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  <section id="numeric-and-mathematical-modules">
<span id="numeric"></span><h1>Numeric and Mathematical Modules<a class="headerlink" href="#numeric-and-mathematical-modules" title="Link to this heading">¶</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.)."><code class="xref py py-mod docutils literal notranslate"><span class="pre">numbers</span></code></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.)."><code class="xref py py-mod docutils literal notranslate"><span class="pre">math</span></code></a> and <a class="reference internal" href="cmath.html#module-cmath" title="cmath: Mathematical functions for complex numbers."><code class="xref py py-mod docutils literal notranslate"><span class="pre">cmath</span></code></a> modules contain various
mathematical functions for floating-point and complex numbers. The <a class="reference internal" href="decimal.html#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic  Specification."><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code></a>
module supports exact representations of decimal numbers, using arbitrary precision
arithmetic.</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"><code class="xref py py-mod docutils literal notranslate"><span class="pre">numbers</span></code> — Numeric abstract base classes</a><ul>
<li class="toctree-l2"><a class="reference internal" href="numbers.html#the-numeric-tower">The numeric tower</a></li>
<li class="toctree-l2"><a class="reference internal" href="numbers.html#notes-for-type-implementors">Notes for type implementors</a><ul>
<li class="toctree-l3"><a class="reference internal" href="numbers.html#adding-more-numeric-abcs">Adding More Numeric ABCs</a></li>
<li class="toctree-l3"><a class="reference internal" href="numbers.html#implementing-the-arithmetic-operations">Implementing the arithmetic operations</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="math.html"><code class="xref py py-mod docutils literal notranslate"><span class="pre">math</span></code> — Mathematical functions</a><ul>
<li class="toctree-l2"><a class="reference internal" href="math.html#number-theoretic-and-representation-functions">Number-theoretic and representation functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="math.html#power-and-logarithmic-functions">Power and logarithmic functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="math.html#trigonometric-functions">Trigonometric functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="math.html#angular-conversion">Angular conversion</a></li>
<li class="toctree-l2"><a class="reference internal" href="math.html#hyperbolic-functions">Hyperbolic functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="math.html#special-functions">Special functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="math.html#constants">Constants</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="cmath.html"><code class="xref py py-mod docutils literal notranslate"><span class="pre">cmath</span></code> — Mathematical functions for complex numbers</a><ul>
<li class="toctree-l2"><a class="reference internal" href="cmath.html#conversions-to-and-from-polar-coordinates">Conversions to and from polar coordinates</a></li>
<li class="toctree-l2"><a class="reference internal" href="cmath.html#power-and-logarithmic-functions">Power and logarithmic functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="cmath.html#trigonometric-functions">Trigonometric functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="cmath.html#hyperbolic-functions">Hyperbolic functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="cmath.html#classification-functions">Classification functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="cmath.html#constants">Constants</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="decimal.html"><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code> — Decimal fixed point and floating point arithmetic</a><ul>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#quick-start-tutorial">Quick-start Tutorial</a></li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#decimal-objects">Decimal objects</a><ul>
<li class="toctree-l3"><a class="reference internal" href="decimal.html#logical-operands">Logical operands</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#context-objects">Context objects</a></li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#constants">Constants</a></li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#rounding-modes">Rounding modes</a></li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#signals">Signals</a></li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#floating-point-notes">Floating Point Notes</a><ul>
<li class="toctree-l3"><a class="reference internal" href="decimal.html#mitigating-round-off-error-with-increased-precision">Mitigating round-off error with increased precision</a></li>
<li class="toctree-l3"><a class="reference internal" href="decimal.html#special-values">Special values</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#working-with-threads">Working with threads</a></li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#recipes">Recipes</a></li>
<li class="toctree-l2"><a class="reference internal" href="decimal.html#decimal-faq">Decimal FAQ</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="fractions.html"><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code> — Rational numbers</a></li>
<li class="toctree-l1"><a class="reference internal" href="random.html"><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> — Generate pseudo-random numbers</a><ul>
<li class="toctree-l2"><a class="reference internal" href="random.html#bookkeeping-functions">Bookkeeping functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#functions-for-bytes">Functions for bytes</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#functions-for-integers">Functions for integers</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#functions-for-sequences">Functions for sequences</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#discrete-distributions">Discrete distributions</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#real-valued-distributions">Real-valued distributions</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#alternative-generator">Alternative Generator</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#notes-on-reproducibility">Notes on Reproducibility</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#examples">Examples</a></li>
<li class="toctree-l2"><a class="reference internal" href="random.html#recipes">Recipes</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="statistics.html"><code class="xref py py-mod docutils literal notranslate"><span class="pre">statistics</span></code> — Mathematical statistics functions</a><ul>
<li class="toctree-l2"><a class="reference internal" href="statistics.html#averages-and-measures-of-central-location">Averages and measures of central location</a></li>
<li class="toctree-l2"><a class="reference internal" href="statistics.html#measures-of-spread">Measures of spread</a></li>
<li class="toctree-l2"><a class="reference internal" href="statistics.html#statistics-for-relations-between-two-inputs">Statistics for relations between two inputs</a></li>
<li class="toctree-l2"><a class="reference internal" href="statistics.html#function-details">Function details</a></li>
<li class="toctree-l2"><a class="reference internal" href="statistics.html#exceptions">Exceptions</a></li>
<li class="toctree-l2"><a class="reference internal" href="statistics.html#normaldist-objects"><code class="xref py py-class docutils literal notranslate"><span class="pre">NormalDist</span></code> objects</a></li>
<li class="toctree-l2"><a class="reference internal" href="statistics.html#examples-and-recipes">Examples and Recipes</a><ul>
<li class="toctree-l3"><a class="reference internal" href="statistics.html#classic-probability-problems">Classic probability problems</a></li>
<li class="toctree-l3"><a class="reference internal" href="statistics.html#monte-carlo-inputs-for-simulations">Monte Carlo inputs for simulations</a></li>
<li class="toctree-l3"><a class="reference internal" href="statistics.html#approximating-binomial-distributions">Approximating binomial distributions</a></li>
<li class="toctree-l3"><a class="reference internal" href="statistics.html#naive-bayesian-classifier">Naive bayesian classifier</a></li>
<li class="toctree-l3"><a class="reference internal" href="statistics.html#kernel-density-estimation">Kernel density estimation</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
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