id="index-4">All other values are considered true — so objects of many types are always
true.</p>
<p id="index-5">Operations and built-in functions that have a Boolean result always return <tt class="docutils literal"><span class="pre">0</span></tt>
or <tt class="xref docutils literal"><span class="pre">False</span></tt> for false and <tt class="docutils literal"><span class="pre">1</span></tt> or <tt class="xref docutils literal"><span class="pre">True</span></tt> for true, unless otherwise stated.
(Important exception: the Boolean operations <tt class="docutils literal"><span class="pre">or</span></tt> and <tt class="docutils literal"><span class="pre">and</span></tt> always return
one of their operands.)</p>
</div>
<div class="section" id="boolean-operations-and-or-not">
<span id="boolean"></span><h2>4.2. Boolean Operations — <a class="reference internal" href="../reference/expressions.html#and"><tt class="xref std std-keyword docutils literal"><span class="pre">and</span></tt></a>, <a class="reference internal" href="../reference/expressions.html#or"><tt class="xref std std-keyword docutils literal"><span class="pre">or</span></tt></a>, <a class="reference internal" href="../reference/expressions.html#not"><tt class="xref std std-keyword docutils literal"><span class="pre">not</span></tt></a><a class="headerlink" href="#boolean-operations-and-or-not" title="Permalink to this headline">¶</a></h2>
<p id="index-6">These are the Boolean operations, ordered by ascending priority:</p>
<table border="1" class="docutils">
<colgroup>
<col width="25%" />
<col width="62%" />
<col width="13%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Operation</th>
<th class="head">Result</th>
<th class="head">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">or</span> <span class="pre">y</span></tt></td>
<td>if <em>x</em> is false, then <em>y</em>, else
<em>x</em></td>
<td>(1)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">and</span> <span class="pre">y</span></tt></td>
<td>if <em>x</em> is false, then <em>x</em>, else
<em>y</em></td>
<td>(2)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">not</span> <span class="pre">x</span></tt></td>
<td>if <em>x</em> is false, then <tt class="xref docutils literal"><span class="pre">True</span></tt>,
else <tt class="xref docutils literal"><span class="pre">False</span></tt></td>
<td>(3)</td>
</tr>
</tbody>
</table>
<p id="index-7">Notes:</p>
<ol class="arabic simple">
<li>This is a short-circuit operator, so it only evaluates the second
argument if the first one is <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const xref docutils literal"><span class="pre">False</span></tt></a>.</li>
<li>This is a short-circuit operator, so it only evaluates the second
argument if the first one is <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const xref docutils literal"><span class="pre">True</span></tt></a>.</li>
<li><tt class="docutils literal"><span class="pre">not</span></tt> has a lower priority than non-Boolean operators, so <tt class="docutils literal"><span class="pre">not</span> <span class="pre">a</span> <span class="pre">==</span> <span class="pre">b</span></tt> is
interpreted as <tt class="docutils literal"><span class="pre">not</span> <span class="pre">(a</span> <span class="pre">==</span> <span class="pre">b)</span></tt>, and <tt class="docutils literal"><span class="pre">a</span> <span class="pre">==</span> <span class="pre">not</span> <span class="pre">b</span></tt> is a syntax error.</li>
</ol>
</div>
<div class="section" id="comparisons">
<span id="stdcomparisons"></span><h2>4.3. Comparisons<a class="headerlink" href="#comparisons" title="Permalink to this headline">¶</a></h2>
<p id="index-8">There are eight comparison operations in Python. They all have the same
priority (which is higher than that of the Boolean operations). Comparisons can
be chained arbitrarily; for example, <tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span> <span class="pre"><=</span> <span class="pre">z</span></tt> is equivalent to <tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span> <span class="pre">and</span>
<span class="pre">y</span> <span class="pre"><=</span> <span class="pre">z</span></tt>, except that <em>y</em> is evaluated only once (but in both cases <em>z</em> is not
evaluated at all when <tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span></tt> is found to be false).</p>
<p>This table summarizes the comparison operations:</p>
<table border="1" class="docutils">
<colgroup>
<col width="32%" />
<col width="68%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Operation</th>
<th class="head">Meaning</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre"><</span></tt></td>
<td>strictly less than</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre"><=</span></tt></td>
<td>less than or equal</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">></span></tt></td>
<td>strictly greater than</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">>=</span></tt></td>
<td>greater than or equal</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">==</span></tt></td>
<td>equal</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">!=</span></tt></td>
<td>not equal</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">is</span></tt></td>
<td>object identity</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">is</span> <span class="pre">not</span></tt></td>
<td>negated object identity</td>
</tr>
</tbody>
</table>
<p id="index-9">Objects of different types, except different numeric types, never compare equal.
Furthermore, some types (for example, function objects) support only a degenerate
notion of comparison where any two objects of that type are unequal. The <tt class="docutils literal"><span class="pre"><</span></tt>,
<tt class="docutils literal"><span class="pre"><=</span></tt>, <tt class="docutils literal"><span class="pre">></span></tt> and <tt class="docutils literal"><span class="pre">>=</span></tt> operators will raise a <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> exception when
comparing a complex number with another built-in numeric type, when the objects
are of different types that cannot be compared, or in other cases where there is
no defined ordering.</p>
<p id="index-10">Non-identical instances of a class normally compare as non-equal unless the
class defines the <a class="reference internal" href="../reference/datamodel.html#object.__eq__" title="object.__eq__"><tt class="xref py py-meth docutils literal"><span class="pre">__eq__()</span></tt></a> method.</p>
<p>Instances of a class cannot be ordered with respect to other instances of the
same class, or other types of object, unless the class defines enough of the
methods <a class="reference internal" href="../reference/datamodel.html#object.__lt__" title="object.__lt__"><tt class="xref py py-meth docutils literal"><span class="pre">__lt__()</span></tt></a>, <a class="reference internal" href="../reference/datamodel.html#object.__le__" title="object.__le__"><tt class="xref py py-meth docutils literal"><span class="pre">__le__()</span></tt></a>, <a class="reference internal" href="../reference/datamodel.html#object.__gt__" title="object.__gt__"><tt class="xref py py-meth docutils literal"><span class="pre">__gt__()</span></tt></a>, and <a class="reference internal" href="../reference/datamodel.html#object.__ge__" title="object.__ge__"><tt class="xref py py-meth docutils literal"><span class="pre">__ge__()</span></tt></a> (in
general, <a class="reference internal" href="../reference/datamodel.html#object.__lt__" title="object.__lt__"><tt class="xref py py-meth docutils literal"><span class="pre">__lt__()</span></tt></a> and <a class="reference internal" href="../reference/datamodel.html#object.__eq__" title="object.__eq__"><tt class="xref py py-meth docutils literal"><span class="pre">__eq__()</span></tt></a> are sufficient, if you want the
conventional meanings of the comparison operators).</p>
<p>The behavior of the <a class="reference internal" href="../reference/expressions.html#is"><tt class="xref std std-keyword docutils literal"><span class="pre">is</span></tt></a> and <a class="reference internal" href="../reference/expressions.html#is-not"><tt class="xref std std-keyword docutils literal"><span class="pre">is</span> <span class="pre">not</span></tt></a> operators cannot be
customized; also they can be applied to any two objects and never raise an
exception.</p>
<p id="index-11">Two more operations with the same syntactic priority, <a class="reference internal" href="../reference/expressions.html#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a> and
<a class="reference internal" href="../reference/expressions.html#not-in"><tt class="xref std std-keyword docutils literal"><span class="pre">not</span> <span class="pre">in</span></tt></a>, are supported only by sequence types (below).</p>
</div>
<div class="section" id="numeric-types-int-float-complex">
<span id="typesnumeric"></span><h2>4.4. Numeric Types — <a class="reference internal" href="functions.html#int" title="int"><tt class="xref py py-class docutils literal"><span class="pre">int</span></tt></a>, <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal"><span class="pre">float</span></tt></a>, <a class="reference internal" href="functions.html#complex" title="complex"><tt class="xref py py-class docutils literal"><span class="pre">complex</span></tt></a><a class="headerlink" href="#numeric-types-int-float-complex" title="Permalink to this headline">¶</a></h2>
<p id="index-12">There are three distinct numeric types: <em class="dfn">integers</em>, <em class="dfn">floating
point numbers</em>, and <em class="dfn">complex numbers</em>. In addition, Booleans are a
subtype of integers. Integers have unlimited precision. Floating point
numbers are usually implemented using <tt class="xref c c-type docutils literal"><span class="pre">double</span></tt> in C; information
about the precision and internal representation of floating point
numbers for the machine on which your program is running is available
in <a class="reference internal" href="sys.html#sys.float_info" title="sys.float_info"><tt class="xref py py-data docutils literal"><span class="pre">sys.float_info</span></tt></a>. Complex numbers have a real and imaginary
part, which are each a floating point number. To extract these parts
from a complex number <em>z</em>, use <tt class="docutils literal"><span class="pre">z.real</span></tt> and <tt class="docutils literal"><span class="pre">z.imag</span></tt>. (The standard
library includes additional numeric types, <a class="reference internal" href="fractions.html#module-fractions" title="fractions: Rational numbers."><tt class="xref py py-mod docutils literal"><span class="pre">fractions</span></tt></a> that hold
rationals, and <a class="reference internal" href="decimal.html#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic Specification."><tt class="xref py py-mod docutils literal"><span class="pre">decimal</span></tt></a> that hold floating-point numbers with
user-definable precision.)</p>
<p id="index-13">Numbers are created by numeric literals or as the result of built-in functions
and operators. Unadorned integer literals (including hex, octal and binary
numbers) yield integers. Numeric literals containing a decimal point or an
exponent sign yield floating point numbers. Appending <tt class="docutils literal"><span class="pre">'j'</span></tt> or <tt class="docutils literal"><span class="pre">'J'</span></tt> to a
numeric literal yields an imaginary number (a complex number with a zero real
part) which you can add to an integer or float to get a complex number with real
and imaginary parts.</p>
<p id="index-14">Python fully supports mixed arithmetic: when a binary arithmetic operator has
operands of different numeric types, the operand with the “narrower” type is
widened to that of the other, where integer is narrower than floating point,
which is narrower than complex. Comparisons between numbers of mixed type use
the same rule. <a class="footnote-reference" href="#id12" id="id2">[2]</a> The constructors <a class="reference internal" href="functions.html#int" title="int"><tt class="xref py py-func docutils literal"><span class="pre">int()</span></tt></a>, <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-func docutils literal"><span class="pre">float()</span></tt></a>, and
<a class="reference internal" href="functions.html#complex" title="complex"><tt class="xref py py-func docutils literal"><span class="pre">complex()</span></tt></a> can be used to produce numbers of a specific type.</p>
<p>All numeric types (except complex) support the following operations, sorted by
ascending priority (operations in the same box have the same priority; all
numeric operations have a higher priority than comparison operations):</p>
<table border="1" class="docutils">
<colgroup>
<col width="25%" />
<col width="40%" />
<col width="11%" />
<col width="24%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Operation</th>
<th class="head">Result</th>
<th class="head">Notes</th>
<th class="head">Full documentation</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">+</span> <span class="pre">y</span></tt></td>
<td>sum of <em>x</em> and <em>y</em></td>
<td> </td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">-</span> <span class="pre">y</span></tt></td>
<td>difference of <em>x</em> and <em>y</em></td>
<td> </td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">*</span> <span class="pre">y</span></tt></td>
<td>product of <em>x</em> and <em>y</em></td>
<td> </td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">/</span> <span class="pre">y</span></tt></td>
<td>quotient of <em>x</em> and <em>y</em></td>
<td> </td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">//</span> <span class="pre">y</span></tt></td>
<td>floored quotient of <em>x</em> and
<em>y</em></td>
<td>(1)</td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">%</span> <span class="pre">y</span></tt></td>
<td>remainder of <tt class="docutils literal"><span class="pre">x</span> <span class="pre">/</span> <span class="pre">y</span></tt></td>
<td>(2)</td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">-x</span></tt></td>
<td><em>x</em> negated</td>
<td> </td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">+x</span></tt></td>
<td><em>x</em> unchanged</td>
<td> </td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">abs(x)</span></tt></td>
<td>absolute value or magnitude of
<em>x</em></td>
<td> </td>
<td><a class="reference internal" href="functions.html#abs" title="abs"><tt class="xref py py-func docutils literal"><span class="pre">abs()</span></tt></a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">int(x)</span></tt></td>
<td><em>x</em> converted to integer</td>
<td>(3)(6)</td>
<td><a class="reference internal" href="functions.html#int" title="int"><tt class="xref py py-func docutils literal"><span class="pre">int()</span></tt></a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">float(x)</span></tt></td>
<td><em>x</em> converted to floating point</td>
<td>(4)(6)</td>
<td><a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-func docutils literal"><span class="pre">float()</span></tt></a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">complex(re,</span> <span class="pre">im)</span></tt></td>
<td>a complex number with real part
<em>re</em>, imaginary part <em>im</em>.
<em>im</em> defaults to zero.</td>
<td>(6)</td>
<td><a class="reference internal" href="functions.html#complex" title="complex"><tt class="xref py py-func docutils literal"><span class="pre">complex()</span></tt></a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">c.conjugate()</span></tt></td>
<td>conjugate of the complex number
<em>c</em></td>
<td> </td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">divmod(x,</span> <span class="pre">y)</span></tt></td>
<td>the pair <tt class="docutils literal"><span class="pre">(x</span> <span class="pre">//</span> <span class="pre">y,</span> <span class="pre">x</span> <span class="pre">%</span> <span class="pre">y)</span></tt></td>
<td>(2)</td>
<td><a class="reference internal" href="functions.html#divmod" title="divmod"><tt class="xref py py-func docutils literal"><span class="pre">divmod()</span></tt></a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">pow(x,</span> <span class="pre">y)</span></tt></td>
<td><em>x</em> to the power <em>y</em></td>
<td>(5)</td>
<td><a class="reference internal" href="functions.html#pow" title="pow"><tt class="xref py py-func docutils literal"><span class="pre">pow()</span></tt></a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">**</span> <span class="pre">y</span></tt></td>
<td><em>x</em> to the power <em>y</em></td>
<td>(5)</td>
<td> </td>
</tr>
</tbody>
</table>
<p id="index-15">Notes:</p>
<ol class="arabic">
<li><p class="first">Also referred to as integer division. The resultant value is a whole
integer, though the result’s type is not necessarily int. The result is
always rounded towards minus infinity: <tt class="docutils literal"><span class="pre">1//2</span></tt> is <tt class="docutils literal"><span class="pre">0</span></tt>, <tt class="docutils literal"><span class="pre">(-1)//2</span></tt> is
<tt class="docutils literal"><span class="pre">-1</span></tt>, <tt class="docutils literal"><span class="pre">1//(-2)</span></tt> is <tt class="docutils literal"><span class="pre">-1</span></tt>, and <tt class="docutils literal"><span class="pre">(-1)//(-2)</span></tt> is <tt class="docutils literal"><span class="pre">0</span></tt>.</p>
</li>
<li><p class="first">Not for complex numbers. Instead convert to floats using <a class="reference internal" href="functions.html#abs" title="abs"><tt class="xref py py-func docutils literal"><span class="pre">abs()</span></tt></a> if
appropriate.</p>
</li>
<li><p id="index-16">Conversion from floating point to integer may round or truncate
as in C; see functions <tt class="xref py py-func docutils literal"><span class="pre">floor()</span></tt> and <tt class="xref py py-func docutils literal"><span class="pre">ceil()</span></tt> in the <a class="reference internal" href="math.html#module-math" title="math: Mathematical functions (sin() etc.)."><tt class="xref py py-mod docutils literal"><span class="pre">math</span></tt></a> module
for well-defined conversions.</p>
</li>
<li><p class="first">float also accepts the strings “nan” and “inf” with an optional prefix “+”
or “-” for Not a Number (NaN) and positive or negative infinity.</p>
</li>
<li><p class="first">Python defines <tt class="docutils literal"><span class="pre">pow(0,</span> <span class="pre">0)</span></tt> and <tt class="docutils literal"><span class="pre">0</span> <span class="pre">**</span> <span class="pre">0</span></tt> to be <tt class="docutils literal"><span class="pre">1</span></tt>, as is common for
programming languages.</p>
</li>
<li><p class="first">The numeric literals accepted include the digits <tt class="docutils literal"><span class="pre">0</span></tt> to <tt class="docutils literal"><span class="pre">9</span></tt> or any
Unicode equivalent (code points with the <tt class="docutils literal"><span class="pre">Nd</span></tt> property).</p>
<p>See <a class="reference external" href="http://www.unicode.org/Public/6.0.0/ucd/extracted/DerivedNumericType.txt">http://www.unicode.org/Public/6.0.0/ucd/extracted/DerivedNumericType.txt</a>
for a complete list of code points with the <tt class="docutils literal"><span class="pre">Nd</span></tt> property.</p>
</li>
</ol>
<p>All <a class="reference internal" href="numbers.html#numbers.Real" title="numbers.Real"><tt class="xref py py-class docutils literal"><span class="pre">numbers.Real</span></tt></a> types (<a class="reference internal" href="functions.html#int" title="int"><tt class="xref py py-class docutils literal"><span class="pre">int</span></tt></a> and <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal"><span class="pre">float</span></tt></a>) also include
the following operations:</p>
<table border="1" class="docutils">
<colgroup>
<col width="31%" />
<col width="56%" />
<col width="13%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Operation</th>
<th class="head">Result</th>
<th class="head">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">math.trunc(x)</span></tt></td>
<td><em>x</em> truncated to Integral</td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">round(x[,</span> <span class="pre">n])</span></tt></td>
<td><em>x</em> rounded to n digits,
rounding half to even. If n is
omitted, it defaults to 0.</td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">math.floor(x)</span></tt></td>
<td>the greatest integral float <= <em>x</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">math.ceil(x)</span></tt></td>
<td>the least integral float >= <em>x</em></td>
<td> </td>
</tr>
</tbody>
</table>
<p>For additional numeric operations see the <a class="reference internal" href="math.html#module-math" title="math: Mathematical functions (sin() etc.)."><tt class="xref py py-mod docutils literal"><span class="pre">math</span></tt></a> and <a class="reference internal" href="cmath.html#module-cmath" title="cmath: Mathematical functions for complex numbers."><tt class="xref py py-mod docutils literal"><span class="pre">cmath</span></tt></a>
modules.</p>
<div class="section" id="bit-string-operations-on-integer-types">
<span id="bitstring-ops"></span><h3>4.4.1. Bit-string Operations on Integer Types<a class="headerlink" href="#bit-string-operations-on-integer-types" title="Permalink to this headline">¶</a></h3>
<p id="index-17">Integers support additional operations that make sense only for bit-strings.
Negative numbers are treated as their 2’s complement value (this assumes a
sufficiently large number of bits that no overflow occurs during the operation).</p>
<p>The priorities of the binary bitwise operations are all lower than the numeric
operations and higher than the comparisons; the unary operation <tt class="docutils literal"><span class="pre">~</span></tt> has the
same priority as the other unary numeric operations (<tt class="docutils literal"><span class="pre">+</span></tt> and <tt class="docutils literal"><span class="pre">-</span></tt>).</p>
<p>This table lists the bit-string operations sorted in ascending priority
(operations in the same box have the same priority):</p>
<table border="1" class="docutils">
<colgroup>
<col width="22%" />
<col width="59%" />
<col width="19%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Operation</th>
<th class="head">Result</th>
<th class="head">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">|</span> <span class="pre">y</span></tt></td>
<td>bitwise <em class="dfn">or</em> of <em>x</em> and
<em>y</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">^</span> <span class="pre">y</span></tt></td>
<td>bitwise <em class="dfn">exclusive or</em> of
<em>x</em> and <em>y</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&</span> <span class="pre">y</span></tt></td>
<td>bitwise <em class="dfn">and</em> of <em>x</em> and
<em>y</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre"><<</span> <span class="pre">n</span></tt></td>
<td><em>x</em> shifted left by <em>n</em> bits</td>
<td>(1)(2)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">>></span> <span class="pre">n</span></tt></td>
<td><em>x</em> shifted right by <em>n</em> bits</td>
<td>(1)(3)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">~x</span></tt></td>
<td>the bits of <em>x</em> inverted</td>
<td> </td>
</tr>
</tbody>
</table>
<p>Notes:</p>
<ol class="arabic simple">
<li>Negative shift counts are illegal and cause a <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><tt class="xref py py-exc docutils literal"><span class="pre">ValueError</span></tt></a> to be raised.</li>
<li>A left shift by <em>n</em> bits is equivalent to multiplication by <tt class="docutils literal"><span class="pre">pow(2,</span> <span class="pre">n)</span></tt>
without overflow check.</li>
<li>A right shift by <em>n</em> bits is equivalent to division by <tt class="docutils literal"><span class="pre">pow(2,</span> <span class="pre">n)</span></tt> without
overflow check.</li>
</ol>
</div>
<div class="section" id="additional-methods-on-integer-types">
<h3>4.4.2. Additional Methods on Integer Types<a class="headerlink" href="#additional-methods-on-integer-types" title="Permalink to this headline">¶</a></h3>
<p>The int type implements the <a class="reference internal" href="numbers.html#numbers.Integral" title="numbers.Integral"><tt class="xref py py-class docutils literal"><span class="pre">numbers.Integral</span></tt></a> <a class="reference internal" href="../glossary.html#term-abstract-base-class"><em class="xref std std-term">abstract base
class</em></a>. In addition, it provides one more method:</p>
<dl class="method">
<dt id="int.bit_length">
<tt class="descclassname">int.</tt><tt class="descname">bit_length</tt><big>(</big><big>)</big><a class="headerlink" href="#int.bit_length" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the number of bits necessary to represent an integer in binary,
excluding the sign and leading zeros:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">n</span> <span class="o">=</span> <span class="o">-</span><span class="mi">37</span>
<span class="gp">>>> </span><span class="nb">bin</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<span class="go">'-0b100101'</span>
<span class="gp">>>> </span><span class="n">n</span><span class="o">.</span><span class="n">bit_length</span><span class="p">()</span>
<span class="go">6</span>
</pre></div>
</div>
<p>More precisely, if <tt class="docutils literal"><span class="pre">x</span></tt> is nonzero, then <tt class="docutils literal"><span class="pre">x.bit_length()</span></tt> is the
unique positive integer <tt class="docutils literal"><span class="pre">k</span></tt> such that <tt class="docutils literal"><span class="pre">2**(k-1)</span> <span class="pre"><=</span> <span class="pre">abs(x)</span> <span class="pre"><</span> <span class="pre">2**k</span></tt>.
Equivalently, when <tt class="docutils literal"><span class="pre">abs(x)</span></tt> is small enough to have a correctly
rounded logarithm, then <tt class="docutils literal"><span class="pre">k</span> <span class="pre">=</span> <span class="pre">1</span> <span class="pre">+</span> <span class="pre">int(log(abs(x),</span> <span class="pre">2))</span></tt>.
If <tt class="docutils literal"><span class="pre">x</span></tt> is zero, then <tt class="docutils literal"><span class="pre">x.bit_length()</span></tt> returns <tt class="docutils literal"><span class="pre">0</span></tt>.</p>
<p>Equivalent to:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="k">def</span> <span class="nf">bit_length</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">bin</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="c"># binary representation: bin(-37) --> '-0b100101'</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">s</span><span class="o">.</span><span class="n">lstrip</span><span class="p">(</span><span class="s">'-0b'</span><span class="p">)</span> <span class="c"># remove leading zeros and minus sign</span>
<span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="c"># len('100101') --> 6</span>
</pre></div>
</div>
<p class="versionadded">
<span class="versionmodified">New in version 3.1.</span></p>
</dd></dl>
<dl class="method">
<dt id="int.to_bytes">
<tt class="descclassname">int.</tt><tt class="descname">to_bytes</tt><big>(</big><em>length</em>, <em>byteorder</em>, <em>*</em>, <em>signed=False</em><big>)</big><a class="headerlink" href="#int.to_bytes" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an array of bytes representing an integer.</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="p">(</span><span class="mi">1024</span><span class="p">)</span><span class="o">.</span><span class="n">to_bytes</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'big'</span><span class="p">)</span>
<span class="go">b'\x04\x00'</span>
<span class="gp">>>> </span><span class="p">(</span><span class="mi">1024</span><span class="p">)</span><span class="o">.</span><span class="n">to_bytes</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'big'</span><span class="p">)</span>
<span class="go">b'\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00'</span>
<span class="gp">>>> </span><span class="p">(</span><span class="o">-</span><span class="mi">1024</span><span class="p">)</span><span class="o">.</span><span class="n">to_bytes</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'big'</span><span class="p">,</span> <span class="n">signed</span><span class="o">=</span><span class="k">True</span><span class="p">)</span>
<span class="go">b'\xff\xff\xff\xff\xff\xff\xff\xff\xfc\x00'</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">to_bytes</span><span class="p">((</span><span class="n">x</span><span class="o">.</span><span class="n">bit_length</span><span class="p">()</span> <span class="o">//</span> <span class="mi">8</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'little'</span><span class="p">)</span>
<span class="go">b'\xe8\x03'</span>
</pre></div>
</div>
<p>The integer is represented using <em>length</em> bytes. An <a class="reference internal" href="exceptions.html#OverflowError" title="OverflowError"><tt class="xref py py-exc docutils literal"><span class="pre">OverflowError</span></tt></a>
is raised if the integer is not representable with the given number of
bytes.</p>
<p>The <em>byteorder</em> argument determines the byte order used to represent the
integer. If <em>byteorder</em> is <tt class="docutils literal"><span class="pre">"big"</span></tt>, the most significant byte is at the
beginning of the byte array. If <em>byteorder</em> is <tt class="docutils literal"><span class="pre">"little"</span></tt>, the most
significant byte is at the end of the byte array. To request the native
byte order of the host system, use <a class="reference internal" href="sys.html#sys.byteorder" title="sys.byteorder"><tt class="xref py py-data docutils literal"><span class="pre">sys.byteorder</span></tt></a> as the byte order
value.</p>
<p>The <em>signed</em> argument determines whether two’s complement is used to
represent the integer. If <em>signed</em> is <tt class="xref docutils literal"><span class="pre">False</span></tt> and a negative integer is
given, an <a class="reference internal" href="exceptions.html#OverflowError" title="OverflowError"><tt class="xref py py-exc docutils literal"><span class="pre">OverflowError</span></tt></a> is raised. The default value for <em>signed</em>
is <tt class="xref docutils literal"><span class="pre">False</span></tt>.</p>
<p class="versionadded">
<span class="versionmodified">New in version 3.2.</span></p>
</dd></dl>
<dl class="classmethod">
<dt id="int.from_bytes">
<em class="property">classmethod </em><tt class="descclassname">int.</tt><tt class="descname">from_bytes</tt><big>(</big><em>bytes</em>, <em>byteorder</em>, <em>*</em>, <em>signed=False</em><big>)</big><a class="headerlink" href="#int.from_bytes" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the integer represented by the given array of bytes.</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">int</span><span class="o">.</span><span class="n">from_bytes</span><span class="p">(</span><span class="n">b</span><span class="s">'</span><span class="se">\x00\x10</span><span class="s">'</span><span class="p">,</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'big'</span><span class="p">)</span>
<span class="go">16</span>
<span class="gp">>>> </span><span class="nb">int</span><span class="o">.</span><span class="n">from_bytes</span><span class="p">(</span><span class="n">b</span><span class="s">'</span><span class="se">\x00\x10</span><span class="s">'</span><span class="p">,</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'little'</span><span class="p">)</span>
<span class="go">4096</span>
<span class="gp">>>> </span><span class="nb">int</span><span class="o">.</span><span class="n">from_bytes</span><span class="p">(</span><span class="n">b</span><span class="s">'</span><span class="se">\xfc\x00</span><span class="s">'</span><span class="p">,</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'big'</span><span class="p">,</span> <span class="n">signed</span><span class="o">=</span><span class="k">True</span><span class="p">)</span>
<span class="go">-1024</span>
<span class="gp">>>> </span><span class="nb">int</span><span class="o">.</span><span class="n">from_bytes</span><span class="p">(</span><span class="n">b</span><span class="s">'</span><span class="se">\xfc\x00</span><span class="s">'</span><span class="p">,</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'big'</span><span class="p">,</span> <span class="n">signed</span><span class="o">=</span><span class="k">False</span><span class="p">)</span>
<span class="go">64512</span>
<span class="gp">>>> </span><span class="nb">int</span><span class="o">.</span><span class="n">from_bytes</span><span class="p">([</span><span class="mi">255</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">byteorder</span><span class="o">=</span><span class="s">'big'</span><span class="p">)</span>
<span class="go">16711680</span>
</pre></div>
</div>
<p>The argument <em>bytes</em> must either support the buffer protocol or be an
iterable producing bytes. <a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a> and <a class="reference internal" href="functions.html#bytearray" title="bytearray"><tt class="xref py py-class docutils literal"><span class="pre">bytearray</span></tt></a> are
examples of built-in objects that support the buffer protocol.</p>
<p>The <em>byteorder</em> argument determines the byte order used to represent the
integer. If <em>byteorder</em> is <tt class="docutils literal"><span class="pre">"big"</span></tt>, the most significant byte is at the
beginning of the byte array. If <em>byteorder</em> is <tt class="docutils literal"><span class="pre">"little"</span></tt>, the most
significant byte is at the end of the byte array. To request the native
byte order of the host system, use <a class="reference internal" href="sys.html#sys.byteorder" title="sys.byteorder"><tt class="xref py py-data docutils literal"><span class="pre">sys.byteorder</span></tt></a> as the byte order
value.</p>
<p>The <em>signed</em> argument indicates whether two’s complement is used to
represent the integer.</p>
<p class="versionadded">
<span class="versionmodified">New in version 3.2.</span></p>
</dd></dl>
</div>
<div class="section" id="additional-methods-on-float">
<h3>4.4.3. Additional Methods on Float<a class="headerlink" href="#additional-methods-on-float" title="Permalink to this headline">¶</a></h3>
<p>The float type implements the <a class="reference internal" href="numbers.html#numbers.Real" title="numbers.Real"><tt class="xref py py-class docutils literal"><span class="pre">numbers.Real</span></tt></a> <a class="reference internal" href="../glossary.html#term-abstract-base-class"><em class="xref std std-term">abstract base
class</em></a>. float also has the following additional methods.</p>
<dl class="method">
<dt id="float.as_integer_ratio">
<tt class="descclassname">float.</tt><tt class="descname">as_integer_ratio</tt><big>(</big><big>)</big><a class="headerlink" href="#float.as_integer_ratio" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a pair of integers whose ratio is exactly equal to the
original float and with a positive denominator. Raises
<a class="reference internal" href="exceptions.html#OverflowError" title="OverflowError"><tt class="xref py py-exc docutils literal"><span class="pre">OverflowError</span></tt></a> on infinities and a <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><tt class="xref py py-exc docutils literal"><span class="pre">ValueError</span></tt></a> on
NaNs.</p>
</dd></dl>
<dl class="method">
<dt id="float.is_integer">
<tt class="descclassname">float.</tt><tt class="descname">is_integer</tt><big>(</big><big>)</big><a class="headerlink" href="#float.is_integer" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <tt class="xref docutils literal"><span class="pre">True</span></tt> if the float instance is finite with integral
value, and <tt class="xref docutils literal"><span class="pre">False</span></tt> otherwise:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="p">(</span><span class="o">-</span><span class="mf">2.0</span><span class="p">)</span><span class="o">.</span><span class="n">is_integer</span><span class="p">()</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="p">(</span><span class="mf">3.2</span><span class="p">)</span><span class="o">.</span><span class="n">is_integer</span><span class="p">()</span>
<span class="go">False</span>
</pre></div>
</div>
</dd></dl>
<p>Two methods support conversion to
and from hexadecimal strings. Since Python’s floats are stored
internally as binary numbers, converting a float to or from a
<em>decimal</em> string usually involves a small rounding error. In
contrast, hexadecimal strings allow exact representation and
specification of floating-point numbers. This can be useful when
debugging, and in numerical work.</p>
<dl class="method">
<dt id="float.hex">
<tt class="descclassname">float.</tt><tt class="descname">hex</tt><big>(</big><big>)</big><a class="headerlink" href="#float.hex" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a representation of a floating-point number as a hexadecimal
string. For finite floating-point numbers, this representation
will always include a leading <tt class="docutils literal"><span class="pre">0x</span></tt> and a trailing <tt class="docutils literal"><span class="pre">p</span></tt> and
exponent.</p>
</dd></dl>
<dl class="classmethod">
<dt id="float.fromhex">
<em class="property">classmethod </em><tt class="descclassname">float.</tt><tt class="descname">fromhex</tt><big>(</big><em>s</em><big>)</big><a class="headerlink" href="#float.fromhex" title="Permalink to this definition">¶</a></dt>
<dd><p>Class method to return the float represented by a hexadecimal
string <em>s</em>. The string <em>s</em> may have leading and trailing
whitespace.</p>
</dd></dl>
<p>Note that <a class="reference internal" href="#float.hex" title="float.hex"><tt class="xref py py-meth docutils literal"><span class="pre">float.hex()</span></tt></a> is an instance method, while
<a class="reference internal" href="#float.fromhex" title="float.fromhex"><tt class="xref py py-meth docutils literal"><span class="pre">float.fromhex()</span></tt></a> is a class method.</p>
<p>A hexadecimal string takes the form:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="p">[</span><span class="n">sign</span><span class="p">]</span> <span class="p">[</span><span class="s">'0x'</span><span class="p">]</span> <span class="n">integer</span> <span class="p">[</span><span class="s">'.'</span> <span class="n">fraction</span><span class="p">]</span> <span class="p">[</span><span class="s">'p'</span> <span class="n">exponent</span><span class="p">]</span>
</pre></div>
</div>
<p>where the optional <tt class="docutils literal"><span class="pre">sign</span></tt> may by either <tt class="docutils literal"><span class="pre">+</span></tt> or <tt class="docutils literal"><span class="pre">-</span></tt>, <tt class="docutils literal"><span class="pre">integer</span></tt>
and <tt class="docutils literal"><span class="pre">fraction</span></tt> are strings of hexadecimal digits, and <tt class="docutils literal"><span class="pre">exponent</span></tt>
is a decimal integer with an optional leading sign. Case is not
significant, and there must be at least one hexadecimal digit in
either the integer or the fraction. This syntax is similar to the
syntax specified in section 6.4.4.2 of the C99 standard, and also to
the syntax used in Java 1.5 onwards. In particular, the output of
<a class="reference internal" href="#float.hex" title="float.hex"><tt class="xref py py-meth docutils literal"><span class="pre">float.hex()</span></tt></a> is usable as a hexadecimal floating-point literal in
C or Java code, and hexadecimal strings produced by C’s <tt class="docutils literal"><span class="pre">%a</span></tt> format
character or Java’s <tt class="docutils literal"><span class="pre">Double.toHexString</span></tt> are accepted by
<a class="reference internal" href="#float.fromhex" title="float.fromhex"><tt class="xref py py-meth docutils literal"><span class="pre">float.fromhex()</span></tt></a>.</p>
<p>Note that the exponent is written in decimal rather than hexadecimal,
and that it gives the power of 2 by which to multiply the coefficient.
For example, the hexadecimal string <tt class="docutils literal"><span class="pre">0x3.a7p10</span></tt> represents the
floating-point number <tt class="docutils literal"><span class="pre">(3</span> <span class="pre">+</span> <span class="pre">10./16</span> <span class="pre">+</span> <span class="pre">7./16**2)</span> <span class="pre">*</span> <span class="pre">2.0**10</span></tt>, or
<tt class="docutils literal"><span class="pre">3740.0</span></tt>:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">float</span><span class="o">.</span><span class="n">fromhex</span><span class="p">(</span><span class="s">'0x3.a7p10'</span><span class="p">)</span>
<span class="go">3740.0</span>
</pre></div>
</div>
<p>Applying the reverse conversion to <tt class="docutils literal"><span class="pre">3740.0</span></tt> gives a different
hexadecimal string representing the same number:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">float</span><span class="o">.</span><span class="n">hex</span><span class="p">(</span><span class="mf">3740.0</span><span class="p">)</span>
<span class="go">'0x1.d380000000000p+11'</span>
</pre></div>
</div>
</div>
<div class="section" id="hashing-of-numeric-types">
<span id="numeric-hash"></span><h3>4.4.4. Hashing of numeric types<a class="headerlink" href="#hashing-of-numeric-types" title="Permalink to this headline">¶</a></h3>
<p>For numbers <tt class="docutils literal"><span class="pre">x</span></tt> and <tt class="docutils literal"><span class="pre">y</span></tt>, possibly of different types, it’s a requirement
that <tt class="docutils literal"><span class="pre">hash(x)</span> <span class="pre">==</span> <span class="pre">hash(y)</span></tt> whenever <tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">y</span></tt> (see the <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><tt class="xref py py-meth docutils literal"><span class="pre">__hash__()</span></tt></a>
method documentation for more details). For ease of implementation and
efficiency across a variety of numeric types (including <a class="reference internal" href="functions.html#int" title="int"><tt class="xref py py-class docutils literal"><span class="pre">int</span></tt></a>,
<a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal"><span class="pre">float</span></tt></a>, <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal"><span class="pre">decimal.Decimal</span></tt></a> and <a class="reference internal" href="fractions.html#fractions.Fraction" title="fractions.Fraction"><tt class="xref py py-class docutils literal"><span class="pre">fractions.Fraction</span></tt></a>)
Python’s hash for numeric types is based on a single mathematical function
that’s defined for any rational number, and hence applies to all instances of
<a class="reference internal" href="functions.html#int" title="int"><tt class="xref py py-class docutils literal"><span class="pre">int</span></tt></a> and <tt class="xref py py-class docutils literal"><span class="pre">fraction.Fraction</span></tt>, and all finite instances of
<a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal"><span class="pre">float</span></tt></a> and <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal"><span class="pre">decimal.Decimal</span></tt></a>. Essentially, this function is
given by reduction modulo <tt class="docutils literal"><span class="pre">P</span></tt> for a fixed prime <tt class="docutils literal"><span class="pre">P</span></tt>. The value of <tt class="docutils literal"><span class="pre">P</span></tt> is
made available to Python as the <tt class="xref py py-attr docutils literal"><span class="pre">modulus</span></tt> attribute of
<a class="reference internal" href="sys.html#sys.hash_info" title="sys.hash_info"><tt class="xref py py-data docutils literal"><span class="pre">sys.hash_info</span></tt></a>.</p>
<div class="impl-detail compound">
<p><strong>CPython implementation detail:</strong> Currently, the prime used is <tt class="docutils literal"><span class="pre">P</span> <span class="pre">=</span> <span class="pre">2**31</span> <span class="pre">-</span> <span class="pre">1</span></tt> on machines with 32-bit C
longs and <tt class="docutils literal"><span class="pre">P</span> <span class="pre">=</span> <span class="pre">2**61</span> <span class="pre">-</span> <span class="pre">1</span></tt> on machines with 64-bit C longs.</p>
</div>
<p>Here are the rules in detail:</p>
<blockquote>
<div><ul class="simple">
<li>If <tt class="docutils literal"><span class="pre">x</span> <span class="pre">=</span> <span class="pre">m</span> <span class="pre">/</span> <span class="pre">n</span></tt> is a nonnegative rational number and <tt class="docutils literal"><span class="pre">n</span></tt> is not divisible
by <tt class="docutils literal"><span class="pre">P</span></tt>, define <tt class="docutils literal"><span class="pre">hash(x)</span></tt> as <tt class="docutils literal"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">invmod(n,</span> <span class="pre">P)</span> <span class="pre">%</span> <span class="pre">P</span></tt>, where <tt class="docutils literal"><span class="pre">invmod(n,</span>
<span class="pre">P)</span></tt> gives the inverse of <tt class="docutils literal"><span class="pre">n</span></tt> modulo <tt class="docutils literal"><span class="pre">P</span></tt>.</li>
<li>If <tt class="docutils literal"><span class="pre">x</span> <span class="pre">=</span> <span class="pre">m</span> <span class="pre">/</span> <span class="pre">n</span></tt> is a nonnegative rational number and <tt class="docutils literal"><span class="pre">n</span></tt> is
divisible by <tt class="docutils literal"><span class="pre">P</span></tt> (but <tt class="docutils literal"><span class="pre">m</span></tt> is not) then <tt class="docutils literal"><span class="pre">n</span></tt> has no inverse
modulo <tt class="docutils literal"><span class="pre">P</span></tt> and the rule above doesn’t apply; in this case define
<tt class="docutils literal"><span class="pre">hash(x)</span></tt> to be the constant value <tt class="docutils literal"><span class="pre">sys.hash_info.inf</span></tt>.</li>
<li>If <tt class="docutils literal"><span class="pre">x</span> <span class="pre">=</span> <span class="pre">m</span> <span class="pre">/</span> <span class="pre">n</span></tt> is a negative rational number define <tt class="docutils literal"><span class="pre">hash(x)</span></tt>
as <tt class="docutils literal"><span class="pre">-hash(-x)</span></tt>. If the resulting hash is <tt class="docutils literal"><span class="pre">-1</span></tt>, replace it with
<tt class="docutils literal"><span class="pre">-2</span></tt>.</li>
<li>The particular values <tt class="docutils literal"><span class="pre">sys.hash_info.inf</span></tt>, <tt class="docutils literal"><span class="pre">-sys.hash_info.inf</span></tt>
and <tt class="docutils literal"><span class="pre">sys.hash_info.nan</span></tt> are used as hash values for positive
infinity, negative infinity, or nans (respectively). (All hashable
nans have the same hash value.)</li>
<li>For a <a class="reference internal" href="functions.html#complex" title="complex"><tt class="xref py py-class docutils literal"><span class="pre">complex</span></tt></a> number <tt class="docutils literal"><span class="pre">z</span></tt>, the hash values of the real
and imaginary parts are combined by computing <tt class="docutils literal"><span class="pre">hash(z.real)</span> <span class="pre">+</span>
<span class="pre">sys.hash_info.imag</span> <span class="pre">*</span> <span class="pre">hash(z.imag)</span></tt>, reduced modulo
<tt class="docutils literal"><span class="pre">2**sys.hash_info.width</span></tt> so that it lies in
<tt class="docutils literal"><span class="pre">range(-2**(sys.hash_info.width</span> <span class="pre">-</span> <span class="pre">1),</span> <span class="pre">2**(sys.hash_info.width</span> <span class="pre">-</span>
<span class="pre">1))</span></tt>. Again, if the result is <tt class="docutils literal"><span class="pre">-1</span></tt>, it’s replaced with <tt class="docutils literal"><span class="pre">-2</span></tt>.</li>
</ul>
</div></blockquote>
<p>To clarify the above rules, here’s some example Python code,
equivalent to the builtin hash, for computing the hash of a rational
number, <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal"><span class="pre">float</span></tt></a>, or <a class="reference internal" href="functions.html#complex" title="complex"><tt class="xref py py-class docutils literal"><span class="pre">complex</span></tt></a>:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">sys</span><span class="o">,</span> <span class="nn">math</span>
<span class="k">def</span> <span class="nf">hash_fraction</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="sd">"""Compute the hash of a rational number m / n.</span>
<span class="sd"> Assumes m and n are integers, with n positive.</span>
<span class="sd"> Equivalent to hash(fractions.Fraction(m, n)).</span>
<span class="sd"> """</span>
<span class="n">P</span> <span class="o">=</span> <span class="n">sys</span><span class="o">.</span><span class="n">hash_info</span><span class="o">.</span><span class="n">modulus</span>
<span class="c"># Remove common factors of P. (Unnecessary if m and n already coprime.)</span>
<span class="k">while</span> <span class="n">m</span> <span class="o">%</span> <span class="n">P</span> <span class="o">==</span> <span class="n">n</span> <span class="o">%</span> <span class="n">P</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">m</span><span class="p">,</span> <span class="n">n</span> <span class="o">=</span> <span class="n">m</span> <span class="o">//</span> <span class="n">P</span><span class="p">,</span> <span class="n">n</span> <span class="o">//</span> <span class="n">P</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">%</span> <span class="n">P</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">hash_</span> <span class="o">=</span> <span class="n">sys</span><span class="o">.</span><span class="n">hash_info</span><span class="o">.</span><span class="n">inf</span>
<span class="k">else</span><span class="p">:</span>
<span class="c"># Fermat's Little Theorem: pow(n, P-1, P) is 1, so</span>
<span class="c"># pow(n, P-2, P) gives the inverse of n modulo P.</span>
<span class="n">hash_</span> <span class="o">=</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">%</span> <span class="n">P</span><span class="p">)</span> <span class="o">*</span> <span class="nb">pow</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">P</span> <span class="o">-</span> <span class="mi">2</span><span class="p">,</span> <span class="n">P</span><span class="p">)</span> <span class="o">%</span> <span class="n">P</span>
<span class="k">if</span> <span class="n">m</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">hash_</span> <span class="o">=</span> <span class="o">-</span><span class="n">hash_</span>
<span class="k">if</span> <span class="n">hash_</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
<span class="n">hash_</span> <span class="o">=</span> <span class="o">-</span><span class="mi">2</span>
<span class="k">return</span> <span class="n">hash_</span>
<span class="k">def</span> <span class="nf">hash_float</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="sd">"""Compute the hash of a float x."""</span>
<span class="k">if</span> <span class="n">math</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">sys</span><span class="o">.</span><span class="n">hash_info</span><span class="o">.</span><span class="n">nan</span>
<span class="k">elif</span> <span class="n">math</span><span class="o">.</span><span class="n">isinf</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">sys</span><span class="o">.</span><span class="n">hash_info</span><span class="o">.</span><span class="n">inf</span> <span class="k">if</span> <span class="n">x</span> <span class="o">></span> <span class="mi">0</span> <span class="k">else</span> <span class="o">-</span><span class="n">sys</span><span class="o">.</span><span class="n">hash_info</span><span class="o">.</span><span class="n">inf</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">hash_fraction</span><span class="p">(</span><span class="o">*</span><span class="n">x</span><span class="o">.</span><span class="n">as_integer_ratio</span><span class="p">())</span>
<span class="k">def</span> <span class="nf">hash_complex</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
<span class="sd">"""Compute the hash of a complex number z."""</span>
<span class="n">hash_</span> <span class="o">=</span> <span class="n">hash_float</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">real</span><span class="p">)</span> <span class="o">+</span> <span class="n">sys</span><span class="o">.</span><span class="n">hash_info</span><span class="o">.</span><span class="n">imag</span> <span class="o">*</span> <span class="n">hash_float</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">imag</span><span class="p">)</span>
<span class="c"># do a signed reduction modulo 2**sys.hash_info.width</span>
<span class="n">M</span> <span class="o">=</span> <span class="mi">2</span><span class="o">**</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">hash_info</span><span class="o">.</span><span class="n">width</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">hash_</span> <span class="o">=</span> <span class="p">(</span><span class="n">hash_</span> <span class="o">&</span> <span class="p">(</span><span class="n">M</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">-</span> <span class="p">(</span><span class="nb">hash</span> <span class="o">&</span> <span class="n">M</span><span class="p">)</span>
<span class="k">if</span> <span class="n">hash_</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
<span class="n">hash_</span> <span class="o">==</span> <span class="o">-</span><span class="mi">2</span>
<span class="k">return</span> <span class="n">hash_</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="iterator-types">
<span id="typeiter"></span><h2>4.5. Iterator Types<a class="headerlink" href="#iterator-types" title="Permalink to this headline">¶</a></h2>
<p id="index-18">Python supports a concept of iteration over containers. This is implemented
using two distinct methods; these are used to allow user-defined classes to
support iteration. Sequences, described below in more detail, always support
the iteration methods.</p>
<p>One method needs to be defined for container objects to provide iteration
support:</p>
<dl class="method">
<dt id="container.__iter__">
<tt class="descclassname">container.</tt><tt class="descname">__iter__</tt><big>(</big><big>)</big><a class="headerlink" href="#container.__iter__" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an iterator object. The object is required to support the iterator
protocol described below. If a container supports different types of
iteration, additional methods can be provided to specifically request
iterators for those iteration types. (An example of an object supporting
multiple forms of iteration would be a tree structure which supports both
breadth-first and depth-first traversal.) This method corresponds to the
<tt class="xref py py-attr docutils literal"><span class="pre">tp_iter</span></tt> slot of the type structure for Python objects in the Python/C
API.</p>
</dd></dl>
<p>The iterator objects themselves are required to support the following two
methods, which together form the <em class="dfn">iterator protocol</em>:</p>
<dl class="method">
<dt id="iterator.__iter__">
<tt class="descclassname">iterator.</tt><tt class="descname">__iter__</tt><big>(</big><big>)</big><a class="headerlink" href="#iterator.__iter__" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the iterator object itself. This is required to allow both containers
and iterators to be used with the <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> and <a class="reference internal" href="../reference/expressions.html#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a> statements.
This method corresponds to the <tt class="xref py py-attr docutils literal"><span class="pre">tp_iter</span></tt> slot of the type structure for
Python objects in the Python/C API.</p>
</dd></dl>
<dl class="method">
<dt id="iterator.__next__">
<tt class="descclassname">iterator.</tt><tt class="descname">__next__</tt><big>(</big><big>)</big><a class="headerlink" href="#iterator.__next__" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the next item from the container. If there are no further items, raise
the <a class="reference internal" href="exceptions.html#StopIteration" title="StopIteration"><tt class="xref py py-exc docutils literal"><span class="pre">StopIteration</span></tt></a> exception. This method corresponds to the
<tt class="xref py py-attr docutils literal"><span class="pre">tp_iternext</span></tt> slot of the type structure for Python objects in the
Python/C API.</p>
</dd></dl>
<p>Python defines several iterator objects to support iteration over general and
specific sequence types, dictionaries, and other more specialized forms. The
specific types are not important beyond their implementation of the iterator
protocol.</p>
<p>Once an iterator’s <tt class="xref py py-meth docutils literal"><span class="pre">__next__()</span></tt> method raises <a class="reference internal" href="exceptions.html#StopIteration" title="StopIteration"><tt class="xref py py-exc docutils literal"><span class="pre">StopIteration</span></tt></a>, it must
continue to do so on subsequent calls. Implementations that do not obey this
property are deemed broken.</p>
<div class="section" id="generator-types">
<span id="id3"></span><h3>4.5.1. Generator Types<a class="headerlink" href="#generator-types" title="Permalink to this headline">¶</a></h3>
<p>Python’s <a class="reference internal" href="../glossary.html#term-generator"><em class="xref std std-term">generator</em></a>s provide a convenient way to implement the iterator
protocol. If a container object’s <a class="reference internal" href="../reference/datamodel.html#object.__iter__" title="object.__iter__"><tt class="xref py py-meth docutils literal"><span class="pre">__iter__()</span></tt></a> method is implemented as a
generator, it will automatically return an iterator object (technically, a
generator object) supplying the <a class="reference internal" href="../reference/datamodel.html#object.__iter__" title="object.__iter__"><tt class="xref py py-meth docutils literal"><span class="pre">__iter__()</span></tt></a> and <tt class="xref py py-meth docutils literal"><span class="pre">__next__()</span></tt> methods.
More information about generators can be found in <a class="reference internal" href="../reference/expressions.html#yieldexpr"><em>the documentation for
the yield expression</em></a>.</p>
</div>
</div>
<div class="section" id="sequence-types-str-bytes-bytearray-list-tuple-range">
<span id="typesseq"></span><h2>4.6. Sequence Types — <a class="reference internal" href="functions.html#str" title="str"><tt class="xref py py-class docutils literal"><span class="pre">str</span></tt></a>, <a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a>, <a class="reference internal" href="functions.html#bytearray" title="bytearray"><tt class="xref py py-class docutils literal"><span class="pre">bytearray</span></tt></a>, <a class="reference internal" href="functions.html#list" title="list"><tt class="xref py py-class docutils literal"><span class="pre">list</span></tt></a>, <a class="reference internal" href="functions.html#tuple" title="tuple"><tt class="xref py py-class docutils literal"><span class="pre">tuple</span></tt></a>, <a class="reference internal" href="functions.html#range" title="range"><tt class="xref py py-class docutils literal"><span class="pre">range</span></tt></a><a class="headerlink" href="#sequence-types-str-bytes-bytearray-list-tuple-range" title="Permalink to this headline">¶</a></h2>
<p>There are six sequence types: strings, byte sequences (<a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a> objects),
byte arrays (<a class="reference internal" href="functions.html#bytearray" title="bytearray"><tt class="xref py py-class docutils literal"><span class="pre">bytearray</span></tt></a> objects), lists, tuples, and range objects. For
other containers see the built in <a class="reference internal" href="#dict" title="dict"><tt class="xref py py-class docutils literal"><span class="pre">dict</span></tt></a> and <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> classes, and
the <a class="reference internal" href="collections.html#module-collections" title="collections: Container datatypes"><tt class="xref py py-mod docutils literal"><span class="pre">collections</span></tt></a> module.</p>
<p id="index-19">Strings contain Unicode characters. Their literals are written in single or
double quotes: <tt class="docutils literal"><span class="pre">'xyzzy'</span></tt>, <tt class="docutils literal"><span class="pre">"frobozz"</span></tt>. See <a class="reference internal" href="../reference/lexical_analysis.html#strings"><em>String and Bytes literals</em></a> for more about
string literals. In addition to the functionality described here, there are
also string-specific methods described in the <a class="reference internal" href="#string-methods"><em>String Methods</em></a> section.</p>
<p>Bytes and bytearray objects contain single bytes – the former is immutable
while the latter is a mutable sequence. Bytes objects can be constructed the
constructor, <a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-func docutils literal"><span class="pre">bytes()</span></tt></a>, and from literals; use a <tt class="docutils literal"><span class="pre">b</span></tt> prefix with normal
string syntax: <tt class="docutils literal"><span class="pre">b'xyzzy'</span></tt>. To construct byte arrays, use the
<a class="reference internal" href="functions.html#bytearray" title="bytearray"><tt class="xref py py-func docutils literal"><span class="pre">bytearray()</span></tt></a> function.</p>
<p>While string objects are sequences of characters (represented by strings of
length 1), bytes and bytearray objects are sequences of <em>integers</em> (between 0
and 255), representing the ASCII value of single bytes. That means that for
a bytes or bytearray object <em>b</em>, <tt class="docutils literal"><span class="pre">b[0]</span></tt> will be an integer, while
<tt class="docutils literal"><span class="pre">b[0:1]</span></tt> will be a bytes or bytearray object of length 1. The
representation of bytes objects uses the literal format (<tt class="docutils literal"><span class="pre">b'...'</span></tt>) since it
is generally more useful than e.g. <tt class="docutils literal"><span class="pre">bytes([50,</span> <span class="pre">19,</span> <span class="pre">100])</span></tt>. You can always
convert a bytes object into a list of integers using <tt class="docutils literal"><span class="pre">list(b)</span></tt>.</p>
<p>Also, while in previous Python versions, byte strings and Unicode strings
could be exchanged for each other rather freely (barring encoding issues),
strings and bytes are now completely separate concepts. There’s no implicit
en-/decoding if you pass an object of the wrong type. A string always
compares unequal to a bytes or bytearray object.</p>
<p>Lists are constructed with square brackets, separating items with commas: <tt class="docutils literal"><span class="pre">[a,</span>
<span class="pre">b,</span> <span class="pre">c]</span></tt>. Tuples are constructed by the comma operator (not within square
brackets), with or without enclosing parentheses, but an empty tuple must have
the enclosing parentheses, such as <tt class="docutils literal"><span class="pre">a,</span> <span class="pre">b,</span> <span class="pre">c</span></tt> or <tt class="docutils literal"><span class="pre">()</span></tt>. A single item tuple
must have a trailing comma, such as <tt class="docutils literal"><span class="pre">(d,)</span></tt>.</p>
<p>Objects of type range are created using the <a class="reference internal" href="functions.html#range" title="range"><tt class="xref py py-func docutils literal"><span class="pre">range()</span></tt></a> function. They don’t
support concatenation or repetition, and using <a class="reference internal" href="functions.html#min" title="min"><tt class="xref py py-func docutils literal"><span class="pre">min()</span></tt></a> or <a class="reference internal" href="functions.html#max" title="max"><tt class="xref py py-func docutils literal"><span class="pre">max()</span></tt></a> on
them is inefficient.</p>
<p>Most sequence types support the following operations. The <tt class="docutils literal"><span class="pre">in</span></tt> and <tt class="docutils literal"><span class="pre">not</span> <span class="pre">in</span></tt>
operations have the same priorities as the comparison operations. The <tt class="docutils literal"><span class="pre">+</span></tt> and
<tt class="docutils literal"><span class="pre">*</span></tt> operations have the same priority as the corresponding numeric operations.
<a class="footnote-reference" href="#id13" id="id4">[3]</a> Additional methods are provided for <a class="reference internal" href="#typesseq-mutable"><em>Mutable Sequence Types</em></a>.</p>
<p>This table lists the sequence operations sorted in ascending priority
(operations in the same box have the same priority). In the table, <em>s</em> and <em>t</em>
are sequences of the same type; <em>n</em>, <em>i</em>, <em>j</em> and <em>k</em> are integers.</p>
<table border="1" class="docutils">
<colgroup>
<col width="30%" />
<col width="53%" />
<col width="17%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Operation</th>
<th class="head">Result</th>
<th class="head">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">s</span></tt></td>
<td><tt class="xref docutils literal"><span class="pre">True</span></tt> if an item of <em>s</em> is
equal to <em>x</em>, else <tt class="xref docutils literal"><span class="pre">False</span></tt></td>
<td>(1)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">not</span> <span class="pre">in</span> <span class="pre">s</span></tt></td>
<td><tt class="xref docutils literal"><span class="pre">False</span></tt> if an item of <em>s</em> is
equal to <em>x</em>, else <tt class="xref docutils literal"><span class="pre">True</span></tt></td>
<td>(1)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s</span> <span class="pre">+</span> <span class="pre">t</span></tt></td>
<td>the concatenation of <em>s</em> and
<em>t</em></td>
<td>(6)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s</span> <span class="pre">*</span> <span class="pre">n,</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">s</span></tt></td>
<td><em>n</em> shallow copies of <em>s</em>
concatenated</td>
<td>(2)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s[i]</span></tt></td>
<td><em>i</em>‘th item of <em>s</em>, origin 0</td>
<td>(3)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s[i:j]</span></tt></td>
<td>slice of <em>s</em> from <em>i</em> to <em>j</em></td>
<td>(3)(4)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s[i:j:k]</span></tt></td>
<td>slice of <em>s</em> from <em>i</em> to <em>j</em>
with step <em>k</em></td>
<td>(3)(5)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">len(s)</span></tt></td>
<td>length of <em>s</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">min(s)</span></tt></td>
<td>smallest item of <em>s</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">max(s)</span></tt></td>
<td>largest item of <em>s</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.index(i)</span></tt></td>
<td>index of the first occurence
of <em>i</em> in <em>s</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.count(i)</span></tt></td>
<td>total number of occurences of
<em>i</em> in <em>s</em></td>
<td> </td>
</tr>
</tbody>
</table>
<p>Sequence types also support comparisons. In particular, tuples and lists are
compared lexicographically by comparing corresponding elements. This means that
to compare equal, every element must compare equal and the two sequences must be
of the same type and have the same length. (For full details see
<a class="reference internal" href="../reference/expressions.html#comparisons"><em>Comparisons</em></a> in the language reference.)</p>
<p id="index-20">Notes:</p>
<ol class="arabic">
<li><p class="first">When <em>s</em> is a string object, the <tt class="docutils literal"><span class="pre">in</span></tt> and <tt class="docutils literal"><span class="pre">not</span> <span class="pre">in</span></tt> operations act like a
substring test.</p>
</li>
<li><p class="first">Values of <em>n</em> less than <tt class="docutils literal"><span class="pre">0</span></tt> are treated as <tt class="docutils literal"><span class="pre">0</span></tt> (which yields an empty
sequence of the same type as <em>s</em>). Note also that the copies are shallow;
nested structures are not copied. This often haunts new Python programmers;
consider:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">lists</span> <span class="o">=</span> <span class="p">[[]]</span> <span class="o">*</span> <span class="mi">3</span>
<span class="gp">>>> </span><span class="n">lists</span>
<span class="go">[[], [], []]</span>
<span class="gp">>>> </span><span class="n">lists</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">lists</span>
<span class="go">[[3], [3], [3]]</span>
</pre></div>
</div>
<p>What has happened is that <tt class="docutils literal"><span class="pre">[[]]</span></tt> is a one-element list containing an empty
list, so all three elements of <tt class="docutils literal"><span class="pre">[[]]</span> <span class="pre">*</span> <span class="pre">3</span></tt> are (pointers to) this single empty
list. Modifying any of the elements of <tt class="docutils literal"><span class="pre">lists</span></tt> modifies this single list.
You can create a list of different lists this way:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">lists</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">)]</span>
<span class="gp">>>> </span><span class="n">lists</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">lists</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">lists</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">lists</span>
<span class="go">[[3], [5], [7]]</span>
</pre></div>
</div>
</li>
<li><p class="first">If <em>i</em> or <em>j</em> is negative, the index is relative to the end of the string:
<tt class="docutils literal"><span class="pre">len(s)</span> <span class="pre">+</span> <span class="pre">i</span></tt> or <tt class="docutils literal"><span class="pre">len(s)</span> <span class="pre">+</span> <span class="pre">j</span></tt> is substituted. But note that <tt class="docutils literal"><span class="pre">-0</span></tt> is
still <tt class="docutils literal"><span class="pre">0</span></tt>.</p>
</li>
<li><p class="first">The slice of <em>s</em> from <em>i</em> to <em>j</em> is defined as the sequence of items with index
<em>k</em> such that <tt class="docutils literal"><span class="pre">i</span> <span class="pre"><=</span> <span class="pre">k</span> <span class="pre"><</span> <span class="pre">j</span></tt>. If <em>i</em> or <em>j</em> is greater than <tt class="docutils literal"><span class="pre">len(s)</span></tt>, use
<tt class="docutils literal"><span class="pre">len(s)</span></tt>. If <em>i</em> is omitted or <tt class="xref docutils literal"><span class="pre">None</span></tt>, use <tt class="docutils literal"><span class="pre">0</span></tt>. If <em>j</em> is omitted or
<tt class="xref docutils literal"><span class="pre">None</span></tt>, use <tt class="docutils literal"><span class="pre">len(s)</span></tt>. If <em>i</em> is greater than or equal to <em>j</em>, the slice is
empty.</p>
</li>
<li><p class="first">The slice of <em>s</em> from <em>i</em> to <em>j</em> with step <em>k</em> is defined as the sequence of
items with index <tt class="docutils literal"><span class="pre">x</span> <span class="pre">=</span> <span class="pre">i</span> <span class="pre">+</span> <span class="pre">n*k</span></tt> such that <tt class="docutils literal"><span class="pre">0</span> <span class="pre"><=</span> <span class="pre">n</span> <span class="pre"><</span> <span class="pre">(j-i)/k</span></tt>. In other words,
the indices are <tt class="docutils literal"><span class="pre">i</span></tt>, <tt class="docutils literal"><span class="pre">i+k</span></tt>, <tt class="docutils literal"><span class="pre">i+2*k</span></tt>, <tt class="docutils literal"><span class="pre">i+3*k</span></tt> and so on, stopping when
<em>j</em> is reached (but never including <em>j</em>). If <em>i</em> or <em>j</em> is greater than
<tt class="docutils literal"><span class="pre">len(s)</span></tt>, use <tt class="docutils literal"><span class="pre">len(s)</span></tt>. If <em>i</em> or <em>j</em> are omitted or <tt class="xref docutils literal"><span class="pre">None</span></tt>, they become
“end” values (which end depends on the sign of <em>k</em>). Note, <em>k</em> cannot be zero.
If <em>k</em> is <tt class="xref docutils literal"><span class="pre">None</span></tt>, it is treated like <tt class="docutils literal"><span class="pre">1</span></tt>.</p>
</li>
<li><div class="impl-detail first compound">
<p><strong>CPython implementation detail:</strong> If <em>s</em> and <em>t</em> are both strings, some Python implementations such as
CPython can usually perform an in-place optimization for assignments of
the form <tt class="docutils literal"><span class="pre">s</span> <span class="pre">=</span> <span class="pre">s</span> <span class="pre">+</span> <span class="pre">t</span></tt> or <tt class="docutils literal"><span class="pre">s</span> <span class="pre">+=</span> <span class="pre">t</span></tt>. When applicable, this optimization
makes quadratic run-time much less likely. This optimization is both
version and implementation dependent. For performance sensitive code, it
is preferable to use the <a class="reference internal" href="#str.join" title="str.join"><tt class="xref py py-meth docutils literal"><span class="pre">str.join()</span></tt></a> method which assures consistent
linear concatenation performance across versions and implementations.</p>
</div>
</li>
</ol>
<div class="section" id="string-methods">
<span id="id5"></span><h3>4.6.1. String Methods<a class="headerlink" href="#string-methods" title="Permalink to this headline">¶</a></h3>
<p id="index-21">String objects support the methods listed below.</p>
<p>In addition, Python’s strings support the sequence type methods described in the
<a class="reference internal" href="#typesseq"><em>Sequence Types — str, bytes, bytearray, list, tuple, range</em></a> section. To output formatted strings, see the
<a class="reference internal" href="string.html#string-formatting"><em>String Formatting</em></a> section. Also, see the <a class="reference internal" href="re.html#module-re" title="re: Regular expression operations."><tt class="xref py py-mod docutils literal"><span class="pre">re</span></tt></a> module for string
functions based on regular expressions.</p>
<dl class="method">
<dt id="str.capitalize">
<tt class="descclassname">str.</tt><tt class="descname">capitalize</tt><big>(</big><big>)</big><a class="headerlink" href="#str.capitalize" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string with its first character capitalized and the
rest lowercased.</p>
</dd></dl>
<dl class="method">
<dt id="str.center">
<tt class="descclassname">str.</tt><tt class="descname">center</tt><big>(</big><em>width</em><span class="optional">[</span>, <em>fillchar</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.center" title="Permalink to this definition">¶</a></dt>
<dd><p>Return centered in a string of length <em>width</em>. Padding is done using the
specified <em>fillchar</em> (default is a space).</p>
</dd></dl>
<dl class="method">
<dt id="str.count">
<tt class="descclassname">str.</tt><tt class="descname">count</tt><big>(</big><em>sub</em><span class="optional">[</span>, <em>start</em><span class="optional">[</span>, <em>end</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.count" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the number of non-overlapping occurrences of substring <em>sub</em> in the
range [<em>start</em>, <em>end</em>]. Optional arguments <em>start</em> and <em>end</em> are
interpreted as in slice notation.</p>
</dd></dl>
<dl class="method">
<dt id="str.encode">
<tt class="descclassname">str.</tt><tt class="descname">encode</tt><big>(</big><em>encoding="utf-8"</em>, <em>errors="strict"</em><big>)</big><a class="headerlink" href="#str.encode" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an encoded version of the string as a bytes object. Default encoding
is <tt class="docutils literal"><span class="pre">'utf-8'</span></tt>. <em>errors</em> may be given to set a different error handling scheme.
The default for <em>errors</em> is <tt class="docutils literal"><span class="pre">'strict'</span></tt>, meaning that encoding errors raise
a <a class="reference internal" href="exceptions.html#UnicodeError" title="UnicodeError"><tt class="xref py py-exc docutils literal"><span class="pre">UnicodeError</span></tt></a>. Other possible
values are <tt class="docutils literal"><span class="pre">'ignore'</span></tt>, <tt class="docutils literal"><span class="pre">'replace'</span></tt>, <tt class="docutils literal"><span class="pre">'xmlcharrefreplace'</span></tt>,
<tt class="docutils literal"><span class="pre">'backslashreplace'</span></tt> and any other name registered via
<a class="reference internal" href="codecs.html#codecs.register_error" title="codecs.register_error"><tt class="xref py py-func docutils literal"><span class="pre">codecs.register_error()</span></tt></a>, see section <a class="reference internal" href="codecs.html#codec-base-classes"><em>Codec Base Classes</em></a>. For a
list of possible encodings, see section <a class="reference internal" href="codecs.html#standard-encodings"><em>Standard Encodings</em></a>.</p>
<p class="versionchanged">
<span class="versionmodified">Changed in version 3.1: </span>Support for keyword arguments added.</p>
</dd></dl>
<dl class="method">
<dt id="str.endswith">
<tt class="descclassname">str.</tt><tt class="descname">endswith</tt><big>(</big><em>suffix</em><span class="optional">[</span>, <em>start</em><span class="optional">[</span>, <em>end</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.endswith" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <tt class="xref docutils literal"><span class="pre">True</span></tt> if the string ends with the specified <em>suffix</em>, otherwise return
<tt class="xref docutils literal"><span class="pre">False</span></tt>. <em>suffix</em> can also be a tuple of suffixes to look for. With optional
<em>start</em>, test beginning at that position. With optional <em>end</em>, stop comparing
at that position.</p>
</dd></dl>
<dl class="method">
<dt id="str.expandtabs">
<tt class="descclassname">str.</tt><tt class="descname">expandtabs</tt><big>(</big><span class="optional">[</span><em>tabsize</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.expandtabs" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string where all tab characters are replaced by one or
more spaces, depending on the current column and the given tab size. The
column number is reset to zero after each newline occurring in the string.
If <em>tabsize</em> is not given, a tab size of <tt class="docutils literal"><span class="pre">8</span></tt> characters is assumed. This
doesn’t understand other non-printing characters or escape sequences.</p>
</dd></dl>
<dl class="method">
<dt id="str.find">
<tt class="descclassname">str.</tt><tt class="descname">find</tt><big>(</big><em>sub</em><span class="optional">[</span>, <em>start</em><span class="optional">[</span>, <em>end</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.find" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the lowest index in the string where substring <em>sub</em> is found, such
that <em>sub</em> is contained in the slice <tt class="docutils literal"><span class="pre">s[start:end]</span></tt>. Optional arguments
<em>start</em> and <em>end</em> are interpreted as in slice notation. Return <tt class="docutils literal"><span class="pre">-1</span></tt> if
<em>sub</em> is not found.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p>The <a class="reference internal" href="#str.find" title="str.find"><tt class="xref py py-meth docutils literal"><span class="pre">find()</span></tt></a> method should be used only if you need to know the
position of <em>sub</em>. To check if <em>sub</em> is a substring or not, use the
<a class="reference internal" href="../reference/expressions.html#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a> operator:</p>
<div class="last highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="s">'Py'</span> <span class="ow">in</span> <span class="s">'Python'</span>
<span class="go">True</span>
</pre></div>
</div>
</div>
</dd></dl>
<dl class="method">
<dt id="str.format">
<tt class="descclassname">str.</tt><tt class="descname">format</tt><big>(</big><em>*args</em>, <em>**kwargs</em><big>)</big><a class="headerlink" href="#str.format" title="Permalink to this definition">¶</a></dt>
<dd><p>Perform a string formatting operation. The string on which this method is
called can contain literal text or replacement fields delimited by braces
<tt class="docutils literal"><span class="pre">{}</span></tt>. Each replacement field contains either the numeric index of a
positional argument, or the name of a keyword argument. Returns a copy of
the string where each replacement field is replaced with the string value of
the corresponding argument.</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="s">"The sum of 1 + 2 is {0}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
<span class="go">'The sum of 1 + 2 is 3'</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="string.html#formatstrings"><em>Format String Syntax</em></a> for a description of the various formatting options
that can be specified in format strings.</p>
</dd></dl>
<dl class="method">
<dt id="str.format_map">
<tt class="descclassname">str.</tt><tt class="descname">format_map</tt><big>(</big><em>mapping</em><big>)</big><a class="headerlink" href="#str.format_map" title="Permalink to this definition">¶</a></dt>
<dd><p>Similar to <tt class="docutils literal"><span class="pre">str.format(**mapping)</span></tt>, except that <tt class="docutils literal"><span class="pre">mapping</span></tt> is
used directly and not copied to a <a class="reference internal" href="#dict" title="dict"><tt class="xref py py-class docutils literal"><span class="pre">dict</span></tt></a> . This is useful
if for example <tt class="docutils literal"><span class="pre">mapping</span></tt> is a dict subclass:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">class</span> <span class="nc">Default</span><span class="p">(</span><span class="nb">dict</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">def</span> <span class="nf">__missing__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">return</span> <span class="n">key</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="s">'{name} was born in {country}'</span><span class="o">.</span><span class="n">format_map</span><span class="p">(</span><span class="n">Default</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s">'Guido'</span><span class="p">))</span>
<span class="go">'Guido was born in country'</span>
</pre></div>
</div>
<p class="versionadded">
<span class="versionmodified">New in version 3.2.</span></p>
</dd></dl>
<dl class="method">
<dt id="str.index">
<tt class="descclassname">str.</tt><tt class="descname">index</tt><big>(</big><em>sub</em><span class="optional">[</span>, <em>start</em><span class="optional">[</span>, <em>end</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.index" title="Permalink to this definition">¶</a></dt>
<dd><p>Like <a class="reference internal" href="#str.find" title="str.find"><tt class="xref py py-meth docutils literal"><span class="pre">find()</span></tt></a>, but raise <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><tt class="xref py py-exc docutils literal"><span class="pre">ValueError</span></tt></a> when the substring is not found.</p>
</dd></dl>
<dl class="method">
<dt id="str.isalnum">
<tt class="descclassname">str.</tt><tt class="descname">isalnum</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isalnum" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if all characters in the string are alphanumeric and there is at
least one character, false otherwise. A character <tt class="docutils literal"><span class="pre">c</span></tt> is alphanumeric if one
of the following returns <tt class="xref docutils literal"><span class="pre">True</span></tt>: <tt class="docutils literal"><span class="pre">c.isalpha()</span></tt>, <tt class="docutils literal"><span class="pre">c.isdecimal()</span></tt>,
<tt class="docutils literal"><span class="pre">c.isdigit()</span></tt>, or <tt class="docutils literal"><span class="pre">c.isnumeric()</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="str.isalpha">
<tt class="descclassname">str.</tt><tt class="descname">isalpha</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isalpha" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if all characters in the string are alphabetic and there is at least
one character, false otherwise. Alphabetic characters are those characters defined
in the Unicode character database as “Letter”, i.e., those with general category
property being one of “Lm”, “Lt”, “Lu”, “Ll”, or “Lo”. Note that this is different
from the “Alphabetic” property defined in the Unicode Standard.</p>
</dd></dl>
<dl class="method">
<dt id="str.isdecimal">
<tt class="descclassname">str.</tt><tt class="descname">isdecimal</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isdecimal" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if all characters in the string are decimal
characters and there is at least one character, false
otherwise. Decimal characters are those from general category “Nd”. This category
includes digit characters, and all characters
that that can be used to form decimal-radix numbers, e.g. U+0660,
ARABIC-INDIC DIGIT ZERO.</p>
</dd></dl>
<dl class="method">
<dt id="str.isdigit">
<tt class="descclassname">str.</tt><tt class="descname">isdigit</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isdigit" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if all characters in the string are digits and there is at least one
character, false otherwise. Digits include decimal characters and digits that need
special handling, such as the compatibility superscript digits. Formally, a digit
is a character that has the property value Numeric_Type=Digit or Numeric_Type=Decimal.</p>
</dd></dl>
<dl class="method">
<dt id="str.isidentifier">
<tt class="descclassname">str.</tt><tt class="descname">isidentifier</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isidentifier" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if the string is a valid identifier according to the language
definition, section <a class="reference internal" href="../reference/lexical_analysis.html#identifiers"><em>Identifiers and keywords</em></a>.</p>
</dd></dl>
<dl class="method">
<dt id="str.islower">
<tt class="descclassname">str.</tt><tt class="descname">islower</tt><big>(</big><big>)</big><a class="headerlink" href="#str.islower" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if all cased characters <a class="footnote-reference" href="#id14" id="id6">[4]</a> in the string are lowercase and
there is at least one cased character, false otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="str.isnumeric">
<tt class="descclassname">str.</tt><tt class="descname">isnumeric</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isnumeric" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if all characters in the string are numeric
characters, and there is at least one character, false
otherwise. Numeric characters include digit characters, and all characters
that have the Unicode numeric value property, e.g. U+2155,
VULGAR FRACTION ONE FIFTH. Formally, numeric characters are those with the property
value Numeric_Type=Digit, Numeric_Type=Decimal or Numeric_Type=Numeric.</p>
</dd></dl>
<dl class="method">
<dt id="str.isprintable">
<tt class="descclassname">str.</tt><tt class="descname">isprintable</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isprintable" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if all characters in the string are printable or the string is
empty, false otherwise. Nonprintable characters are those characters defined
in the Unicode character database as “Other” or “Separator”, excepting the
ASCII space (0x20) which is considered printable. (Note that printable
characters in this context are those which should not be escaped when
<a class="reference internal" href="functions.html#repr" title="repr"><tt class="xref py py-func docutils literal"><span class="pre">repr()</span></tt></a> is invoked on a string. It has no bearing on the handling of
strings written to <a class="reference internal" href="sys.html#sys.stdout" title="sys.stdout"><tt class="xref py py-data docutils literal"><span class="pre">sys.stdout</span></tt></a> or <a class="reference internal" href="sys.html#sys.stderr" title="sys.stderr"><tt class="xref py py-data docutils literal"><span class="pre">sys.stderr</span></tt></a>.)</p>
</dd></dl>
<dl class="method">
<dt id="str.isspace">
<tt class="descclassname">str.</tt><tt class="descname">isspace</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isspace" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if there are only whitespace characters in the string and there is
at least one character, false otherwise. Whitespace characters are those
characters defined in the Unicode character database as “Other” or “Separator”
and those with bidirectional property being one of “WS”, “B”, or “S”.</p>
</dd></dl>
<dl class="method">
<dt id="str.istitle">
<tt class="descclassname">str.</tt><tt class="descname">istitle</tt><big>(</big><big>)</big><a class="headerlink" href="#str.istitle" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if the string is a titlecased string and there is at least one
character, for example uppercase characters may only follow uncased characters
and lowercase characters only cased ones. Return false otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="str.isupper">
<tt class="descclassname">str.</tt><tt class="descname">isupper</tt><big>(</big><big>)</big><a class="headerlink" href="#str.isupper" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true if all cased characters <a class="footnote-reference" href="#id14" id="id7">[4]</a> in the string are uppercase and
there is at least one cased character, false otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="str.join">
<tt class="descclassname">str.</tt><tt class="descname">join</tt><big>(</big><em>iterable</em><big>)</big><a class="headerlink" href="#str.join" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a string which is the concatenation of the strings in the
<a class="reference internal" href="../glossary.html#term-iterable"><em class="xref std std-term">iterable</em></a> <em>iterable</em>. A <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> will be raised if there are
any non-string values in <em>seq</em>, including <a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a> objects. The
separator between elements is the string providing this method.</p>
</dd></dl>
<dl class="method">
<dt id="str.ljust">
<tt class="descclassname">str.</tt><tt class="descname">ljust</tt><big>(</big><em>width</em><span class="optional">[</span>, <em>fillchar</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.ljust" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the string left justified in a string of length <em>width</em>. Padding is done
using the specified <em>fillchar</em> (default is a space). The original string is
returned if <em>width</em> is less than <tt class="docutils literal"><span class="pre">len(s)</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="str.lower">
<tt class="descclassname">str.</tt><tt class="descname">lower</tt><big>(</big><big>)</big><a class="headerlink" href="#str.lower" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string with all the cased characters <a class="footnote-reference" href="#id14" id="id8">[4]</a> converted to
lowercase.</p>
</dd></dl>
<dl class="method">
<dt id="str.lstrip">
<tt class="descclassname">str.</tt><tt class="descname">lstrip</tt><big>(</big><span class="optional">[</span><em>chars</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.lstrip" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string with leading characters removed. The <em>chars</em>
argument is a string specifying the set of characters to be removed. If omitted
or <tt class="xref docutils literal"><span class="pre">None</span></tt>, the <em>chars</em> argument defaults to removing whitespace. The <em>chars</em>
argument is not a prefix; rather, all combinations of its values are stripped:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="s">' spacious '</span><span class="o">.</span><span class="n">lstrip</span><span class="p">()</span>
<span class="go">'spacious '</span>
<span class="gp">>>> </span><span class="s">'www.example.com'</span><span class="o">.</span><span class="n">lstrip</span><span class="p">(</span><span class="s">'cmowz.'</span><span class="p">)</span>
<span class="go">'example.com'</span>
</pre></div>
</div>
</dd></dl>
<dl class="staticmethod">
<dt id="str.maketrans">
<em class="property">static </em><tt class="descclassname">str.</tt><tt class="descname">maketrans</tt><big>(</big><em>x</em><span class="optional">[</span>, <em>y</em><span class="optional">[</span>, <em>z</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.maketrans" title="Permalink to this definition">¶</a></dt>
<dd><p>This static method returns a translation table usable for <a class="reference internal" href="#str.translate" title="str.translate"><tt class="xref py py-meth docutils literal"><span class="pre">str.translate()</span></tt></a>.</p>
<p>If there is only one argument, it must be a dictionary mapping Unicode
ordinals (integers) or characters (strings of length 1) to Unicode ordinals,
strings (of arbitrary lengths) or None. Character keys will then be
converted to ordinals.</p>
<p>If there are two arguments, they must be strings of equal length, and in the
resulting dictionary, each character in x will be mapped to the character at
the same position in y. If there is a third argument, it must be a string,
whose characters will be mapped to None in the result.</p>
</dd></dl>
<dl class="method">
<dt id="str.partition">
<tt class="descclassname">str.</tt><tt class="descname">partition</tt><big>(</big><em>sep</em><big>)</big><a class="headerlink" href="#str.partition" title="Permalink to this definition">¶</a></dt>
<dd><p>Split the string at the first occurrence of <em>sep</em>, and return a 3-tuple
containing the part before the separator, the separator itself, and the part
after the separator. If the separator is not found, return a 3-tuple containing
the string itself, followed by two empty strings.</p>
</dd></dl>
<dl class="method">
<dt id="str.replace">
<tt class="descclassname">str.</tt><tt class="descname">replace</tt><big>(</big><em>old</em>, <em>new</em><span class="optional">[</span>, <em>count</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.replace" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string with all occurrences of substring <em>old</em> replaced by
<em>new</em>. If the optional argument <em>count</em> is given, only the first <em>count</em>
occurrences are replaced.</p>
</dd></dl>
<dl class="method">
<dt id="str.rfind">
<tt class="descclassname">str.</tt><tt class="descname">rfind</tt><big>(</big><em>sub</em><span class="optional">[</span>, <em>start</em><span class="optional">[</span>, <em>end</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.rfind" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the highest index in the string where substring <em>sub</em> is found, such
that <em>sub</em> is contained within <tt class="docutils literal"><span class="pre">s[start:end]</span></tt>. Optional arguments <em>start</em>
and <em>end</em> are interpreted as in slice notation. Return <tt class="docutils literal"><span class="pre">-1</span></tt> on failure.</p>
</dd></dl>
<dl class="method">
<dt id="str.rindex">
<tt class="descclassname">str.</tt><tt class="descname">rindex</tt><big>(</big><em>sub</em><span class="optional">[</span>, <em>start</em><span class="optional">[</span>, <em>end</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.rindex" title="Permalink to this definition">¶</a></dt>
<dd><p>Like <a class="reference internal" href="#str.rfind" title="str.rfind"><tt class="xref py py-meth docutils literal"><span class="pre">rfind()</span></tt></a> but raises <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><tt class="xref py py-exc docutils literal"><span class="pre">ValueError</span></tt></a> when the substring <em>sub</em> is not
found.</p>
</dd></dl>
<dl class="method">
<dt id="str.rjust">
<tt class="descclassname">str.</tt><tt class="descname">rjust</tt><big>(</big><em>width</em><span class="optional">[</span>, <em>fillchar</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.rjust" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the string right justified in a string of length <em>width</em>. Padding is done
using the specified <em>fillchar</em> (default is a space). The original string is
returned if <em>width</em> is less than <tt class="docutils literal"><span class="pre">len(s)</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="str.rpartition">
<tt class="descclassname">str.</tt><tt class="descname">rpartition</tt><big>(</big><em>sep</em><big>)</big><a class="headerlink" href="#str.rpartition" title="Permalink to this definition">¶</a></dt>
<dd><p>Split the string at the last occurrence of <em>sep</em>, and return a 3-tuple
containing the part before the separator, the separator itself, and the part
after the separator. If the separator is not found, return a 3-tuple containing
two empty strings, followed by the string itself.</p>
</dd></dl>
<dl class="method">
<dt id="str.rsplit">
<tt class="descclassname">str.</tt><tt class="descname">rsplit</tt><big>(</big><span class="optional">[</span><em>sep</em><span class="optional">[</span>, <em>maxsplit</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.rsplit" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a list of the words in the string, using <em>sep</em> as the delimiter string.
If <em>maxsplit</em> is given, at most <em>maxsplit</em> splits are done, the <em>rightmost</em>
ones. If <em>sep</em> is not specified or <tt class="xref docutils literal"><span class="pre">None</span></tt>, any whitespace string is a
separator. Except for splitting from the right, <a class="reference internal" href="#str.rsplit" title="str.rsplit"><tt class="xref py py-meth docutils literal"><span class="pre">rsplit()</span></tt></a> behaves like
<a class="reference internal" href="#str.split" title="str.split"><tt class="xref py py-meth docutils literal"><span class="pre">split()</span></tt></a> which is described in detail below.</p>
</dd></dl>
<dl class="method">
<dt id="str.rstrip">
<tt class="descclassname">str.</tt><tt class="descname">rstrip</tt><big>(</big><span class="optional">[</span><em>chars</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.rstrip" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string with trailing characters removed. The <em>chars</em>
argument is a string specifying the set of characters to be removed. If omitted
or <tt class="xref docutils literal"><span class="pre">None</span></tt>, the <em>chars</em> argument defaults to removing whitespace. The <em>chars</em>
argument is not a suffix; rather, all combinations of its values are stripped:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="s">' spacious '</span><span class="o">.</span><span class="n">rstrip</span><span class="p">()</span>
<span class="go">' spacious'</span>
<span class="gp">>>> </span><span class="s">'mississippi'</span><span class="o">.</span><span class="n">rstrip</span><span class="p">(</span><span class="s">'ipz'</span><span class="p">)</span>
<span class="go">'mississ'</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="str.split">
<tt class="descclassname">str.</tt><tt class="descname">split</tt><big>(</big><span class="optional">[</span><em>sep</em><span class="optional">[</span>, <em>maxsplit</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.split" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a list of the words in the string, using <em>sep</em> as the delimiter
string. If <em>maxsplit</em> is given, at most <em>maxsplit</em> splits are done (thus,
the list will have at most <tt class="docutils literal"><span class="pre">maxsplit+1</span></tt> elements). If <em>maxsplit</em> is not
specified, then there is no limit on the number of splits (all possible
splits are made).</p>
<p>If <em>sep</em> is given, consecutive delimiters are not grouped together and are
deemed to delimit empty strings (for example, <tt class="docutils literal"><span class="pre">'1,,2'.split(',')</span></tt> returns
<tt class="docutils literal"><span class="pre">['1',</span> <span class="pre">'',</span> <span class="pre">'2']</span></tt>). The <em>sep</em> argument may consist of multiple characters
(for example, <tt class="docutils literal"><span class="pre">'1<>2<>3'.split('<>')</span></tt> returns <tt class="docutils literal"><span class="pre">['1',</span> <span class="pre">'2',</span> <span class="pre">'3']</span></tt>).
Splitting an empty string with a specified separator returns <tt class="docutils literal"><span class="pre">['']</span></tt>.</p>
<p>If <em>sep</em> is not specified or is <tt class="xref docutils literal"><span class="pre">None</span></tt>, a different splitting algorithm is
applied: runs of consecutive whitespace are regarded as a single separator,
and the result will contain no empty strings at the start or end if the
string has leading or trailing whitespace. Consequently, splitting an empty
string or a string consisting of just whitespace with a <tt class="xref docutils literal"><span class="pre">None</span></tt> separator
returns <tt class="docutils literal"><span class="pre">[]</span></tt>.</p>
<p>For example, <tt class="docutils literal"><span class="pre">'</span> <span class="pre">1</span> <span class="pre">2</span> <span class="pre">3</span> <span class="pre">'.split()</span></tt> returns <tt class="docutils literal"><span class="pre">['1',</span> <span class="pre">'2',</span> <span class="pre">'3']</span></tt>, and
<tt class="docutils literal"><span class="pre">'</span> <span class="pre">1</span> <span class="pre">2</span> <span class="pre">3</span> <span class="pre">'.split(None,</span> <span class="pre">1)</span></tt> returns <tt class="docutils literal"><span class="pre">['1',</span> <span class="pre">'2</span> <span class="pre">3</span> <span class="pre">']</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="str.splitlines">
<tt class="descclassname">str.</tt><tt class="descname">splitlines</tt><big>(</big><span class="optional">[</span><em>keepends</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.splitlines" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a list of the lines in the string, breaking at line boundaries. Line
breaks are not included in the resulting list unless <em>keepends</em> is given and
true.</p>
</dd></dl>
<dl class="method">
<dt id="str.startswith">
<tt class="descclassname">str.</tt><tt class="descname">startswith</tt><big>(</big><em>prefix</em><span class="optional">[</span>, <em>start</em><span class="optional">[</span>, <em>end</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.startswith" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <tt class="xref docutils literal"><span class="pre">True</span></tt> if string starts with the <em>prefix</em>, otherwise return <tt class="xref docutils literal"><span class="pre">False</span></tt>.
<em>prefix</em> can also be a tuple of prefixes to look for. With optional <em>start</em>,
test string beginning at that position. With optional <em>end</em>, stop comparing
string at that position.</p>
</dd></dl>
<dl class="method">
<dt id="str.strip">
<tt class="descclassname">str.</tt><tt class="descname">strip</tt><big>(</big><span class="optional">[</span><em>chars</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#str.strip" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string with the leading and trailing characters removed.
The <em>chars</em> argument is a string specifying the set of characters to be removed.
If omitted or <tt class="xref docutils literal"><span class="pre">None</span></tt>, the <em>chars</em> argument defaults to removing whitespace.
The <em>chars</em> argument is not a prefix or suffix; rather, all combinations of its
values are stripped:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="s">' spacious '</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span>
<span class="go">'spacious'</span>
<span class="gp">>>> </span><span class="s">'www.example.com'</span><span class="o">.</span><span class="n">strip</span><span class="p">(</span><span class="s">'cmowz.'</span><span class="p">)</span>
<span class="go">'example'</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="str.swapcase">
<tt class="descclassname">str.</tt><tt class="descname">swapcase</tt><big>(</big><big>)</big><a class="headerlink" href="#str.swapcase" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string with uppercase characters converted to lowercase and
vice versa.</p>
</dd></dl>
<dl class="method">
<dt id="str.title">
<tt class="descclassname">str.</tt><tt class="descname">title</tt><big>(</big><big>)</big><a class="headerlink" href="#str.title" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a titlecased version of the string where words start with an uppercase
character and the remaining characters are lowercase.</p>
<p>The algorithm uses a simple language-independent definition of a word as
groups of consecutive letters. The definition works in many contexts but
it means that apostrophes in contractions and possessives form word
boundaries, which may not be the desired result:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="s">"they're bill's friends from the UK"</span><span class="o">.</span><span class="n">title</span><span class="p">()</span>
<span class="go">"They'Re Bill'S Friends From The Uk"</span>
</pre></div>
</div>
<p>A workaround for apostrophes can be constructed using regular expressions:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">re</span>
<span class="gp">>>> </span><span class="k">def</span> <span class="nf">titlecase</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
<span class="go"> return re.sub(r"[A-Za-z]+('[A-Za-z]+)?",</span>
<span class="go"> lambda mo: mo.group(0)[0].upper() +</span>
<span class="go"> mo.group(0)[1:].lower(),</span>
<span class="go"> s)</span>
<span class="gp">>>> </span><span class="n">titlecase</span><span class="p">(</span><span class="s">"they're bill's friends."</span><span class="p">)</span>
<span class="go">"They're Bill's Friends."</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="str.translate">
<tt class="descclassname">str.</tt><tt class="descname">translate</tt><big>(</big><em>map</em><big>)</big><a class="headerlink" href="#str.translate" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the <em>s</em> where all characters have been mapped through the
<em>map</em> which must be a dictionary of Unicode ordinals (integers) to Unicode
ordinals, strings or <tt class="xref docutils literal"><span class="pre">None</span></tt>. Unmapped characters are left untouched.
Characters mapped to <tt class="xref docutils literal"><span class="pre">None</span></tt> are deleted.</p>
<p>You can use <a class="reference internal" href="#str.maketrans" title="str.maketrans"><tt class="xref py py-meth docutils literal"><span class="pre">str.maketrans()</span></tt></a> to create a translation map from
character-to-character mappings in different formats.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">An even more flexible approach is to create a custom character mapping
codec using the <a class="reference internal" href="codecs.html#module-codecs" title="codecs: Encode and decode data and streams."><tt class="xref py py-mod docutils literal"><span class="pre">codecs</span></tt></a> module (see <tt class="xref py py-mod docutils literal"><span class="pre">encodings.cp1251</span></tt> for an
example).</p>
</div>
</dd></dl>
<dl class="method">
<dt id="str.upper">
<tt class="descclassname">str.</tt><tt class="descname">upper</tt><big>(</big><big>)</big><a class="headerlink" href="#str.upper" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the string with all the cased characters <a class="footnote-reference" href="#id14" id="id9">[4]</a> converted to
uppercase. Note that <tt class="docutils literal"><span class="pre">str.upper().isupper()</span></tt> might be <tt class="xref docutils literal"><span class="pre">False</span></tt> if <tt class="docutils literal"><span class="pre">s</span></tt>
contains uncased characters or if the Unicode category of the resulting
character(s) is not “Lu” (Letter, uppercase), but e.g. “Lt” (Letter, titlecase).</p>
</dd></dl>
<dl class="method">
<dt id="str.zfill">
<tt class="descclassname">str.</tt><tt class="descname">zfill</tt><big>(</big><em>width</em><big>)</big><a class="headerlink" href="#str.zfill" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the numeric string left filled with zeros in a string of length
<em>width</em>. A sign prefix is handled correctly. The original string is
returned if <em>width</em> is less than <tt class="docutils literal"><span class="pre">len(s)</span></tt>.</p>
</dd></dl>
</div>
<div class="section" id="old-string-formatting-operations">
<span id="old-string-formatting"></span><h3>4.6.2. Old String Formatting Operations<a class="headerlink" href="#old-string-formatting-operations" title="Permalink to this headline">¶</a></h3>
<span class="target" id="index-22"></span><div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The formatting operations described here are obsolete and may go away in future
versions of Python. Use the new <a class="reference internal" href="string.html#string-formatting"><em>String Formatting</em></a> in new code.</p>
</div>
<p>String objects have one unique built-in operation: the <tt class="docutils literal"><span class="pre">%</span></tt> operator (modulo).
This is also known as the string <em>formatting</em> or <em>interpolation</em> operator.
Given <tt class="docutils literal"><span class="pre">format</span> <span class="pre">%</span> <span class="pre">values</span></tt> (where <em>format</em> is a string), <tt class="docutils literal"><span class="pre">%</span></tt> conversion
specifications in <em>format</em> are replaced with zero or more elements of <em>values</em>.
The effect is similar to the using <tt class="xref c c-func docutils literal"><span class="pre">sprintf()</span></tt> in the C language.</p>
<p>If <em>format</em> requires a single argument, <em>values</em> may be a single non-tuple
object. <a class="footnote-reference" href="#id15" id="id10">[5]</a> Otherwise, <em>values</em> must be a tuple with exactly the number of
items specified by the format string, or a single mapping object (for example, a
dictionary).</p>
<p>A conversion specifier contains two or more characters and has the following
components, which must occur in this order:</p>
<ol class="arabic simple">
<li>The <tt class="docutils literal"><span class="pre">'%'</span></tt> character, which marks the start of the specifier.</li>
<li>Mapping key (optional), consisting of a parenthesised sequence of characters
(for example, <tt class="docutils literal"><span class="pre">(somename)</span></tt>).</li>
<li>Conversion flags (optional), which affect the result of some conversion
types.</li>
<li>Minimum field width (optional). If specified as an <tt class="docutils literal"><span class="pre">'*'</span></tt> (asterisk), the
actual width is read from the next element of the tuple in <em>values</em>, and the
object to convert comes after the minimum field width and optional precision.</li>
<li>Precision (optional), given as a <tt class="docutils literal"><span class="pre">'.'</span></tt> (dot) followed by the precision. If
specified as <tt class="docutils literal"><span class="pre">'*'</span></tt> (an asterisk), the actual precision is read from the next
element of the tuple in <em>values</em>, and the value to convert comes after the
precision.</li>
<li>Length modifier (optional).</li>
<li>Conversion type.</li>
</ol>
<p>When the right argument is a dictionary (or other mapping type), then the
formats in the string <em>must</em> include a parenthesised mapping key into that
dictionary inserted immediately after the <tt class="docutils literal"><span class="pre">'%'</span></tt> character. The mapping key
selects the value to be formatted from the mapping. For example:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s">'%(language)s has %(number)03d quote types.'</span> <span class="o">%</span>
<span class="gp">... </span> <span class="p">{</span><span class="s">'language'</span><span class="p">:</span> <span class="s">"Python"</span><span class="p">,</span> <span class="s">"number"</span><span class="p">:</span> <span class="mi">2</span><span class="p">})</span>
<span class="go">Python has 002 quote types.</span>
</pre></div>
</div>
<p>In this case no <tt class="docutils literal"><span class="pre">*</span></tt> specifiers may occur in a format (since they require a
sequential parameter list).</p>
<p>The conversion flag characters are:</p>
<table border="1" class="docutils">
<colgroup>
<col width="12%" />
<col width="88%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Flag</th>
<th class="head">Meaning</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">'#'</span></tt></td>
<td>The value conversion will use the “alternate form” (where defined
below).</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'0'</span></tt></td>
<td>The conversion will be zero padded for numeric values.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'-'</span></tt></td>
<td>The converted value is left adjusted (overrides the <tt class="docutils literal"><span class="pre">'0'</span></tt>
conversion if both are given).</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'</span> <span class="pre">'</span></tt></td>
<td>(a space) A blank should be left before a positive number (or empty
string) produced by a signed conversion.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'+'</span></tt></td>
<td>A sign character (<tt class="docutils literal"><span class="pre">'+'</span></tt> or <tt class="docutils literal"><span class="pre">'-'</span></tt>) will precede the conversion
(overrides a “space” flag).</td>
</tr>
</tbody>
</table>
<p>A length modifier (<tt class="docutils literal"><span class="pre">h</span></tt>, <tt class="docutils literal"><span class="pre">l</span></tt>, or <tt class="docutils literal"><span class="pre">L</span></tt>) may be present, but is ignored as it
is not necessary for Python – so e.g. <tt class="docutils literal"><span class="pre">%ld</span></tt> is identical to <tt class="docutils literal"><span class="pre">%d</span></tt>.</p>
<p>The conversion types are:</p>
<table border="1" class="docutils">
<colgroup>
<col width="17%" />
<col width="74%" />
<col width="10%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Conversion</th>
<th class="head">Meaning</th>
<th class="head">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">'d'</span></tt></td>
<td>Signed integer decimal.</td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'i'</span></tt></td>
<td>Signed integer decimal.</td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'o'</span></tt></td>
<td>Signed octal value.</td>
<td>(1)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'u'</span></tt></td>
<td>Obsolete type – it is identical to <tt class="docutils literal"><span class="pre">'d'</span></tt>.</td>
<td>(7)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'x'</span></tt></td>
<td>Signed hexadecimal (lowercase).</td>
<td>(2)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'X'</span></tt></td>
<td>Signed hexadecimal (uppercase).</td>
<td>(2)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'e'</span></tt></td>
<td>Floating point exponential format (lowercase).</td>
<td>(3)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'E'</span></tt></td>
<td>Floating point exponential format (uppercase).</td>
<td>(3)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'f'</span></tt></td>
<td>Floating point decimal format.</td>
<td>(3)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'F'</span></tt></td>
<td>Floating point decimal format.</td>
<td>(3)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'g'</span></tt></td>
<td>Floating point format. Uses lowercase exponential
format if exponent is less than -4 or not less than
precision, decimal format otherwise.</td>
<td>(4)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'G'</span></tt></td>
<td>Floating point format. Uses uppercase exponential
format if exponent is less than -4 or not less than
precision, decimal format otherwise.</td>
<td>(4)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'c'</span></tt></td>
<td>Single character (accepts integer or single
character string).</td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'r'</span></tt></td>
<td>String (converts any Python object using
<a class="reference internal" href="functions.html#repr" title="repr"><tt class="xref py py-func docutils literal"><span class="pre">repr()</span></tt></a>).</td>
<td>(5)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'s'</span></tt></td>
<td>String (converts any Python object using
<a class="reference internal" href="functions.html#str" title="str"><tt class="xref py py-func docutils literal"><span class="pre">str()</span></tt></a>).</td>
<td>(5)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'a'</span></tt></td>
<td>String (converts any Python object using
<a class="reference internal" href="functions.html#ascii" title="ascii"><tt class="xref py py-func docutils literal"><span class="pre">ascii()</span></tt></a>).</td>
<td>(5)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">'%'</span></tt></td>
<td>No argument is converted, results in a <tt class="docutils literal"><span class="pre">'%'</span></tt>
character in the result.</td>
<td> </td>
</tr>
</tbody>
</table>
<p>Notes:</p>
<ol class="arabic">
<li><p class="first">The alternate form causes a leading zero (<tt class="docutils literal"><span class="pre">'0'</span></tt>) to be inserted between
left-hand padding and the formatting of the number if the leading character
of the result is not already a zero.</p>
</li>
<li><p class="first">The alternate form causes a leading <tt class="docutils literal"><span class="pre">'0x'</span></tt> or <tt class="docutils literal"><span class="pre">'0X'</span></tt> (depending on whether
the <tt class="docutils literal"><span class="pre">'x'</span></tt> or <tt class="docutils literal"><span class="pre">'X'</span></tt> format was used) to be inserted between left-hand padding
and the formatting of the number if the leading character of the result is not
already a zero.</p>
</li>
<li><p class="first">The alternate form causes the result to always contain a decimal point, even if
no digits follow it.</p>
<p>The precision determines the number of digits after the decimal point and
defaults to 6.</p>
</li>
<li><p class="first">The alternate form causes the result to always contain a decimal point, and
trailing zeroes are not removed as they would otherwise be.</p>
<p>The precision determines the number of significant digits before and after the
decimal point and defaults to 6.</p>
</li>
<li><p class="first">If precision is <tt class="docutils literal"><span class="pre">N</span></tt>, the output is truncated to <tt class="docutils literal"><span class="pre">N</span></tt> characters.</p>
</li>
</ol>
<ol class="arabic simple" start="7">
<li>See <span class="target" id="index-23"></span><a class="pep reference external" href="http://www.python.org/dev/peps/pep-0237"><strong>PEP 237</strong></a>.</li>
</ol>
<p>Since Python strings have an explicit length, <tt class="docutils literal"><span class="pre">%s</span></tt> conversions do not assume
that <tt class="docutils literal"><span class="pre">'\0'</span></tt> is the end of the string.</p>
<p class="versionchanged">
<span class="versionmodified">Changed in version 3.1: </span><tt class="docutils literal"><span class="pre">%f</span></tt> conversions for numbers whose absolute value is over 1e50 are no
longer replaced by <tt class="docutils literal"><span class="pre">%g</span></tt> conversions.</p>
<p id="index-24">Additional string operations are defined in standard modules <a class="reference internal" href="string.html#module-string" title="string: Common string operations."><tt class="xref py py-mod docutils literal"><span class="pre">string</span></tt></a> and
<a class="reference internal" href="re.html#module-re" title="re: Regular expression operations."><tt class="xref py py-mod docutils literal"><span class="pre">re</span></tt></a>.</p>
</div>
<div class="section" id="range-type">
<span id="typesseq-range"></span><h3>4.6.3. Range Type<a class="headerlink" href="#range-type" title="Permalink to this headline">¶</a></h3>
<p id="index-25">The <a class="reference internal" href="functions.html#range" title="range"><tt class="xref py py-class docutils literal"><span class="pre">range</span></tt></a> type is an immutable sequence which is commonly used for
looping. The advantage of the <a class="reference internal" href="functions.html#range" title="range"><tt class="xref py py-class docutils literal"><span class="pre">range</span></tt></a> type is that an <a class="reference internal" href="functions.html#range" title="range"><tt class="xref py py-class docutils literal"><span class="pre">range</span></tt></a>
object will always take the same amount of memory, no matter the size of the
range it represents.</p>
<p>Range objects have relatively little behavior: they support indexing, contains,
iteration, the <a class="reference internal" href="functions.html#len" title="len"><tt class="xref py py-func docutils literal"><span class="pre">len()</span></tt></a> function, and the following methods:</p>
<dl class="method">
<dt id="range.count">
<tt class="descclassname">range.</tt><tt class="descname">count</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#range.count" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the number of <em>i</em>‘s for which <tt class="docutils literal"><span class="pre">s[i]</span> <span class="pre">==</span> <span class="pre">x</span></tt>.</p>
<blockquote>
<div><p class="versionadded">
<span class="versionmodified">New in version 3.2.</span></p>
</div></blockquote>
</dd></dl>
<dl class="method">
<dt id="range.index">
<tt class="descclassname">range.</tt><tt class="descname">index</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#range.index" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the smallest <em>i</em> such that <tt class="docutils literal"><span class="pre">s[i]</span> <span class="pre">==</span> <span class="pre">x</span></tt>. Raises
<a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><tt class="xref py py-exc docutils literal"><span class="pre">ValueError</span></tt></a> when <em>x</em> is not in the range.</p>
<blockquote>
<div><p class="versionadded">
<span class="versionmodified">New in version 3.2.</span></p>
</div></blockquote>
</dd></dl>
</div>
<div class="section" id="mutable-sequence-types">
<span id="typesseq-mutable"></span><h3>4.6.4. Mutable Sequence Types<a class="headerlink" href="#mutable-sequence-types" title="Permalink to this headline">¶</a></h3>
<p id="index-26">List and bytearray objects support additional operations that allow in-place
modification of the object. Other mutable sequence types (when added to the
language) should also support these operations. Strings and tuples are
immutable sequence types: such objects cannot be modified once created. The
following operations are defined on mutable sequence types (where <em>x</em> is an
arbitrary object).</p>
<p>Note that while lists allow their items to be of any type, bytearray object
“items” are all integers in the range 0 <= x < 256.</p>
<table border="1" class="docutils" id="index-27">
<colgroup>
<col width="36%" />
<col width="39%" />
<col width="25%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Operation</th>
<th class="head">Result</th>
<th class="head">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">s[i]</span> <span class="pre">=</span> <span class="pre">x</span></tt></td>
<td>item <em>i</em> of <em>s</em> is replaced by
<em>x</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s[i:j]</span> <span class="pre">=</span> <span class="pre">t</span></tt></td>
<td>slice of <em>s</em> from <em>i</em> to <em>j</em>
is replaced by the contents of
the iterable <em>t</em></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">del</span> <span class="pre">s[i:j]</span></tt></td>
<td>same as <tt class="docutils literal"><span class="pre">s[i:j]</span> <span class="pre">=</span> <span class="pre">[]</span></tt></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s[i:j:k]</span> <span class="pre">=</span> <span class="pre">t</span></tt></td>
<td>the elements of <tt class="docutils literal"><span class="pre">s[i:j:k]</span></tt>
are replaced by those of <em>t</em></td>
<td>(1)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">del</span> <span class="pre">s[i:j:k]</span></tt></td>
<td>removes the elements of
<tt class="docutils literal"><span class="pre">s[i:j:k]</span></tt> from the list</td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.append(x)</span></tt></td>
<td>same as <tt class="docutils literal"><span class="pre">s[len(s):len(s)]</span> <span class="pre">=</span>
<span class="pre">[x]</span></tt></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.extend(x)</span></tt></td>
<td>same as <tt class="docutils literal"><span class="pre">s[len(s):len(s)]</span> <span class="pre">=</span>
<span class="pre">x</span></tt></td>
<td>(2)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.count(x)</span></tt></td>
<td>return number of <em>i</em>‘s for
which <tt class="docutils literal"><span class="pre">s[i]</span> <span class="pre">==</span> <span class="pre">x</span></tt></td>
<td> </td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.index(x[,</span> <span class="pre">i[,</span> <span class="pre">j]])</span></tt></td>
<td>return smallest <em>k</em> such that
<tt class="docutils literal"><span class="pre">s[k]</span> <span class="pre">==</span> <span class="pre">x</span></tt> and <tt class="docutils literal"><span class="pre">i</span> <span class="pre"><=</span> <span class="pre">k</span> <span class="pre"><</span>
<span class="pre">j</span></tt></td>
<td>(3)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.insert(i,</span> <span class="pre">x)</span></tt></td>
<td>same as <tt class="docutils literal"><span class="pre">s[i:i]</span> <span class="pre">=</span> <span class="pre">[x]</span></tt></td>
<td>(4)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.pop([i])</span></tt></td>
<td>same as <tt class="docutils literal"><span class="pre">x</span> <span class="pre">=</span> <span class="pre">s[i];</span> <span class="pre">del</span> <span class="pre">s[i];</span>
<span class="pre">return</span> <span class="pre">x</span></tt></td>
<td>(5)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.remove(x)</span></tt></td>
<td>same as <tt class="docutils literal"><span class="pre">del</span> <span class="pre">s[s.index(x)]</span></tt></td>
<td>(3)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.reverse()</span></tt></td>
<td>reverses the items of <em>s</em> in
place</td>
<td>(6)</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">s.sort([key[,</span> <span class="pre">reverse]])</span></tt></td>
<td>sort the items of <em>s</em> in place</td>
<td>(6), (7), (8)</td>
</tr>
</tbody>
</table>
<p>Notes:</p>
<ol class="arabic">
<li><p class="first"><em>t</em> must have the same length as the slice it is replacing.</p>
</li>
<li><p class="first"><em>x</em> can be any iterable object.</p>
</li>
<li><p class="first">Raises <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><tt class="xref py py-exc docutils literal"><span class="pre">ValueError</span></tt></a> when <em>x</em> is not found in <em>s</em>. When a negative index is
passed as the second or third parameter to the <tt class="xref py py-meth docutils literal"><span class="pre">index()</span></tt> method, the sequence
length is added, as for slice indices. If it is still negative, it is truncated
to zero, as for slice indices.</p>
</li>
<li><p class="first">When a negative index is passed as the first parameter to the <tt class="xref py py-meth docutils literal"><span class="pre">insert()</span></tt>
method, the sequence length is added, as for slice indices. If it is still
negative, it is truncated to zero, as for slice indices.</p>
</li>
<li><p class="first">The optional argument <em>i</em> defaults to <tt class="docutils literal"><span class="pre">-1</span></tt>, so that by default the last
item is removed and returned.</p>
</li>
<li><p class="first">The <tt class="xref py py-meth docutils literal"><span class="pre">sort()</span></tt> and <tt class="xref py py-meth docutils literal"><span class="pre">reverse()</span></tt> methods modify the sequence in place for
economy of space when sorting or reversing a large sequence. To remind you
that they operate by side effect, they don’t return the sorted or reversed
sequence.</p>
</li>
<li><p class="first">The <tt class="xref py py-meth docutils literal"><span class="pre">sort()</span></tt> method takes optional arguments for controlling the
comparisons. Each must be specified as a keyword argument.</p>
<p><em>key</em> specifies a function of one argument that is used to extract a comparison
key from each list element: <tt class="docutils literal"><span class="pre">key=str.lower</span></tt>. The default value is <tt class="xref docutils literal"><span class="pre">None</span></tt>.
Use <a class="reference internal" href="functools.html#functools.cmp_to_key" title="functools.cmp_to_key"><tt class="xref py py-func docutils literal"><span class="pre">functools.cmp_to_key()</span></tt></a> to convert an
old-style <em>cmp</em> function to a <em>key</em> function.</p>
<p><em>reverse</em> is a boolean value. If set to <tt class="xref docutils literal"><span class="pre">True</span></tt>, then the list elements are
sorted as if each comparison were reversed.</p>
<p>The <tt class="xref py py-meth docutils literal"><span class="pre">sort()</span></tt> method is guaranteed to be stable. A
sort is stable if it guarantees not to change the relative order of elements
that compare equal — this is helpful for sorting in multiple passes (for
example, sort by department, then by salary grade).</p>
<div class="impl-detail compound">
<p><strong>CPython implementation detail:</strong> While a list is being sorted, the effect of attempting to mutate, or even
inspect, the list is undefined. The C implementation of Python makes the
list appear empty for the duration, and raises <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><tt class="xref py py-exc docutils literal"><span class="pre">ValueError</span></tt></a> if it can
detect that the list has been mutated during a sort.</p>
</div>
</li>
<li><p class="first"><tt class="xref py py-meth docutils literal"><span class="pre">sort()</span></tt> is not supported by <a class="reference internal" href="functions.html#bytearray" title="bytearray"><tt class="xref py py-class docutils literal"><span class="pre">bytearray</span></tt></a> objects.</p>
</li>
</ol>
</div>
<div class="section" id="bytes-and-byte-array-methods">
<span id="bytes-methods"></span><h3>4.6.5. Bytes and Byte Array Methods<a class="headerlink" href="#bytes-and-byte-array-methods" title="Permalink to this headline">¶</a></h3>
<p id="index-28">Bytes and bytearray objects, being “strings of bytes”, have all methods found on
strings, with the exception of <tt class="xref py py-func docutils literal"><span class="pre">encode()</span></tt>, <a class="reference internal" href="functions.html#format" title="format"><tt class="xref py py-func docutils literal"><span class="pre">format()</span></tt></a> and
<tt class="xref py py-func docutils literal"><span class="pre">isidentifier()</span></tt>, which do not make sense with these types. For converting
the objects to strings, they have a <tt class="xref py py-func docutils literal"><span class="pre">decode()</span></tt> method.</p>
<p>Wherever one of these methods needs to interpret the bytes as characters
(e.g. the <tt class="xref py py-func docutils literal"><span class="pre">is...()</span></tt> methods), the ASCII character set is assumed.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p>The methods on bytes and bytearray objects don’t accept strings as their
arguments, just as the methods on strings don’t accept bytes as their
arguments. For example, you have to write</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="n">a</span> <span class="o">=</span> <span class="s">"abc"</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s">"a"</span><span class="p">,</span> <span class="s">"f"</span><span class="p">)</span>
</pre></div>
</div>
<p>and</p>
<div class="last highlight-python3"><div class="highlight"><pre><span class="n">a</span> <span class="o">=</span> <span class="n">b</span><span class="s">"abc"</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="n">b</span><span class="s">"a"</span><span class="p">,</span> <span class="n">b</span><span class="s">"f"</span><span class="p">)</span>
</pre></div>
</div>
</div>
<dl class="method">
<dt id="bytes.decode">
<tt class="descclassname">bytes.</tt><tt class="descname">decode</tt><big>(</big><em>encoding="utf-8"</em>, <em>errors="strict"</em><big>)</big><a class="headerlink" href="#bytes.decode" title="Permalink to this definition">¶</a></dt>
<dt id="bytearray.decode">
<tt class="descclassname">bytearray.</tt><tt class="descname">decode</tt><big>(</big><em>encoding="utf-8"</em>, <em>errors="strict"</em><big>)</big><a class="headerlink" href="#bytearray.decode" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a string decoded from the given bytes. Default encoding is
<tt class="docutils literal"><span class="pre">'utf-8'</span></tt>. <em>errors</em> may be given to set a different
error handling scheme. The default for <em>errors</em> is <tt class="docutils literal"><span class="pre">'strict'</span></tt>, meaning
that encoding errors raise a <a class="reference internal" href="exceptions.html#UnicodeError" title="UnicodeError"><tt class="xref py py-exc docutils literal"><span class="pre">UnicodeError</span></tt></a>. Other possible values are
<tt class="docutils literal"><span class="pre">'ignore'</span></tt>, <tt class="docutils literal"><span class="pre">'replace'</span></tt> and any other name registered via
<a class="reference internal" href="codecs.html#codecs.register_error" title="codecs.register_error"><tt class="xref py py-func docutils literal"><span class="pre">codecs.register_error()</span></tt></a>, see section <a class="reference internal" href="codecs.html#codec-base-classes"><em>Codec Base Classes</em></a>. For a
list of possible encodings, see section <a class="reference internal" href="codecs.html#standard-encodings"><em>Standard Encodings</em></a>.</p>
<p class="versionchanged">
<span class="versionmodified">Changed in version 3.1: </span>Added support for keyword arguments.</p>
</dd></dl>
<p>The bytes and bytearray types have an additional class method:</p>
<dl class="classmethod">
<dt id="bytes.fromhex">
<em class="property">classmethod </em><tt class="descclassname">bytes.</tt><tt class="descname">fromhex</tt><big>(</big><em>string</em><big>)</big><a class="headerlink" href="#bytes.fromhex" title="Permalink to this definition">¶</a></dt>
<dt id="bytearray.fromhex">
<em class="property">classmethod </em><tt class="descclassname">bytearray.</tt><tt class="descname">fromhex</tt><big>(</big><em>string</em><big>)</big><a class="headerlink" href="#bytearray.fromhex" title="Permalink to this definition">¶</a></dt>
<dd><p>This <a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a> class method returns a bytes or bytearray object,
decoding the given string object. The string must contain two hexadecimal
digits per byte, spaces are ignored.</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">bytes</span><span class="o">.</span><span class="n">fromhex</span><span class="p">(</span><span class="s">'f0 f1f2 '</span><span class="p">)</span>
<span class="go">b'\xf0\xf1\xf2'</span>
</pre></div>
</div>
</dd></dl>
<p>The maketrans and translate methods differ in semantics from the versions
available on strings:</p>
<dl class="method">
<dt id="bytes.translate">
<tt class="descclassname">bytes.</tt><tt class="descname">translate</tt><big>(</big><em>table</em><span class="optional">[</span>, <em>delete</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#bytes.translate" title="Permalink to this definition">¶</a></dt>
<dt id="bytearray.translate">
<tt class="descclassname">bytearray.</tt><tt class="descname">translate</tt><big>(</big><em>table</em><span class="optional">[</span>, <em>delete</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#bytearray.translate" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the bytes or bytearray object where all bytes occurring in
the optional argument <em>delete</em> are removed, and the remaining bytes have been
mapped through the given translation table, which must be a bytes object of
length 256.</p>
<p>You can use the <a class="reference internal" href="#bytes.maketrans" title="bytes.maketrans"><tt class="xref py py-func docutils literal"><span class="pre">bytes.maketrans()</span></tt></a> method to create a translation table.</p>
<p>Set the <em>table</em> argument to <tt class="xref docutils literal"><span class="pre">None</span></tt> for translations that only delete
characters:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">b</span><span class="s">'read this short text'</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="k">None</span><span class="p">,</span> <span class="n">b</span><span class="s">'aeiou'</span><span class="p">)</span>
<span class="go">b'rd ths shrt txt'</span>
</pre></div>
</div>
</dd></dl>
<dl class="staticmethod">
<dt id="bytes.maketrans">
<em class="property">static </em><tt class="descclassname">bytes.</tt><tt class="descname">maketrans</tt><big>(</big><em>from</em>, <em>to</em><big>)</big><a class="headerlink" href="#bytes.maketrans" title="Permalink to this definition">¶</a></dt>
<dt id="bytearray.maketrans">
<em class="property">static </em><tt class="descclassname">bytearray.</tt><tt class="descname">maketrans</tt><big>(</big><em>from</em>, <em>to</em><big>)</big><a class="headerlink" href="#bytearray.maketrans" title="Permalink to this definition">¶</a></dt>
<dd><p>This static method returns a translation table usable for
<a class="reference internal" href="#bytes.translate" title="bytes.translate"><tt class="xref py py-meth docutils literal"><span class="pre">bytes.translate()</span></tt></a> that will map each character in <em>from</em> into the
character at the same position in <em>to</em>; <em>from</em> and <em>to</em> must be bytes objects
and have the same length.</p>
<p class="versionadded">
<span class="versionmodified">New in version 3.1.</span></p>
</dd></dl>
</div>
</div>
<div class="section" id="set-types-set-frozenset">
<span id="types-set"></span><h2>4.7. Set Types — <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a>, <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a><a class="headerlink" href="#set-types-set-frozenset" title="Permalink to this headline">¶</a></h2>
<p id="index-29">A <em class="dfn">set</em> object is an unordered collection of distinct <a class="reference internal" href="../glossary.html#term-hashable"><em class="xref std std-term">hashable</em></a> objects.
Common uses include membership testing, removing duplicates from a sequence, and
computing mathematical operations such as intersection, union, difference, and
symmetric difference.
(For other containers see the built in <a class="reference internal" href="#dict" title="dict"><tt class="xref py py-class docutils literal"><span class="pre">dict</span></tt></a>, <a class="reference internal" href="functions.html#list" title="list"><tt class="xref py py-class docutils literal"><span class="pre">list</span></tt></a>,
and <a class="reference internal" href="functions.html#tuple" title="tuple"><tt class="xref py py-class docutils literal"><span class="pre">tuple</span></tt></a> classes, and the <a class="reference internal" href="collections.html#module-collections" title="collections: Container datatypes"><tt class="xref py py-mod docutils literal"><span class="pre">collections</span></tt></a> module.)</p>
<p>Like other collections, sets support <tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">set</span></tt>, <tt class="docutils literal"><span class="pre">len(set)</span></tt>, and <tt class="docutils literal"><span class="pre">for</span> <span class="pre">x</span> <span class="pre">in</span>
<span class="pre">set</span></tt>. Being an unordered collection, sets do not record element position or
order of insertion. Accordingly, sets do not support indexing, slicing, or
other sequence-like behavior.</p>
<p>There are currently two built-in set types, <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> and <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a>.
The <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> type is mutable — the contents can be changed using methods
like <tt class="xref py py-meth docutils literal"><span class="pre">add()</span></tt> and <tt class="xref py py-meth docutils literal"><span class="pre">remove()</span></tt>. Since it is mutable, it has no hash value
and cannot be used as either a dictionary key or as an element of another set.
The <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a> type is immutable and <a class="reference internal" href="../glossary.html#term-hashable"><em class="xref std std-term">hashable</em></a> — its contents cannot be
altered after it is created; it can therefore be used as a dictionary key or as
an element of another set.</p>
<p>Non-empty sets (not frozensets) can be created by placing a comma-separated list
of elements within braces, for example: <tt class="docutils literal"><span class="pre">{'jack',</span> <span class="pre">'sjoerd'}</span></tt>, in addition to the
<a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> constructor.</p>
<p>The constructors for both classes work the same:</p>
<dl class="class">
<dt id="set">
<em class="property">class </em><tt class="descname">set</tt><big>(</big><span class="optional">[</span><em>iterable</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#set" title="Permalink to this definition">¶</a></dt>
<dt id="frozenset">
<em class="property">class </em><tt class="descname">frozenset</tt><big>(</big><span class="optional">[</span><em>iterable</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#frozenset" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a new set or frozenset object whose elements are taken from
<em>iterable</em>. The elements of a set must be hashable. To represent sets of
sets, the inner sets must be <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a> objects. If <em>iterable</em> is
not specified, a new empty set is returned.</p>
<p>Instances of <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> and <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a> provide the following
operations:</p>
<dl class="describe">
<dt>
<tt class="descname">len(s)</tt></dt>
<dd><p>Return the cardinality of set <em>s</em>.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">x in s</tt></dt>
<dd><p>Test <em>x</em> for membership in <em>s</em>.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">x not in s</tt></dt>
<dd><p>Test <em>x</em> for non-membership in <em>s</em>.</p>
</dd></dl>
<dl class="method">
<dt id="set.isdisjoint">
<tt class="descname">isdisjoint</tt><big>(</big><em>other</em><big>)</big><a class="headerlink" href="#set.isdisjoint" title="Permalink to this definition">¶</a></dt>
<dd><p>Return True if the set has no elements in common with <em>other</em>. Sets are
disjoint if and only if their intersection is the empty set.</p>
</dd></dl>
<dl class="method">
<dt id="set.issubset">
<tt class="descname">issubset</tt><big>(</big><em>other</em><big>)</big><a class="headerlink" href="#set.issubset" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set <= other</tt></dt>
<dd><p>Test whether every element in the set is in <em>other</em>.</p>
</dd></dl>
<dl class="method">
<dt>
<tt class="descname">set < other</tt></dt>
<dd><p>Test whether the set is a true subset of <em>other</em>, that is,
<tt class="docutils literal"><span class="pre">set</span> <span class="pre"><=</span> <span class="pre">other</span> <span class="pre">and</span> <span class="pre">set</span> <span class="pre">!=</span> <span class="pre">other</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="set.issuperset">
<tt class="descname">issuperset</tt><big>(</big><em>other</em><big>)</big><a class="headerlink" href="#set.issuperset" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set >= other</tt></dt>
<dd><p>Test whether every element in <em>other</em> is in the set.</p>
</dd></dl>
<dl class="method">
<dt>
<tt class="descname">set > other</tt></dt>
<dd><p>Test whether the set is a true superset of <em>other</em>, that is, <tt class="docutils literal"><span class="pre">set</span> <span class="pre">>=</span>
<span class="pre">other</span> <span class="pre">and</span> <span class="pre">set</span> <span class="pre">!=</span> <span class="pre">other</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="set.union">
<tt class="descname">union</tt><big>(</big><em>other</em>, <em>...</em><big>)</big><a class="headerlink" href="#set.union" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set | other | ...</tt></dt>
<dd><p>Return a new set with elements from the set and all others.</p>
</dd></dl>
<dl class="method">
<dt id="set.intersection">
<tt class="descname">intersection</tt><big>(</big><em>other</em>, <em>...</em><big>)</big><a class="headerlink" href="#set.intersection" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set & other & ...</tt></dt>
<dd><p>Return a new set with elements common to the set and all others.</p>
</dd></dl>
<dl class="method">
<dt id="set.difference">
<tt class="descname">difference</tt><big>(</big><em>other</em>, <em>...</em><big>)</big><a class="headerlink" href="#set.difference" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set - other - ...</tt></dt>
<dd><p>Return a new set with elements in the set that are not in the others.</p>
</dd></dl>
<dl class="method">
<dt id="set.symmetric_difference">
<tt class="descname">symmetric_difference</tt><big>(</big><em>other</em><big>)</big><a class="headerlink" href="#set.symmetric_difference" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set ^ other</tt></dt>
<dd><p>Return a new set with elements in either the set or <em>other</em> but not both.</p>
</dd></dl>
<dl class="method">
<dt id="set.copy">
<tt class="descname">copy</tt><big>(</big><big>)</big><a class="headerlink" href="#set.copy" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a new set with a shallow copy of <em>s</em>.</p>
</dd></dl>
<p>Note, the non-operator versions of <a class="reference internal" href="#set.union" title="set.union"><tt class="xref py py-meth docutils literal"><span class="pre">union()</span></tt></a>, <a class="reference internal" href="#set.intersection" title="set.intersection"><tt class="xref py py-meth docutils literal"><span class="pre">intersection()</span></tt></a>,
<a class="reference internal" href="#set.difference" title="set.difference"><tt class="xref py py-meth docutils literal"><span class="pre">difference()</span></tt></a>, and <a class="reference internal" href="#set.symmetric_difference" title="set.symmetric_difference"><tt class="xref py py-meth docutils literal"><span class="pre">symmetric_difference()</span></tt></a>, <a class="reference internal" href="#set.issubset" title="set.issubset"><tt class="xref py py-meth docutils literal"><span class="pre">issubset()</span></tt></a>, and
<a class="reference internal" href="#set.issuperset" title="set.issuperset"><tt class="xref py py-meth docutils literal"><span class="pre">issuperset()</span></tt></a> methods will accept any iterable as an argument. In
contrast, their operator based counterparts require their arguments to be
sets. This precludes error-prone constructions like <tt class="docutils literal"><span class="pre">set('abc')</span> <span class="pre">&</span> <span class="pre">'cbs'</span></tt>
in favor of the more readable <tt class="docutils literal"><span class="pre">set('abc').intersection('cbs')</span></tt>.</p>
<p>Both <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> and <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a> support set to set comparisons. Two
sets are equal if and only if every element of each set is contained in the
other (each is a subset of the other). A set is less than another set if and
only if the first set is a proper subset of the second set (is a subset, but
is not equal). A set is greater than another set if and only if the first set
is a proper superset of the second set (is a superset, but is not equal).</p>
<p>Instances of <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> are compared to instances of <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a>
based on their members. For example, <tt class="docutils literal"><span class="pre">set('abc')</span> <span class="pre">==</span> <span class="pre">frozenset('abc')</span></tt>
returns <tt class="xref docutils literal"><span class="pre">True</span></tt> and so does <tt class="docutils literal"><span class="pre">set('abc')</span> <span class="pre">in</span> <span class="pre">set([frozenset('abc')])</span></tt>.</p>
<p>The subset and equality comparisons do not generalize to a complete ordering
function. For example, any two disjoint sets are not equal and are not
subsets of each other, so <em>all</em> of the following return <tt class="xref docutils literal"><span class="pre">False</span></tt>: <tt class="docutils literal"><span class="pre">a<b</span></tt>,
<tt class="docutils literal"><span class="pre">a==b</span></tt>, or <tt class="docutils literal"><span class="pre">a>b</span></tt>.</p>
<p>Since sets only define partial ordering (subset relationships), the output of
the <tt class="xref py py-meth docutils literal"><span class="pre">list.sort()</span></tt> method is undefined for lists of sets.</p>
<p>Set elements, like dictionary keys, must be <a class="reference internal" href="../glossary.html#term-hashable"><em class="xref std std-term">hashable</em></a>.</p>
<p>Binary operations that mix <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> instances with <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a>
return the type of the first operand. For example: <tt class="docutils literal"><span class="pre">frozenset('ab')</span> <span class="pre">|</span>
<span class="pre">set('bc')</span></tt> returns an instance of <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a>.</p>
<p>The following table lists operations available for <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a> that do not
apply to immutable instances of <a class="reference internal" href="#frozenset" title="frozenset"><tt class="xref py py-class docutils literal"><span class="pre">frozenset</span></tt></a>:</p>
<dl class="method">
<dt id="set.update">
<tt class="descname">update</tt><big>(</big><em>other</em>, <em>...</em><big>)</big><a class="headerlink" href="#set.update" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set |= other | ...</tt></dt>
<dd><p>Update the set, adding elements from all others.</p>
</dd></dl>
<dl class="method">
<dt id="set.intersection_update">
<tt class="descname">intersection_update</tt><big>(</big><em>other</em>, <em>...</em><big>)</big><a class="headerlink" href="#set.intersection_update" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set &= other & ...</tt></dt>
<dd><p>Update the set, keeping only elements found in it and all others.</p>
</dd></dl>
<dl class="method">
<dt id="set.difference_update">
<tt class="descname">difference_update</tt><big>(</big><em>other</em>, <em>...</em><big>)</big><a class="headerlink" href="#set.difference_update" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set -= other | ...</tt></dt>
<dd><p>Update the set, removing elements found in others.</p>
</dd></dl>
<dl class="method">
<dt id="set.symmetric_difference_update">
<tt class="descname">symmetric_difference_update</tt><big>(</big><em>other</em><big>)</big><a class="headerlink" href="#set.symmetric_difference_update" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descname">set ^= other</tt></dt>
<dd><p>Update the set, keeping only elements found in either set, but not in both.</p>
</dd></dl>
<dl class="method">
<dt id="set.add">
<tt class="descname">add</tt><big>(</big><em>elem</em><big>)</big><a class="headerlink" href="#set.add" title="Permalink to this definition">¶</a></dt>
<dd><p>Add element <em>elem</em> to the set.</p>
</dd></dl>
<dl class="method">
<dt id="set.remove">
<tt class="descname">remove</tt><big>(</big><em>elem</em><big>)</big><a class="headerlink" href="#set.remove" title="Permalink to this definition">¶</a></dt>
<dd><p>Remove element <em>elem</em> from the set. Raises <a class="reference internal" href="exceptions.html#KeyError" title="KeyError"><tt class="xref py py-exc docutils literal"><span class="pre">KeyError</span></tt></a> if <em>elem</em> is
not contained in the set.</p>
</dd></dl>
<dl class="method">
<dt id="set.discard">
<tt class="descname">discard</tt><big>(</big><em>elem</em><big>)</big><a class="headerlink" href="#set.discard" title="Permalink to this definition">¶</a></dt>
<dd><p>Remove element <em>elem</em> from the set if it is present.</p>
</dd></dl>
<dl class="method">
<dt id="set.pop">
<tt class="descname">pop</tt><big>(</big><big>)</big><a class="headerlink" href="#set.pop" title="Permalink to this definition">¶</a></dt>
<dd><p>Remove and return an arbitrary element from the set. Raises
<a class="reference internal" href="exceptions.html#KeyError" title="KeyError"><tt class="xref py py-exc docutils literal"><span class="pre">KeyError</span></tt></a> if the set is empty.</p>
</dd></dl>
<dl class="method">
<dt id="set.clear">
<tt class="descname">clear</tt><big>(</big><big>)</big><a class="headerlink" href="#set.clear" title="Permalink to this definition">¶</a></dt>
<dd><p>Remove all elements from the set.</p>
</dd></dl>
<p>Note, the non-operator versions of the <a class="reference internal" href="#set.update" title="set.update"><tt class="xref py py-meth docutils literal"><span class="pre">update()</span></tt></a>,
<a class="reference internal" href="#set.intersection_update" title="set.intersection_update"><tt class="xref py py-meth docutils literal"><span class="pre">intersection_update()</span></tt></a>, <a class="reference internal" href="#set.difference_update" title="set.difference_update"><tt class="xref py py-meth docutils literal"><span class="pre">difference_update()</span></tt></a>, and
<a class="reference internal" href="#set.symmetric_difference_update" title="set.symmetric_difference_update"><tt class="xref py py-meth docutils literal"><span class="pre">symmetric_difference_update()</span></tt></a> methods will accept any iterable as an
argument.</p>
<p>Note, the <em>elem</em> argument to the <a class="reference internal" href="../reference/datamodel.html#object.__contains__" title="object.__contains__"><tt class="xref py py-meth docutils literal"><span class="pre">__contains__()</span></tt></a>, <a class="reference internal" href="#set.remove" title="set.remove"><tt class="xref py py-meth docutils literal"><span class="pre">remove()</span></tt></a>, and
<a class="reference internal" href="#set.discard" title="set.discard"><tt class="xref py py-meth docutils literal"><span class="pre">discard()</span></tt></a> methods may be a set. To support searching for an equivalent
frozenset, the <em>elem</em> set is temporarily mutated during the search and then
restored. During the search, the <em>elem</em> set should not be read or mutated
since it does not have a meaningful value.</p>
</dd></dl>
</div>
<div class="section" id="mapping-types-dict">
<span id="typesmapping"></span><h2>4.8. Mapping Types — <a class="reference internal" href="#dict" title="dict"><tt class="xref py py-class docutils literal"><span class="pre">dict</span></tt></a><a class="headerlink" href="#mapping-types-dict" title="Permalink to this headline">¶</a></h2>
<p id="index-30">A <em class="dfn">mapping</em> object maps <a class="reference internal" href="../glossary.html#term-hashable"><em class="xref std std-term">hashable</em></a> values to arbitrary objects.
Mappings are mutable objects. There is currently only one standard mapping
type, the <em class="dfn">dictionary</em>. (For other containers see the built in
<a class="reference internal" href="functions.html#list" title="list"><tt class="xref py py-class docutils literal"><span class="pre">list</span></tt></a>, <a class="reference internal" href="#set" title="set"><tt class="xref py py-class docutils literal"><span class="pre">set</span></tt></a>, and <a class="reference internal" href="functions.html#tuple" title="tuple"><tt class="xref py py-class docutils literal"><span class="pre">tuple</span></tt></a> classes, and the
<a class="reference internal" href="collections.html#module-collections" title="collections: Container datatypes"><tt class="xref py py-mod docutils literal"><span class="pre">collections</span></tt></a> module.)</p>
<p>A dictionary’s keys are <em>almost</em> arbitrary values. Values that are not
<a class="reference internal" href="../glossary.html#term-hashable"><em class="xref std std-term">hashable</em></a>, that is, values containing lists, dictionaries or other
mutable types (that are compared by value rather than by object identity) may
not be used as keys. Numeric types used for keys obey the normal rules for
numeric comparison: if two numbers compare equal (such as <tt class="docutils literal"><span class="pre">1</span></tt> and <tt class="docutils literal"><span class="pre">1.0</span></tt>)
then they can be used interchangeably to index the same dictionary entry. (Note
however, that since computers store floating-point numbers as approximations it
is usually unwise to use them as dictionary keys.)</p>
<p>Dictionaries can be created by placing a comma-separated list of <tt class="docutils literal"><span class="pre">key:</span> <span class="pre">value</span></tt>
pairs within braces, for example: <tt class="docutils literal"><span class="pre">{'jack':</span> <span class="pre">4098,</span> <span class="pre">'sjoerd':</span> <span class="pre">4127}</span></tt> or <tt class="docutils literal"><span class="pre">{4098:</span>
<span class="pre">'jack',</span> <span class="pre">4127:</span> <span class="pre">'sjoerd'}</span></tt>, or by the <a class="reference internal" href="#dict" title="dict"><tt class="xref py py-class docutils literal"><span class="pre">dict</span></tt></a> constructor.</p>
<dl class="class">
<dt id="dict">
<em class="property">class </em><tt class="descname">dict</tt><big>(</big><span class="optional">[</span><em>arg</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a new dictionary initialized from an optional positional argument or
from a set of keyword arguments. If no arguments are given, return a new
empty dictionary. If the positional argument <em>arg</em> is a mapping object,
return a dictionary mapping the same keys to the same values as does the
mapping object. Otherwise the positional argument must be a sequence, a
container that supports iteration, or an iterator object. The elements of
the argument must each also be of one of those kinds, and each must in turn
contain exactly two objects. The first is used as a key in the new
dictionary, and the second as the key’s value. If a given key is seen more
than once, the last value associated with it is retained in the new
dictionary.</p>
<p>If keyword arguments are given, the keywords themselves with their associated
values are added as items to the dictionary. If a key is specified both in
the positional argument and as a keyword argument, the value associated with
the keyword is retained in the dictionary. For example, these all return a
dictionary equal to <tt class="docutils literal"><span class="pre">{"one":</span> <span class="pre">1,</span> <span class="pre">"two":</span> <span class="pre">2}</span></tt>:</p>
<ul class="simple">
<li><tt class="docutils literal"><span class="pre">dict(one=1,</span> <span class="pre">two=2)</span></tt></li>
<li><tt class="docutils literal"><span class="pre">dict({'one':</span> <span class="pre">1,</span> <span class="pre">'two':</span> <span class="pre">2})</span></tt></li>
<li><tt class="docutils literal"><span class="pre">dict(zip(('one',</span> <span class="pre">'two'),</span> <span class="pre">(1,</span> <span class="pre">2)))</span></tt></li>
<li><tt class="docutils literal"><span class="pre">dict([['two',</span> <span class="pre">2],</span> <span class="pre">['one',</span> <span class="pre">1]])</span></tt></li>
</ul>
<p>The first example only works for keys that are valid Python identifiers; the
others work with any valid keys.</p>
<p>These are the operations that dictionaries support (and therefore, custom
mapping types should support too):</p>
<dl class="describe">
<dt>
<tt class="descname">len(d)</tt></dt>
<dd><p>Return the number of items in the dictionary <em>d</em>.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">d[key]</tt></dt>
<dd><p>Return the item of <em>d</em> with key <em>key</em>. Raises a <a class="reference internal" href="exceptions.html#KeyError" title="KeyError"><tt class="xref py py-exc docutils literal"><span class="pre">KeyError</span></tt></a> if <em>key</em> is
not in the map.</p>
<p>If a subclass of dict defines a method <tt class="xref py py-meth docutils literal"><span class="pre">__missing__()</span></tt>, if the key <em>key</em>
is not present, the <tt class="docutils literal"><span class="pre">d[key]</span></tt> operation calls that method with the key <em>key</em>
as argument. The <tt class="docutils literal"><span class="pre">d[key]</span></tt> operation then returns or raises whatever is
returned or raised by the <tt class="docutils literal"><span class="pre">__missing__(key)</span></tt> call if the key is not
present. No other operations or methods invoke <tt class="xref py py-meth docutils literal"><span class="pre">__missing__()</span></tt>. If
<tt class="xref py py-meth docutils literal"><span class="pre">__missing__()</span></tt> is not defined, <a class="reference internal" href="exceptions.html#KeyError" title="KeyError"><tt class="xref py py-exc docutils literal"><span class="pre">KeyError</span></tt></a> is raised.
<tt class="xref py py-meth docutils literal"><span class="pre">__missing__()</span></tt> must be a method; it cannot be an instance variable:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">class</span> <span class="nc">Counter</span><span class="p">(</span><span class="nb">dict</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">def</span> <span class="nf">__missing__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">return</span> <span class="mi">0</span>
<span class="gp">>>> </span><span class="n">c</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">c</span><span class="p">[</span><span class="s">'red'</span><span class="p">]</span>
<span class="go">0</span>
<span class="gp">>>> </span><span class="n">c</span><span class="p">[</span><span class="s">'red'</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="gp">>>> </span><span class="n">c</span><span class="p">[</span><span class="s">'red'</span><span class="p">]</span>
<span class="go">1</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="collections.html#collections.Counter" title="collections.Counter"><tt class="xref py py-class docutils literal"><span class="pre">collections.Counter</span></tt></a> for a complete implementation including
other methods helpful for accumulating and managing tallies.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">d[key] = value</tt></dt>
<dd><p>Set <tt class="docutils literal"><span class="pre">d[key]</span></tt> to <em>value</em>.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">del d[key]</tt></dt>
<dd><p>Remove <tt class="docutils literal"><span class="pre">d[key]</span></tt> from <em>d</em>. Raises a <a class="reference internal" href="exceptions.html#KeyError" title="KeyError"><tt class="xref py py-exc docutils literal"><span class="pre">KeyError</span></tt></a> if <em>key</em> is not in the
map.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">key in d</tt></dt>
<dd><p>Return <tt class="xref docutils literal"><span class="pre">True</span></tt> if <em>d</em> has a key <em>key</em>, else <tt class="xref docutils literal"><span class="pre">False</span></tt>.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">key not in d</tt></dt>
<dd><p>Equivalent to <tt class="docutils literal"><span class="pre">not</span> <span class="pre">key</span> <span class="pre">in</span> <span class="pre">d</span></tt>.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">iter(d)</tt></dt>
<dd><p>Return an iterator over the keys of the dictionary. This is a shortcut
for <tt class="docutils literal"><span class="pre">iter(d.keys())</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="dict.clear">
<tt class="descname">clear</tt><big>(</big><big>)</big><a class="headerlink" href="#dict.clear" title="Permalink to this definition">¶</a></dt>
<dd><p>Remove all items from the dictionary.</p>
</dd></dl>
<dl class="method">
<dt id="dict.copy">
<tt class="descname">copy</tt><big>(</big><big>)</big><a class="headerlink" href="#dict.copy" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a shallow copy of the dictionary.</p>
</dd></dl>
<dl class="classmethod">
<dt id="dict.fromkeys">
<em class="property">classmethod </em><tt class="descname">fromkeys</tt><big>(</big><em>seq</em><span class="optional">[</span>, <em>value</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#dict.fromkeys" title="Permalink to this definition">¶</a></dt>
<dd><p>Create a new dictionary with keys from <em>seq</em> and values set to <em>value</em>.</p>
<p><a class="reference internal" href="#dict.fromkeys" title="dict.fromkeys"><tt class="xref py py-meth docutils literal"><span class="pre">fromkeys()</span></tt></a> is a class method that returns a new dictionary. <em>value</em>
defaults to <tt class="xref docutils literal"><span class="pre">None</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="dict.get">
<tt class="descname">get</tt><big>(</big><em>key</em><span class="optional">[</span>, <em>default</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#dict.get" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the value for <em>key</em> if <em>key</em> is in the dictionary, else <em>default</em>.
If <em>default</em> is not given, it defaults to <tt class="xref docutils literal"><span class="pre">None</span></tt>, so that this method
never raises a <a class="reference internal" href="exceptions.html#KeyError" title="KeyError"><tt class="xref py py-exc docutils literal"><span class="pre">KeyError</span></tt></a>.</p>
</dd></dl>
<dl class="method">
<dt id="dict.items">
<tt class="descname">items</tt><big>(</big><big>)</big><a class="headerlink" href="#dict.items" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a new view of the dictionary’s items (<tt class="docutils literal"><span class="pre">(key,</span> <span class="pre">value)</span></tt> pairs). See
below for documentation of view objects.</p>
</dd></dl>
<dl class="method">
<dt id="dict.keys">
<tt class="descname">keys</tt><big>(</big><big>)</big><a class="headerlink" href="#dict.keys" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a new view of the dictionary’s keys. See below for documentation of
view objects.</p>
</dd></dl>
<dl class="method">
<dt id="dict.pop">
<tt class="descname">pop</tt><big>(</big><em>key</em><span class="optional">[</span>, <em>default</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#dict.pop" title="Permalink to this definition">¶</a></dt>
<dd><p>If <em>key</em> is in the dictionary, remove it and return its value, else return
<em>default</em>. If <em>default</em> is not given and <em>key</em> is not in the dictionary,
a <a class="reference internal" href="exceptions.html#KeyError" title="KeyError"><tt class="xref py py-exc docutils literal"><span class="pre">KeyError</span></tt></a> is raised.</p>
</dd></dl>
<dl class="method">
<dt id="dict.popitem">
<tt class="descname">popitem</tt><big>(</big><big>)</big><a class="headerlink" href="#dict.popitem" title="Permalink to this definition">¶</a></dt>
<dd><p>Remove and return an arbitrary <tt class="docutils literal"><span class="pre">(key,</span> <span class="pre">value)</span></tt> pair from the dictionary.</p>
<p><a class="reference internal" href="#dict.popitem" title="dict.popitem"><tt class="xref py py-meth docutils literal"><span class="pre">popitem()</span></tt></a> is useful to destructively iterate over a dictionary, as
often used in set algorithms. If the dictionary is empty, calling
<a class="reference internal" href="#dict.popitem" title="dict.popitem"><tt class="xref py py-meth docutils literal"><span class="pre">popitem()</span></tt></a> raises a <a class="reference internal" href="exceptions.html#KeyError" title="KeyError"><tt class="xref py py-exc docutils literal"><span class="pre">KeyError</span></tt></a>.</p>
</dd></dl>
<dl class="method">
<dt id="dict.setdefault">
<tt class="descname">setdefault</tt><big>(</big><em>key</em><span class="optional">[</span>, <em>default</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#dict.setdefault" title="Permalink to this definition">¶</a></dt>
<dd><p>If <em>key</em> is in the dictionary, return its value. If not, insert <em>key</em>
with a value of <em>default</em> and return <em>default</em>. <em>default</em> defaults to
<tt class="xref docutils literal"><span class="pre">None</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="dict.update">
<tt class="descname">update</tt><big>(</big><span class="optional">[</span><em>other</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#dict.update" title="Permalink to this definition">¶</a></dt>
<dd><p>Update the dictionary with the key/value pairs from <em>other</em>, overwriting
existing keys. Return <tt class="xref docutils literal"><span class="pre">None</span></tt>.</p>
<p><a class="reference internal" href="#dict.update" title="dict.update"><tt class="xref py py-meth docutils literal"><span class="pre">update()</span></tt></a> accepts either another dictionary object or an iterable of
key/value pairs (as tuples or other iterables of length two). If keyword
arguments are specified, the dictionary is then updated with those
key/value pairs: <tt class="docutils literal"><span class="pre">d.update(red=1,</span> <span class="pre">blue=2)</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="dict.values">
<tt class="descname">values</tt><big>(</big><big>)</big><a class="headerlink" href="#dict.values" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a new view of the dictionary’s values. See below for documentation of
view objects.</p>
</dd></dl>
</dd></dl>
<div class="section" id="dictionary-view-objects">
<span id="dict-views"></span><h3>4.8.1. Dictionary view objects<a class="headerlink" href="#dictionary-view-objects" title="Permalink to this headline">¶</a></h3>
<p>The objects returned by <a class="reference internal" href="#dict.keys" title="dict.keys"><tt class="xref py py-meth docutils literal"><span class="pre">dict.keys()</span></tt></a>, <a class="reference internal" href="#dict.values" title="dict.values"><tt class="xref py py-meth docutils literal"><span class="pre">dict.values()</span></tt></a> and
<a class="reference internal" href="#dict.items" title="dict.items"><tt class="xref py py-meth docutils literal"><span class="pre">dict.items()</span></tt></a> are <em>view objects</em>. They provide a dynamic view on the
dictionary’s entries, which means that when the dictionary changes, the view
reflects these changes.</p>
<p>Dictionary views can be iterated over to yield their respective data, and
support membership tests:</p>
<dl class="describe">
<dt>
<tt class="descname">len(dictview)</tt></dt>
<dd><p>Return the number of entries in the dictionary.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">iter(dictview)</tt></dt>
<dd><p>Return an iterator over the keys, values or items (represented as tuples of
<tt class="docutils literal"><span class="pre">(key,</span> <span class="pre">value)</span></tt>) in the dictionary.</p>
<p>Keys and values are iterated over in an arbitrary order which is non-random,
varies across Python implementations, and depends on the dictionary’s history
of insertions and deletions. If keys, values and items views are iterated
over with no intervening modifications to the dictionary, the order of items
will directly correspond. This allows the creation of <tt class="docutils literal"><span class="pre">(value,</span> <span class="pre">key)</span></tt> pairs
using <a class="reference internal" href="functions.html#zip" title="zip"><tt class="xref py py-func docutils literal"><span class="pre">zip()</span></tt></a>: <tt class="docutils literal"><span class="pre">pairs</span> <span class="pre">=</span> <span class="pre">zip(d.values(),</span> <span class="pre">d.keys())</span></tt>. Another way to
create the same list is <tt class="docutils literal"><span class="pre">pairs</span> <span class="pre">=</span> <span class="pre">[(v,</span> <span class="pre">k)</span> <span class="pre">for</span> <span class="pre">(k,</span> <span class="pre">v)</span> <span class="pre">in</span> <span class="pre">d.items()]</span></tt>.</p>
<p>Iterating views while adding or deleting entries in the dictionary may raise
a <a class="reference internal" href="exceptions.html#RuntimeError" title="RuntimeError"><tt class="xref py py-exc docutils literal"><span class="pre">RuntimeError</span></tt></a> or fail to iterate over all entries.</p>
</dd></dl>
<dl class="describe">
<dt>
<tt class="descname">x in dictview</tt></dt>
<dd><p>Return <tt class="xref docutils literal"><span class="pre">True</span></tt> if <em>x</em> is in the underlying dictionary’s keys, values or
items (in the latter case, <em>x</em> should be a <tt class="docutils literal"><span class="pre">(key,</span> <span class="pre">value)</span></tt> tuple).</p>
</dd></dl>
<p>Keys views are set-like since their entries are unique and hashable. If all
values are hashable, so that <tt class="docutils literal"><span class="pre">(key,</span> <span class="pre">value)</span></tt> pairs are unique and hashable,
then the items view is also set-like. (Values views are not treated as set-like
since the entries are generally not unique.) For set-like views, all of the
operations defined for the abstract base class <a class="reference internal" href="collections.html#collections.Set" title="collections.Set"><tt class="xref py py-class docutils literal"><span class="pre">collections.Set</span></tt></a> are
available (for example, <tt class="docutils literal"><span class="pre">==</span></tt>, <tt class="docutils literal"><span class="pre"><</span></tt>, or <tt class="docutils literal"><span class="pre">^</span></tt>).</p>
<p>An example of dictionary view usage:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">dishes</span> <span class="o">=</span> <span class="p">{</span><span class="s">'eggs'</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s">'sausage'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s">'bacon'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s">'spam'</span><span class="p">:</span> <span class="mi">500</span><span class="p">}</span>
<span class="gp">>>> </span><span class="n">keys</span> <span class="o">=</span> <span class="n">dishes</span><span class="o">.</span><span class="n">keys</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">values</span> <span class="o">=</span> <span class="n">dishes</span><span class="o">.</span><span class="n">values</span><span class="p">()</span>
<span class="gp">>>> </span><span class="c"># iteration</span>
<span class="gp">>>> </span><span class="n">n</span> <span class="o">=</span> <span class="mi">0</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">val</span> <span class="ow">in</span> <span class="n">values</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">n</span> <span class="o">+=</span> <span class="n">val</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<span class="go">504</span>
<span class="gp">>>> </span><span class="c"># keys and values are iterated over in the same order</span>
<span class="gp">>>> </span><span class="nb">list</span><span class="p">(</span><span class="n">keys</span><span class="p">)</span>
<span class="go">['eggs', 'bacon', 'sausage', 'spam']</span>
<span class="gp">>>> </span><span class="nb">list</span><span class="p">(</span><span class="n">values</span><span class="p">)</span>
<span class="go">[2, 1, 1, 500]</span>
<span class="gp">>>> </span><span class="c"># view objects are dynamic and reflect dict changes</span>
<span class="gp">>>> </span><span class="k">del</span> <span class="n">dishes</span><span class="p">[</span><span class="s">'eggs'</span><span class="p">]</span>
<span class="gp">>>> </span><span class="k">del</span> <span class="n">dishes</span><span class="p">[</span><span class="s">'sausage'</span><span class="p">]</span>
<span class="gp">>>> </span><span class="nb">list</span><span class="p">(</span><span class="n">keys</span><span class="p">)</span>
<span class="go">['spam', 'bacon']</span>
<span class="gp">>>> </span><span class="c"># set operations</span>
<span class="gp">>>> </span><span class="n">keys</span> <span class="o">&</span> <span class="p">{</span><span class="s">'eggs'</span><span class="p">,</span> <span class="s">'bacon'</span><span class="p">,</span> <span class="s">'salad'</span><span class="p">}</span>
<span class="go">{'bacon'}</span>
<span class="gp">>>> </span><span class="n">keys</span> <span class="o">^</span> <span class="p">{</span><span class="s">'sausage'</span><span class="p">,</span> <span class="s">'juice'</span><span class="p">}</span>
<span class="go">{'juice', 'sausage', 'bacon', 'spam'}</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="memoryview-type">
<span id="typememoryview"></span><h2>4.9. memoryview type<a class="headerlink" href="#memoryview-type" title="Permalink to this headline">¶</a></h2>
<p><a class="reference internal" href="#memoryview" title="memoryview"><tt class="xref py py-class docutils literal"><span class="pre">memoryview</span></tt></a> objects allow Python code to access the internal data
of an object that supports the <a class="reference internal" href="../c-api/buffer.html#bufferobjects"><em>buffer protocol</em></a> without
copying. Memory is generally interpreted as simple bytes.</p>
<dl class="class">
<dt id="memoryview">
<em class="property">class </em><tt class="descname">memoryview</tt><big>(</big><em>obj</em><big>)</big><a class="headerlink" href="#memoryview" title="Permalink to this definition">¶</a></dt>
<dd><p>Create a <a class="reference internal" href="#memoryview" title="memoryview"><tt class="xref py py-class docutils literal"><span class="pre">memoryview</span></tt></a> that references <em>obj</em>. <em>obj</em> must support the
buffer protocol. Built-in objects that support the buffer protocol include
<a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a> and <a class="reference internal" href="functions.html#bytearray" title="bytearray"><tt class="xref py py-class docutils literal"><span class="pre">bytearray</span></tt></a>.</p>
<p>A <a class="reference internal" href="#memoryview" title="memoryview"><tt class="xref py py-class docutils literal"><span class="pre">memoryview</span></tt></a> has the notion of an <em>element</em>, which is the
atomic memory unit handled by the originating object <em>obj</em>. For many
simple types such as <a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a> and <a class="reference internal" href="functions.html#bytearray" title="bytearray"><tt class="xref py py-class docutils literal"><span class="pre">bytearray</span></tt></a>, an element
is a single byte, but other types such as <a class="reference internal" href="array.html#array.array" title="array.array"><tt class="xref py py-class docutils literal"><span class="pre">array.array</span></tt></a> may have
bigger elements.</p>
<p><tt class="docutils literal"><span class="pre">len(view)</span></tt> returns the total number of elements in the memoryview,
<em>view</em>. The <a class="reference internal" href="#memoryview.itemsize" title="memoryview.itemsize"><tt class="xref py py-class docutils literal"><span class="pre">itemsize</span></tt></a> attribute will give you the
number of bytes in a single element.</p>
<p>A <a class="reference internal" href="#memoryview" title="memoryview"><tt class="xref py py-class docutils literal"><span class="pre">memoryview</span></tt></a> supports slicing to expose its data. Taking a single
index will return a single element as a <a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a> object. Full
slicing will result in a subview:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">v</span> <span class="o">=</span> <span class="nb">memoryview</span><span class="p">(</span><span class="n">b</span><span class="s">'abcefg'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="go">b'b'</span>
<span class="gp">>>> </span><span class="n">v</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="go">b'g'</span>
<span class="gp">>>> </span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">4</span><span class="p">]</span>
<span class="go"><memory at 0x77ab28></span>
<span class="gp">>>> </span><span class="nb">bytes</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">4</span><span class="p">])</span>
<span class="go">b'bce'</span>
</pre></div>
</div>
<p>If the object the memoryview is over supports changing its data, the
memoryview supports slice assignment:</p>
<div class="highlight-python3"><pre>>>> data = bytearray(b'abcefg')
>>> v = memoryview(data)
>>> v.readonly
False
>>> v[0] = b'z'
>>> data
bytearray(b'zbcefg')
>>> v[1:4] = b'123'
>>> data
bytearray(b'a123fg')
>>> v[2] = b'spam'
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: cannot modify size of memoryview object</pre>
</div>
<p>Notice how the size of the memoryview object cannot be changed.</p>
<p><a class="reference internal" href="#memoryview" title="memoryview"><tt class="xref py py-class docutils literal"><span class="pre">memoryview</span></tt></a> has several methods:</p>
<dl class="method">
<dt id="memoryview.tobytes">
<tt class="descname">tobytes</tt><big>(</big><big>)</big><a class="headerlink" href="#memoryview.tobytes" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the data in the buffer as a bytestring. This is equivalent to
calling the <a class="reference internal" href="functions.html#bytes" title="bytes"><tt class="xref py py-class docutils literal"><span class="pre">bytes</span></tt></a> constructor on the memoryview.</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="nb">memoryview</span><span class="p">(</span><span class="n">b</span><span class="s">"abc"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">m</span><span class="o">.</span><span class="n">tobytes</span><span class="p">()</span>
<span class="go">b'abc'</span>
<span class="gp">>>> </span><span class="nb">bytes</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="go">b'abc'</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="memoryview.tolist">
<tt class="descname">tolist</tt><big>(</big><big>)</big><a class="headerlink" href="#memoryview.tolist" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the data in the buffer as a list of integers.</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">memoryview</span><span class="p">(</span><span class="n">b</span><span class="s">'abc'</span><span class="p">)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
<span class="go">[97, 98, 99]</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="memoryview.release">
<tt class="descname">release</tt><big>(</big><big>)</big><a class="headerlink" href="#memoryview.release" title="Permalink to this definition">¶</a></dt>
<dd><p>Release the underlying buffer exposed by the memoryview object. Many
objects take special actions when a view is held on them (for example,
a <a class="reference internal" href="functions.html#bytearray" title="bytearray"><tt class="xref py py-class docutils literal"><span class="pre">bytearray</span></tt></a> would temporarily forbid resizing); therefore,
calling release() is handy to remove these restrictions (and free any
dangling resources) as soon as possible.</p>
<p>After this method has been called, any further operation on the view
raises a <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><tt class="xref py py-class docutils literal"><span class="pre">ValueError</span></tt></a> (except <a class="reference internal" href="#memoryview.release" title="memoryview.release"><tt class="xref py py-meth docutils literal"><span class="pre">release()</span></tt></a> itself which can
be called multiple times):</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="nb">memoryview</span><span class="p">(</span><span class="n">b</span><span class="s">'abc'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">m</span><span class="o">.</span><span class="n">release</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<stdin>"</span>, line <span class="m">1</span>, in <span class="n-Identifier"><module></span>
<span class="nc">ValueError</span>: <span class="n-Identifier">operation forbidden on released memoryview object</span>
</pre></div>
</div>
<p>The context management protocol can be used for a similar effect,
using the <tt class="docutils literal"><span class="pre">with</span></tt> statement:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">with</span> <span class="nb">memoryview</span><span class="p">(</span><span class="n">b</span><span class="s">'abc'</span><span class="p">)</span> <span class="k">as</span> <span class="n">m</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="gp">...</span>
<span class="go">b'a'</span>
<span class="gp">>>> </span><span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<stdin>"</span>, line <span class="m">1</span>, in <span class="n-Identifier"><module></span>
<span class="nc">ValueError</span>: <span class="n-Identifier">operation forbidden on released memoryview object</span>
</pre></div>
</div>
<p class="versionadded">
<span class="versionmodified">New in version 3.2.</span></p>
</dd></dl>
<p>There are also several readonly attributes available:</p>
<dl class="attribute">
<dt id="memoryview.format">
<tt class="descname">format</tt><a class="headerlink" href="#memoryview.format" title="Permalink to this definition">¶</a></dt>
<dd><p>A string containing the format (in <a class="reference internal" href="struct.html#module-struct" title="struct: Interpret bytes as packed binary data."><tt class="xref py py-mod docutils literal"><span class="pre">struct</span></tt></a> module style) for each
element in the view. This defaults to <tt class="docutils literal"><span class="pre">'B'</span></tt>, a simple bytestring.</p>
</dd></dl>
<dl class="attribute">
<dt id="memoryview.itemsize">
<tt class="descname">itemsize</tt><a class="headerlink" href="#memoryview.itemsize" title="Permalink to this definition">¶</a></dt>
<dd><p>The size in bytes of each element of the memoryview:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="nb">memoryview</span><span class="p">(</span><span class="n">array</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="s">'H'</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]))</span>
<span class="gp">>>> </span><span class="n">m</span><span class="o">.</span><span class="n">itemsize</span>
<span class="go">2</span>
<span class="gp">>>> </span><span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="go">b'\x01\x00'</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">==</span> <span class="n">m</span><span class="o">.</span><span class="n">itemsize</span>
<span class="go">True</span>
</pre></div>
</div>
</dd></dl>
<dl class="attribute">
<dt id="memoryview.shape">
<tt class="descname">shape</tt><a class="headerlink" href="#memoryview.shape" title="Permalink to this definition">¶</a></dt>
<dd><p>A tuple of integers the length of <a class="reference internal" href="#memoryview.ndim" title="memoryview.ndim"><tt class="xref py py-attr docutils literal"><span class="pre">ndim</span></tt></a> giving the shape of the
memory as a N-dimensional array.</p>
</dd></dl>
<dl class="attribute">
<dt id="memoryview.ndim">
<tt class="descname">ndim</tt><a class="headerlink" href="#memoryview.ndim" title="Permalink to this definition">¶</a></dt>
<dd><p>An integer indicating how many dimensions of a multi-dimensional array the
memory represents.</p>
</dd></dl>
<dl class="attribute">
<dt id="memoryview.strides">
<tt class="descname">strides</tt><a class="headerlink" href="#memoryview.strides" title="Permalink to this definition">¶</a></dt>
<dd><p>A tuple of integers the length of <a class="reference internal" href="#memoryview.ndim" title="memoryview.ndim"><tt class="xref py py-attr docutils literal"><span class="pre">ndim</span></tt></a> giving the size in bytes to
access each element for each dimension of the array.</p>
</dd></dl>
<dl class="attribute">
<dt id="memoryview.readonly">
<tt class="descname">readonly</tt><a class="headerlink" href="#memoryview.readonly" title="Permalink to this definition">¶</a></dt>
<dd><p>A bool indicating whether the memory is read only.</p>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="context-manager-types">
<span id="typecontextmanager"></span><h2>4.10. Context Manager Types<a class="headerlink" href="#context-manager-types" title="Permalink to this headline">¶</a></h2>
<p id="index-31">Python’s <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statement supports the concept of a runtime context
defined by a context manager. This is implemented using a pair of methods
that allow user-defined classes to define a runtime context that is entered
before the statement body is executed and exited when the statement ends:</p>
<dl class="method">
<dt id="contextmanager.__enter__">
<tt class="descclassname">contextmanager.</tt><tt class="descname">__enter__</tt><big>(</big><big>)</big><a class="headerlink" href="#contextmanager.__enter__" title="Permalink to this definition">¶</a></dt>
<dd><p>Enter the runtime context and return either this object or another object
related to the runtime context. The value returned by this method is bound to
the identifier in the <a class="reference internal" href="../reference/compound_stmts.html#as"><tt class="xref std std-keyword docutils literal"><span class="pre">as</span></tt></a> clause of <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statements using
this context manager.</p>
<p>An example of a context manager that returns itself is a <a class="reference internal" href="../glossary.html#term-file-object"><em class="xref std std-term">file object</em></a>.
File objects return themselves from __enter__() to allow <a class="reference internal" href="functions.html#open" title="open"><tt class="xref py py-func docutils literal"><span class="pre">open()</span></tt></a> to be
used as the context expression in a <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statement.</p>
<p>An example of a context manager that returns a related object is the one
returned by <a class="reference internal" href="decimal.html#decimal.localcontext" title="decimal.localcontext"><tt class="xref py py-func docutils literal"><span class="pre">decimal.localcontext()</span></tt></a>. These managers set the active
decimal context to a copy of the original decimal context and then return the
copy. This allows changes to be made to the current decimal context in the body
of the <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statement without affecting code outside the
<a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statement.</p>
</dd></dl>
<dl class="method">
<dt id="contextmanager.__exit__">
<tt class="descclassname">contextmanager.</tt><tt class="descname">__exit__</tt><big>(</big><em>exc_type</em>, <em>exc_val</em>, <em>exc_tb</em><big>)</big><a class="headerlink" href="#contextmanager.__exit__" title="Permalink to this definition">¶</a></dt>
<dd><p>Exit the runtime context and return a Boolean flag indicating if any exception
that occurred should be suppressed. If an exception occurred while executing the
body of the <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statement, the arguments contain the exception type,
value and traceback information. Otherwise, all three arguments are <tt class="xref docutils literal"><span class="pre">None</span></tt>.</p>
<p>Returning a true value from this method will cause the <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statement
to suppress the exception and continue execution with the statement immediately
following the <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statement. Otherwise the exception continues
propagating after this method has finished executing. Exceptions that occur
during execution of this method will replace any exception that occurred in the
body of the <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal"><span class="pre">with</span></tt></a> statement.</p>
<p>The exception passed in should never be reraised explicitly - instead, this
method should return a false value to indicate that the method completed
successfully and does not want to suppress the raised exception. This allows
context management code (such as <tt class="docutils literal"><span class="pre">contextlib.nested</span></tt>) to easily detect whether
or not an <a class="reference internal" href="#contextmanager.__exit__" title="contextmanager.__exit__"><tt class="xref py py-meth docutils literal"><span class="pre">__exit__()</span></tt></a> method has actually failed.</p>
</dd></dl>
<p>Python defines several context managers to support easy thread synchronisation,
prompt closure of files or other objects, and simpler manipulation of the active
decimal arithmetic context. The specific types are not treated specially beyond
their implementation of the context management protocol. See the
<a class="reference internal" href="contextlib.html#module-contextlib" title="contextlib: Utilities for with-statement contexts."><tt class="xref py py-mod docutils literal"><span class="pre">contextlib</span></tt></a> module for some examples.</p>
<p>Python’s <a class="reference internal" href="../glossary.html#term-generator"><em class="xref std std-term">generator</em></a>s and the <a class="reference internal" href="contextlib.html#contextlib.contextmanager" title="contextlib.contextmanager"><tt class="xref py py-class docutils literal"><span class="pre">contextlib.contextmanager</span></tt></a> decorator
provide a convenient way to implement these protocols. If a generator function is
decorated with the <a class="reference internal" href="contextlib.html#contextlib.contextmanager" title="contextlib.contextmanager"><tt class="xref py py-class docutils literal"><span class="pre">contextlib.contextmanager</span></tt></a> decorator, it will return a
context manager implementing the necessary <a class="reference internal" href="../reference/datamodel.html#object.__enter__" title="object.__enter__"><tt class="xref py py-meth docutils literal"><span class="pre">__enter__()</span></tt></a> and
<a class="reference internal" href="../reference/datamodel.html#object.__exit__" title="object.__exit__"><tt class="xref py py-meth docutils literal"><span class="pre">__exit__()</span></tt></a> methods, rather than the iterator produced by an undecorated
generator function.</p>
<p>Note that there is no specific slot for any of these methods in the type
structure for Python objects in the Python/C API. Extension types wanting to
define these methods must provide them as a normal Python accessible method.
Compared to the overhead of setting up the runtime context, the overhead of a
single class dictionary lookup is negligible.</p>
</div>
<div class="section" id="other-built-in-types">
<span id="typesother"></span><h2>4.11. Other Built-in Types<a class="headerlink" href="#other-built-in-types" title="Permalink to this headline">¶</a></h2>
<p>The interpreter supports several other kinds of objects. Most of these support
only one or two operations.</p>
<div class="section" id="modules">
<span id="typesmodules"></span><h3>4.11.1. Modules<a class="headerlink" href="#modules" title="Permalink to this headline">¶</a></h3>
<p>The only special operation on a module is attribute access: <tt class="docutils literal"><span class="pre">m.name</span></tt>, where
<em>m</em> is a module and <em>name</em> accesses a name defined in <em>m</em>‘s symbol table.
Module attributes can be assigned to. (Note that the <a class="reference internal" href="../reference/simple_stmts.html#import"><tt class="xref std std-keyword docutils literal"><span class="pre">import</span></tt></a>
statement is not, strictly speaking, an operation on a module object; <tt class="docutils literal"><span class="pre">import</span>
<span class="pre">foo</span></tt> does not require a module object named <em>foo</em> to exist, rather it requires
an (external) <em>definition</em> for a module named <em>foo</em> somewhere.)</p>
<p>A special attribute of every module is <tt class="xref py py-attr docutils literal"><span class="pre">__dict__</span></tt>. This is the dictionary
containing the module’s symbol table. Modifying this dictionary will actually
change the module’s symbol table, but direct assignment to the <tt class="xref py py-attr docutils literal"><span class="pre">__dict__</span></tt>
attribute is not possible (you can write <tt class="docutils literal"><span class="pre">m.__dict__['a']</span> <span class="pre">=</span> <span class="pre">1</span></tt>, which defines
<tt class="docutils literal"><span class="pre">m.a</span></tt> to be <tt class="docutils literal"><span class="pre">1</span></tt>, but you can’t write <tt class="docutils literal"><span class="pre">m.__dict__</span> <span class="pre">=</span> <span class="pre">{}</span></tt>). Modifying
<tt class="xref py py-attr docutils literal"><span class="pre">__dict__</span></tt> directly is not recommended.</p>
<p>Modules built into the interpreter are written like this: <tt class="docutils literal"><span class="pre"><module</span> <span class="pre">'sys'</span>
<span class="pre">(built-in)></span></tt>. If loaded from a file, they are written as <tt class="docutils literal"><span class="pre"><module</span> <span class="pre">'os'</span> <span class="pre">from</span>
<span class="pre">'/usr/local/lib/pythonX.Y/os.pyc'></span></tt>.</p>
</div>
<div class="section" id="classes-and-class-instances">
<span id="typesobjects"></span><h3>4.11.2. Classes and Class Instances<a class="headerlink" href="#classes-and-class-instances" title="Permalink to this headline">¶</a></h3>
<p>See <a class="reference internal" href="../reference/datamodel.html#objects"><em>Objects, values and types</em></a> and <a class="reference internal" href="../reference/compound_stmts.html#class"><em>Class definitions</em></a> for these.</p>
</div>
<div class="section" id="functions">
<span id="typesfunctions"></span><h3>4.11.3. Functions<a class="headerlink" href="#functions" title="Permalink to this headline">¶</a></h3>
<p>Function objects are created by function definitions. The only operation on a
function object is to call it: <tt class="docutils literal"><span class="pre">func(argument-list)</span></tt>.</p>
<p>There are really two flavors of function objects: built-in functions and
user-defined functions. Both support the same operation (to call the function),
but the implementation is different, hence the different object types.</p>
<p>See <a class="reference internal" href="../reference/compound_stmts.html#function"><em>Function definitions</em></a> for more information.</p>
</div>
<div class="section" id="methods">
<span id="typesmethods"></span><h3>4.11.4. Methods<a class="headerlink" href="#methods" title="Permalink to this headline">¶</a></h3>
<p id="index-32">Methods are functions that are called using the attribute notation. There are
two flavors: built-in methods (such as <tt class="xref py py-meth docutils literal"><span class="pre">append()</span></tt> on lists) and class
instance methods. Built-in methods are described with the types that support
them.</p>
<p>If you access a method (a function defined in a class namespace) through an
instance, you get a special object: a <em class="dfn">bound method</em> (also called
<em class="dfn">instance method</em>) object. When called, it will add the <tt class="docutils literal"><span class="pre">self</span></tt> argument
to the argument list. Bound methods have two special read-only attributes:
<tt class="docutils literal"><span class="pre">m.__self__</span></tt> is the object on which the method operates, and <tt class="docutils literal"><span class="pre">m.__func__</span></tt> is
the function implementing the method. Calling <tt class="docutils literal"><span class="pre">m(arg-1,</span> <span class="pre">arg-2,</span> <span class="pre">...,</span> <span class="pre">arg-n)</span></tt>
is completely equivalent to calling <tt class="docutils literal"><span class="pre">m.__func__(m.__self__,</span> <span class="pre">arg-1,</span> <span class="pre">arg-2,</span> <span class="pre">...,</span>
<span class="pre">arg-n)</span></tt>.</p>
<p>Like function objects, bound method objects support getting arbitrary
attributes. However, since method attributes are actually stored on the
underlying function object (<tt class="docutils literal"><span class="pre">meth.__func__</span></tt>), setting method attributes on
bound methods is disallowed. Attempting to set a method attribute results in a
<a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> being raised. In order to set a method attribute, you need to
explicitly set it on the underlying function object:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="k">class</span> <span class="nc">C</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">method</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">pass</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">C</span><span class="p">()</span>
<span class="n">c</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">__func__</span><span class="o">.</span><span class="n">whoami</span> <span class="o">=</span> <span class="s">'my name is c'</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="../reference/datamodel.html#types"><em>The standard type hierarchy</em></a> for more information.</p>
</div>
<div class="section" id="code-objects">
<span id="bltin-code-objects"></span><h3>4.11.5. Code Objects<a class="headerlink" href="#code-objects" title="Permalink to this headline">¶</a></h3>
<span class="target" id="index-33"></span><p id="index-34">Code objects are used by the implementation to represent “pseudo-compiled”
executable Python code such as a function body. They differ from function
objects because they don’t contain a reference to their global execution
environment. Code objects are returned by the built-in <a class="reference internal" href="functions.html#compile" title="compile"><tt class="xref py py-func docutils literal"><span class="pre">compile()</span></tt></a> function
and can be extracted from function objects through their <tt class="xref py py-attr docutils literal"><span class="pre">__code__</span></tt>
attribute. See also the <a class="reference internal" href="code.html#module-code" title="code: Facilities to implement read-eval-print loops."><tt class="xref py py-mod docutils literal"><span class="pre">code</span></tt></a> module.</p>
<p id="index-35">A code object can be executed or evaluated by passing it (instead of a source
string) to the <a class="reference internal" href="functions.html#exec" title="exec"><tt class="xref py py-func docutils literal"><span class="pre">exec()</span></tt></a> or <a class="reference internal" href="functions.html#eval" title="eval"><tt class="xref py py-func docutils literal"><span class="pre">eval()</span></tt></a> built-in functions.</p>
<p>See <a class="reference internal" href="../reference/datamodel.html#types"><em>The standard type hierarchy</em></a> for more information.</p>
</div>
<div class="section" id="type-objects">
<span id="bltin-type-objects"></span><h3>4.11.6. Type Objects<a class="headerlink" href="#type-objects" title="Permalink to this headline">¶</a></h3>
<p id="index-36">Type objects represent the various object types. An object’s type is accessed
by the built-in function <a class="reference internal" href="functions.html#type" title="type"><tt class="xref py py-func docutils literal"><span class="pre">type()</span></tt></a>. There are no special operations on
types. The standard module <a class="reference internal" href="types.html#module-types" title="types: Names for built-in types."><tt class="xref py py-mod docutils literal"><span class="pre">types</span></tt></a> defines names for all standard built-in
types.</p>
<p>Types are written like this: <tt class="docutils literal"><span class="pre"><class</span> <span class="pre">'int'></span></tt>.</p>
</div>
<div class="section" id="the-null-object">
<span id="bltin-null-object"></span><h3>4.11.7. The Null Object<a class="headerlink" href="#the-null-object" title="Permalink to this headline">¶</a></h3>
<p>This object is returned by functions that don’t explicitly return a value. It
supports no special operations. There is exactly one null object, named
<tt class="xref docutils literal"><span class="pre">None</span></tt> (a built-in name).</p>
<p>It is written as <tt class="xref docutils literal"><span class="pre">None</span></tt>.</p>
</div>
<div class="section" id="the-ellipsis-object">
<span id="bltin-ellipsis-object"></span><h3>4.11.8. The Ellipsis Object<a class="headerlink" href="#the-ellipsis-object" title="Permalink to this headline">¶</a></h3>
<p>This object is commonly used by slicing (see <a class="reference internal" href="../reference/expressions.html#slicings"><em>Slicings</em></a>). It supports no
special operations. There is exactly one ellipsis object, named
<a class="reference internal" href="constants.html#Ellipsis" title="Ellipsis"><tt class="xref py py-const docutils literal"><span class="pre">Ellipsis</span></tt></a> (a built-in name).</p>
<p>It is written as <tt class="docutils literal"><span class="pre">Ellipsis</span></tt> or <tt class="docutils literal"><span class="pre">...</span></tt>.</p>
</div>
<div class="section" id="the-notimplemented-object">
<span id="bltin-notimplemented-object"></span><h3>4.11.9. The NotImplemented Object<a class="headerlink" href="#the-notimplemented-object" title="Permalink to this headline">¶</a></h3>
<p>This object is returned from comparisons and binary operations when they are
asked to operate on types they don’t support. See <a class="reference internal" href="../reference/expressions.html#comparisons"><em>Comparisons</em></a> for more
information.</p>
<p>It is written as <tt class="docutils literal"><span class="pre">NotImplemented</span></tt>.</p>
</div>
<div class="section" id="boolean-values">
<span id="bltin-boolean-values"></span><h3>4.11.10. Boolean Values<a class="headerlink" href="#boolean-values" title="Permalink to this headline">¶</a></h3>
<p>Boolean values are the two constant objects <tt class="xref docutils literal"><span class="pre">False</span></tt> and <tt class="xref docutils literal"><span class="pre">True</span></tt>. They are
used to represent truth values (although other values can also be considered
false or true). In numeric contexts (for example when used as the argument to
an arithmetic operator), they behave like the integers 0 and 1, respectively.
The built-in function <a class="reference internal" href="functions.html#bool" title="bool"><tt class="xref py py-func docutils literal"><span class="pre">bool()</span></tt></a> can be used to cast any value to a Boolean,
if the value can be interpreted as a truth value (see section Truth Value
Testing above).</p>
<p id="index-37">They are written as <tt class="xref docutils literal"><span class="pre">False</span></tt> and <tt class="xref docutils literal"><span class="pre">True</span></tt>, respectively.</p>
</div>
<div class="section" id="internal-objects">
<span id="typesinternal"></span><h3>4.11.11. Internal Objects<a class="headerlink" href="#internal-objects" title="Permalink to this headline">¶</a></h3>
<p>See <a class="reference internal" href="../reference/datamodel.html#types"><em>The standard type hierarchy</em></a> for this information. It describes stack frame objects,
traceback objects, and slice objects.</p>
</div>
</div>
<div class="section" id="special-attributes">
<span id="specialattrs"></span><h2>4.12. Special Attributes<a class="headerlink" href="#special-attributes" title="Permalink to this headline">¶</a></h2>
<p>The implementation adds a few special read-only attributes to several object
types, where they are relevant. Some of these are not reported by the
<a class="reference internal" href="functions.html#dir" title="dir"><tt class="xref py py-func docutils literal"><span class="pre">dir()</span></tt></a> built-in function.</p>
<dl class="attribute">
<dt id="object.__dict__">
<tt class="descclassname">object.</tt><tt class="descname">__dict__</tt><a class="headerlink" href="#object.__dict__" title="Permalink to this definition">¶</a></dt>
<dd><p>A dictionary or other mapping object used to store an object’s (writable)
attributes.</p>
</dd></dl>
<dl class="attribute">
<dt id="instance.__class__">
<tt class="descclassname">instance.</tt><tt class="descname">__class__</tt><a class="headerlink" href="#instance.__class__" title="Permalink to this definition">¶</a></dt>
<dd><p>The class to which a class instance belongs.</p>
</dd></dl>
<dl class="attribute">
<dt id="class.__bases__">
<tt class="descclassname">class.</tt><tt class="descname">__bases__</tt><a class="headerlink" href="#class.__bases__" title="Permalink to this definition">¶</a></dt>
<dd><p>The tuple of base classes of a class object.</p>
</dd></dl>
<dl class="attribute">
<dt id="class.__name__">
<tt class="descclassname">class.</tt><tt class="descname">__name__</tt><a class="headerlink" href="#class.__name__" title="Permalink to this definition">¶</a></dt>
<dd><p>The name of the class or type.</p>
</dd></dl>
<p>The following attributes are only supported by <a class="reference internal" href="../glossary.html#term-new-style-class"><em class="xref std std-term">new-style class</em></a>es.</p>
<dl class="attribute">
<dt id="class.__mro__">
<tt class="descclassname">class.</tt><tt class="descname">__mro__</tt><a class="headerlink" href="#class.__mro__" title="Permalink to this definition">¶</a></dt>
<dd><p>This attribute is a tuple of classes that are considered when looking for
base classes during method resolution.</p>
</dd></dl>
<dl class="method">
<dt id="class.mro">
<tt class="descclassname">class.</tt><tt class="descname">mro</tt><big>(</big><big>)</big><a class="headerlink" href="#class.mro" title="Permalink to this definition">¶</a></dt>
<dd><p>This method can be overridden by a metaclass to customize the method
resolution order for its instances. It is called at class instantiation, and
its result is stored in <a class="reference internal" href="#class.__mro__" title="class.__mro__"><tt class="xref py py-attr docutils literal"><span class="pre">__mro__</span></tt></a>.</p>
</dd></dl>
<dl class="method">
<dt id="class.__subclasses__">
<tt class="descclassname">class.</tt><tt class="descname">__subclasses__</tt><big>(</big><big>)</big><a class="headerlink" href="#class.__subclasses__" title="Permalink to this definition">¶</a></dt>
<dd><p>Each new-style class keeps a list of weak references to its immediate
subclasses. This method returns a list of all those references still alive.
Example:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">int</span><span class="o">.</span><span class="n">__subclasses__</span><span class="p">()</span>
<span class="go">[<type 'bool'>]</span>
</pre></div>
</div>
</dd></dl>
<p class="rubric">Footnotes</p>
<table class="docutils footnote" frame="void" id="id11" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[1]</a></td><td>Additional information on these special methods may be found in the Python
Reference Manual (<a class="reference internal" href="../reference/datamodel.html#customization"><em>Basic customization</em></a>).</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id12" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[2]</a></td><td>As a consequence, the list <tt class="docutils literal"><span class="pre">[1,</span> <span class="pre">2]</span></tt> is considered equal to <tt class="docutils literal"><span class="pre">[1.0,</span> <span class="pre">2.0]</span></tt>, and
similarly for tuples.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id13" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id4">[3]</a></td><td>They must have since the parser can’t tell the type of the operands.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id14" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[4]</td><td><em>(<a class="fn-backref" href="#id6">1</a>, <a class="fn-backref" href="#id7">2</a>, <a class="fn-backref" href="#id8">3</a>, <a class="fn-backref" href="#id9">4</a>)</em> Cased characters are those with general category property being one of
“Lu” (Letter, uppercase), “Ll” (Letter, lowercase), or “Lt” (Letter, titlecase).</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id15" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id10">[5]</a></td><td>To format only a tuple you should therefore provide a singleton tuple whose only
element is the tuple to be formatted.</td></tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="sphinxsidebar">
<div class="sphinxsidebarwrapper">
<h3><a href="../contents.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">4. Built-in Types</a><ul>
<li><a class="reference internal" href="#truth-value-testing">4.1. Truth Value Testing</a></li>
<li><a class="reference internal" href="#boolean-operations-and-or-not">4.2. Boolean Operations — <tt class="docutils literal"><span class="pre">and</span></tt>, <tt class="docutils literal"><span class="pre">or</span></tt>, <tt class="docutils literal"><span class="pre">not</span></tt></a></li>
<li><a class="reference internal" href="#comparisons">4.3. Comparisons</a></li>
<li><a class="reference internal" href="#numeric-types-int-float-complex">4.4. Numeric Types — <tt class="docutils literal"><span class="pre">int</span></tt>, <tt class="docutils literal"><span class="pre">float</span></tt>, <tt class="docutils literal"><span class="pre">complex</span></tt></a><ul>
<li><a class="reference internal" href="#bit-string-operations-on-integer-types">4.4.1. Bit-string Operations on Integer Types</a></li>
<li><a class="reference internal" href="#additional-methods-on-integer-types">4.4.2. Additional Methods on Integer Types</a></li>
<li><a class="reference internal" href="#additional-methods-on-float">4.4.3. Additional Methods on Float</a></li>
<li><a class="reference internal" href="#hashing-of-numeric-types">4.4.4. Hashing of numeric types</a></li>
</ul>
</li>
<li><a class="reference internal" href="#iterator-types">4.5. Iterator Types</a><ul>
<li><a class="reference internal" href="#generator-types">4.5.1. Generator Types</a></li>
</ul>
</li>
<li><a class="reference internal" href="#sequence-types-str-bytes-bytearray-list-tuple-range">4.6. Sequence Types — <tt class="docutils literal"><span class="pre">str</span></tt>, <tt class="docutils literal"><span class="pre">bytes</span></tt>, <tt class="docutils literal"><span class="pre">bytearray</span></tt>, <tt class="docutils literal"><span class="pre">list</span></tt>, <tt class="docutils literal"><span class="pre">tuple</span></tt>, <tt class="docutils literal"><span class="pre">range</span></tt></a><ul>
<li><a class="reference internal" href="#string-methods">4.6.1. String Methods</a></li>
<li><a class="reference internal" href="#old-string-formatting-operations">4.6.2. Old String Formatting Operations</a></li>
<li><a class="reference internal" href="#range-type">4.6.3. Range Type</a></li>
<li><a class="reference internal" href="#mutable-sequence-types">4.6.4. Mutable Sequence Types</a></li>
<li><a class="reference internal" href="#bytes-and-byte-array-methods">4.6.5. Bytes and Byte Array Methods</a></li>
</ul>
</li>
<li><a class="reference internal" href="#set-types-set-frozenset">4.7. Set Types — <tt class="docutils literal"><span class="pre">set</span></tt>, <tt class="docutils literal"><span class="pre">frozenset</span></tt></a></li>
<li><a class="reference internal" href="#mapping-types-dict">4.8. Mapping Types — <tt class="docutils literal"><span class="pre">dict</span></tt></a><ul>
<li><a class="reference internal" href="#dictionary-view-objects">4.8.1. Dictionary view objects</a></li>
</ul>
</li>
<li><a class="reference internal" href="#memoryview-type">4.9. memoryview type</a></li>
<li><a class="reference internal" href="#context-manager-types">4.10. Context Manager Types</a></li>
<li><a class="reference internal" href="#other-built-in-types">4.11. Other Built-in Types</a><ul>
<li><a class="reference internal" href="#modules">4.11.1. Modules</a></li>
<li><a class="reference internal" href="#classes-and-class-instances">4.11.2. Classes and Class Instances</a></li>
<li><a class="reference internal" href="#functions">4.11.3. Functions</a></li>
<li><a class="reference internal" href="#methods">4.11.4. Methods</a></li>
<li><a class="reference internal" href="#code-objects">4.11.5. Code Objects</a></li>
<li><a class="reference internal" href="#type-objects">4.11.6. Type Objects</a></li>
<li><a class="reference internal" href="#the-null-object">4.11.7. The Null Object</a></li>
<li><a class="reference internal" href="#the-ellipsis-object">4.11.8. The Ellipsis Object</a></li>
<li><a class="reference internal" href="#the-notimplemented-object">4.11.9. The NotImplemented Object</a></li>
<li><a class="reference internal" href="#boolean-values">4.11.10. Boolean Values</a></li>
<li><a class="reference internal" href="#internal-objects">4.11.11. Internal Objects</a></li>
</ul>
</li>
<li><a class="reference internal" href="#special-attributes">4.12. Special Attributes</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
<p class="topless"><a href="constants.html"
title="previous chapter">3. Built-in Constants</a></p>
<h4>Next topic</h4>
<p class="topless"><a href="exceptions.html"
title="next chapter">5. Built-in Exceptions</a></p>
<h3>This Page</h3>
<ul class="this-page-menu">
<li><a href="../bugs.html">Report a Bug</a></li>
<li><a href="../_sources/library/stdtypes.txt"
rel="nofollow">Show Source</a></li>
</ul>
<div id="searchbox" style="display: none">
<h3>Quick search</h3>
<form class="search" action="../search.html" method="get">
<input type="text" name="q" size="18" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
<p class="searchtip" style="font-size: 90%">
Enter search terms or a module, class or function name.
</p>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="related">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="General Index"
>index</a></li>
<li class="right" >
<a href="../py-modindex.html" title="Python Module Index"
>modules</a> |</li>
<li class="right" >
<a href="exceptions.html" title="5. Built-in Exceptions"
>next</a> |</li>
<li class="right" >
<a href="constants.html" title="3. Built-in Constants"
>previous</a> |</li>
<li><img src="../_static/py.png" alt=""
style="vertical-align: middle; margin-top: -1px"/></li>
<li><a href="../index.html">Python v3.2.2 documentation</a> »</li>
<li><a href="index.html" >The Python Standard Library</a> »</li>
</ul>
</div>
<div class="footer">
© <a href="../copyright.html">Copyright</a> 1990-2011, Python Software Foundation.
<br />
The Python Software Foundation is a non-profit corporation.
<a href="http://www.python.org/psf/donations/">Please donate.</a>
<br />
Last updated on Sep 04, 2011.
<a href="../bugs.html">Found a bug</a>?
<br />
Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.0.7.
</div>
</body>
</html>
distrib
>
Mandriva
>
2010.1
>
x86_64
>
media
>
contrib-backports
>
by-pkgid
>
3ba3bd1608c672ba2129b098a48e9e4d
>
files
>
802
