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Numeric and Mathematical Modules — Python 2.7.5 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: '2.7.5', 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 2.7.5 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 2.7.5 documentation" href="../index.html" /> <link rel="up" title="The Python Standard Library" href="index.html" /> <link rel="next" title="9.1. numbers — Numeric abstract base classes" href="numbers.html" /> <link rel="prev" title="8.19. repr — Alternate repr() implementation" href="repr.html" /> <link rel="shortcut icon" type="image/png" href="../_static/py.png" /> <script type="text/javascript" src="../_static/copybutton.js"></script> </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="numbers.html" title="9.1. numbers — Numeric abstract base classes" accesskey="N">next</a> |</li> <li class="right" > <a href="repr.html" title="8.19. repr — Alternate repr() implementation" accesskey="P">previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="http://www.python.org/">Python</a> »</li> <li> <a href="../index.html">Python 2.7.5 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="numeric-and-mathematical-modules"> <span id="numeric"></span><h1>9. Numeric and Mathematical Modules<a class="headerlink" href="#numeric-and-mathematical-modules" title="Permalink to this headline">¶</a></h1> <p>The modules described in this chapter provide numeric and math-related functions and data types. The <a class="reference internal" href="numbers.html#module-numbers" title="numbers: Numeric abstract base classes (Complex, Real, Integral, etc.)."><tt class="xref py py-mod docutils literal"><span class="pre">numbers</span></tt></a> module defines an abstract hierarchy of numeric types. 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 contain various mathematical functions for floating-point and complex numbers. For users more interested in decimal accuracy than in speed, the <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> module supports exact representations of decimal numbers.</p> <p>The following modules are documented in this chapter:</p> <div class="toctree-wrapper compound"> <ul> <li class="toctree-l1"><a class="reference internal" href="numbers.html">9.1. <tt class="docutils literal"><span class="pre">numbers</span></tt> — Numeric abstract base classes</a><ul> <li class="toctree-l2"><a class="reference internal" href="numbers.html#the-numeric-tower">9.1.1. The numeric tower</a></li> <li class="toctree-l2"><a class="reference internal" href="numbers.html#notes-for-type-implementors">9.1.2. Notes for type implementors</a><ul> <li class="toctree-l3"><a class="reference internal" href="numbers.html#adding-more-numeric-abcs">9.1.2.1. Adding More Numeric ABCs</a></li> <li class="toctree-l3"><a class="reference internal" href="numbers.html#implementing-the-arithmetic-operations">9.1.2.2. Implementing the arithmetic operations</a></li> </ul> </li> </ul> </li> <li class="toctree-l1"><a class="reference internal" href="math.html">9.2. <tt class="docutils literal"><span class="pre">math</span></tt> — Mathematical functions</a><ul> <li class="toctree-l2"><a class="reference internal" href="math.html#number-theoretic-and-representation-functions">9.2.1. Number-theoretic and representation functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math.html#power-and-logarithmic-functions">9.2.2. Power and logarithmic functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math.html#trigonometric-functions">9.2.3. Trigonometric functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math.html#angular-conversion">9.2.4. Angular conversion</a></li> <li class="toctree-l2"><a class="reference internal" href="math.html#hyperbolic-functions">9.2.5. Hyperbolic functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math.html#special-functions">9.2.6. Special functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math.html#constants">9.2.7. Constants</a></li> </ul> </li> <li class="toctree-l1"><a class="reference internal" href="cmath.html">9.3. <tt class="docutils literal"><span class="pre">cmath</span></tt> — Mathematical functions for complex numbers</a><ul> <li class="toctree-l2"><a class="reference internal" href="cmath.html#conversions-to-and-from-polar-coordinates">9.3.1. Conversions to and from polar coordinates</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath.html#power-and-logarithmic-functions">9.3.2. Power and logarithmic functions</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath.html#trigonometric-functions">9.3.3. Trigonometric functions</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath.html#hyperbolic-functions">9.3.4. Hyperbolic functions</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath.html#classification-functions">9.3.5. Classification functions</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath.html#constants">9.3.6. Constants</a></li> </ul> </li> <li class="toctree-l1"><a class="reference internal" href="decimal.html">9.4. <tt class="docutils literal"><span class="pre">decimal</span></tt> — Decimal fixed point and floating point arithmetic</a><ul> <li class="toctree-l2"><a class="reference internal" href="decimal.html#quick-start-tutorial">9.4.1. Quick-start Tutorial</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal.html#decimal-objects">9.4.2. Decimal objects</a><ul> <li class="toctree-l3"><a class="reference internal" href="decimal.html#logical-operands">9.4.2.1. Logical operands</a></li> </ul> </li> <li class="toctree-l2"><a class="reference internal" href="decimal.html#context-objects">9.4.3. Context objects</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal.html#signals">9.4.4. Signals</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal.html#floating-point-notes">9.4.5. Floating Point Notes</a><ul> <li class="toctree-l3"><a class="reference internal" href="decimal.html#mitigating-round-off-error-with-increased-precision">9.4.5.1. Mitigating round-off error with increased precision</a></li> <li class="toctree-l3"><a class="reference internal" href="decimal.html#special-values">9.4.5.2. Special values</a></li> </ul> </li> <li class="toctree-l2"><a class="reference internal" href="decimal.html#working-with-threads">9.4.6. Working with threads</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal.html#recipes">9.4.7. Recipes</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal.html#decimal-faq">9.4.8. Decimal FAQ</a></li> </ul> </li> <li class="toctree-l1"><a class="reference internal" href="fractions.html">9.5. <tt class="docutils literal"><span class="pre">fractions</span></tt> — Rational numbers</a></li> <li class="toctree-l1"><a class="reference internal" href="random.html">9.6. <tt class="docutils literal"><span class="pre">random</span></tt> — Generate pseudo-random numbers</a></li> <li class="toctree-l1"><a class="reference internal" href="itertools.html">9.7. <tt class="docutils literal"><span class="pre">itertools</span></tt> — Functions creating iterators for efficient looping</a><ul> <li class="toctree-l2"><a class="reference internal" href="itertools.html#itertool-functions">9.7.1. Itertool functions</a></li> <li class="toctree-l2"><a class="reference internal" href="itertools.html#recipes">9.7.2. Recipes</a></li> </ul> </li> <li class="toctree-l1"><a class="reference internal" href="functools.html">9.8. <tt class="docutils literal"><span class="pre">functools</span></tt> — Higher-order functions and operations on callable objects</a><ul> <li class="toctree-l2"><a class="reference internal" href="functools.html#partial-objects">9.8.1. <tt class="docutils literal"><span class="pre">partial</span></tt> Objects</a></li> </ul> </li> <li class="toctree-l1"><a class="reference internal" href="operator.html">9.9. <tt class="docutils literal"><span class="pre">operator</span></tt> — Standard operators as functions</a><ul> <li class="toctree-l2"><a class="reference internal" href="operator.html#mapping-operators-to-functions">9.9.1. 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