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<div class="section" id="numeric-and-mathematical-modules">
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<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>
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<p>The modules described in this chapter provide numeric and math-related functions
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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"><span class="pre">numbers</span></code></a> module defines an abstract hierarchy of
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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"><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"><span class="pre">cmath</span></code></a> modules contain various
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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"><span class="pre">decimal</span></code></a>
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module supports exact representations of decimal numbers, using arbitrary precision
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<p>The following modules are documented in this chapter:</p>
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<div class="toctree-wrapper compound">
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<li class="toctree-l1"><a class="reference internal" href="numbers.html">9.1. <code class="docutils literal"><span class="pre">numbers</span></code> — Numeric abstract base classes</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="numbers.html#the-numeric-tower">9.1.1. The numeric tower</a></li>
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<li class="toctree-l2"><a class="reference internal" href="numbers.html#notes-for-type-implementors">9.1.2. Notes for type implementors</a><ul>
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<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>
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<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>
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<li class="toctree-l1"><a class="reference internal" href="math.html">9.2. <code class="docutils literal"><span class="pre">math</span></code> — Mathematical functions</a><ul>
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<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>
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<li class="toctree-l2"><a class="reference internal" href="math.html#power-and-logarithmic-functions">9.2.2. Power and logarithmic functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="math.html#trigonometric-functions">9.2.3. Trigonometric functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="math.html#angular-conversion">9.2.4. Angular conversion</a></li>
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<li class="toctree-l2"><a class="reference internal" href="math.html#hyperbolic-functions">9.2.5. Hyperbolic functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="math.html#special-functions">9.2.6. Special functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="math.html#constants">9.2.7. Constants</a></li>
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<li class="toctree-l1"><a class="reference internal" href="cmath.html">9.3. <code class="docutils literal"><span class="pre">cmath</span></code> — Mathematical functions for complex numbers</a><ul>
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<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>
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<li class="toctree-l2"><a class="reference internal" href="cmath.html#power-and-logarithmic-functions">9.3.2. Power and logarithmic functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="cmath.html#trigonometric-functions">9.3.3. Trigonometric functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="cmath.html#hyperbolic-functions">9.3.4. Hyperbolic functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="cmath.html#classification-functions">9.3.5. Classification functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="cmath.html#constants">9.3.6. Constants</a></li>
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<li class="toctree-l1"><a class="reference internal" href="decimal.html">9.4. <code class="docutils literal"><span class="pre">decimal</span></code> — Decimal fixed point and floating point arithmetic</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#quick-start-tutorial">9.4.1. Quick-start Tutorial</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#decimal-objects">9.4.2. Decimal objects</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="decimal.html#logical-operands">9.4.2.1. Logical operands</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#context-objects">9.4.3. Context objects</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#constants">9.4.4. Constants</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#rounding-modes">9.4.5. Rounding modes</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#signals">9.4.6. Signals</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#floating-point-notes">9.4.7. Floating Point Notes</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="decimal.html#mitigating-round-off-error-with-increased-precision">9.4.7.1. Mitigating round-off error with increased precision</a></li>
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<li class="toctree-l3"><a class="reference internal" href="decimal.html#special-values">9.4.7.2. Special values</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#working-with-threads">9.4.8. Working with threads</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#recipes">9.4.9. Recipes</a></li>
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<li class="toctree-l2"><a class="reference internal" href="decimal.html#decimal-faq">9.4.10. Decimal FAQ</a></li>
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<li class="toctree-l1"><a class="reference internal" href="fractions.html">9.5. <code class="docutils literal"><span class="pre">fractions</span></code> — Rational numbers</a></li>
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<li class="toctree-l1"><a class="reference internal" href="random.html">9.6. <code class="docutils literal"><span class="pre">random</span></code> — Generate pseudo-random numbers</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="random.html#notes-on-reproducibility">9.6.1. Notes on Reproducibility</a></li>
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<li class="toctree-l2"><a class="reference internal" href="random.html#examples-and-recipes">9.6.2. Examples and Recipes</a></li>
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<li class="toctree-l1"><a class="reference internal" href="statistics.html">9.7. <code class="docutils literal"><span class="pre">statistics</span></code> — Mathematical statistics functions</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="statistics.html#averages-and-measures-of-central-location">9.7.1. Averages and measures of central location</a></li>
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<li class="toctree-l2"><a class="reference internal" href="statistics.html#measures-of-spread">9.7.2. Measures of spread</a></li>
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<li class="toctree-l2"><a class="reference internal" href="statistics.html#function-details">9.7.3. Function details</a></li>
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<li class="toctree-l2"><a class="reference internal" href="statistics.html#exceptions">9.7.4. Exceptions</a></li>
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