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+ <span id="numeric"></span><h1>Numeric and Mathematical Modules</h1> <p>The modules described in this chapter provide numeric and math-related functions and data types. The <a class="reference internal" href="numbers#module-numbers" title="numbers: Numeric abstract base classes (Complex, Real, Integral, etc.)."><code>numbers</code></a> module defines an abstract hierarchy of numeric types. The <a class="reference internal" href="math#module-math" title="math: Mathematical functions (sin() etc.)."><code>math</code></a> and <a class="reference internal" href="cmath#module-cmath" title="cmath: Mathematical functions for complex numbers."><code>cmath</code></a> modules contain various mathematical functions for floating-point and complex numbers. The <a class="reference internal" href="decimal#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic  Specification."><code>decimal</code></a> module supports exact representations of decimal numbers, using arbitrary precision arithmetic.</p> <p>The following modules are documented in this chapter:</p>  <ul> <li class="toctree-l1">
+<a class="reference internal" href="numbers"><code>numbers</code> — Numeric abstract base classes</a><ul> <li class="toctree-l2"><a class="reference internal" href="numbers#the-numeric-tower">The numeric tower</a></li> <li class="toctree-l2">
+<a class="reference internal" href="numbers#notes-for-type-implementors">Notes for type implementors</a><ul> <li class="toctree-l3"><a class="reference internal" href="numbers#adding-more-numeric-abcs">Adding More Numeric ABCs</a></li> <li class="toctree-l3"><a class="reference internal" href="numbers#implementing-the-arithmetic-operations">Implementing the arithmetic operations</a></li> </ul> </li> </ul> </li> <li class="toctree-l1">
+<a class="reference internal" href="math"><code>math</code> — Mathematical functions</a><ul> <li class="toctree-l2"><a class="reference internal" href="math#number-theoretic-and-representation-functions">Number-theoretic and representation functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math#power-and-logarithmic-functions">Power and logarithmic functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math#trigonometric-functions">Trigonometric functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math#angular-conversion">Angular conversion</a></li> <li class="toctree-l2"><a class="reference internal" href="math#hyperbolic-functions">Hyperbolic functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math#special-functions">Special functions</a></li> <li class="toctree-l2"><a class="reference internal" href="math#constants">Constants</a></li> </ul> </li> <li class="toctree-l1">
+<a class="reference internal" href="cmath"><code>cmath</code> — Mathematical functions for complex numbers</a><ul> <li class="toctree-l2"><a class="reference internal" href="cmath#conversions-to-and-from-polar-coordinates">Conversions to and from polar coordinates</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath#power-and-logarithmic-functions">Power and logarithmic functions</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath#trigonometric-functions">Trigonometric functions</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath#hyperbolic-functions">Hyperbolic functions</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath#classification-functions">Classification functions</a></li> <li class="toctree-l2"><a class="reference internal" href="cmath#constants">Constants</a></li> </ul> </li> <li class="toctree-l1">
+<a class="reference internal" href="decimal"><code>decimal</code> — Decimal fixed point and floating point arithmetic</a><ul> <li class="toctree-l2"><a class="reference internal" href="decimal#quick-start-tutorial">Quick-start Tutorial</a></li> <li class="toctree-l2">
+<a class="reference internal" href="decimal#decimal-objects">Decimal objects</a><ul> <li class="toctree-l3"><a class="reference internal" href="decimal#logical-operands">Logical operands</a></li> </ul> </li> <li class="toctree-l2"><a class="reference internal" href="decimal#context-objects">Context objects</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal#constants">Constants</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal#rounding-modes">Rounding modes</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal#signals">Signals</a></li> <li class="toctree-l2">
+<a class="reference internal" href="decimal#floating-point-notes">Floating Point Notes</a><ul> <li class="toctree-l3"><a class="reference internal" href="decimal#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#special-values">Special values</a></li> </ul> </li> <li class="toctree-l2"><a class="reference internal" href="decimal#working-with-threads">Working with threads</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal#recipes">Recipes</a></li> <li class="toctree-l2"><a class="reference internal" href="decimal#decimal-faq">Decimal FAQ</a></li> </ul> </li> <li class="toctree-l1"><a class="reference internal" href="fractions"><code>fractions</code> — Rational numbers</a></li> <li class="toctree-l1">
+<a class="reference internal" href="random"><code>random</code> — Generate pseudo-random numbers</a><ul> <li class="toctree-l2"><a class="reference internal" href="random#bookkeeping-functions">Bookkeeping functions</a></li> <li class="toctree-l2"><a class="reference internal" href="random#functions-for-bytes">Functions for bytes</a></li> <li class="toctree-l2"><a class="reference internal" href="random#functions-for-integers">Functions for integers</a></li> <li class="toctree-l2"><a class="reference internal" href="random#functions-for-sequences">Functions for sequences</a></li> <li class="toctree-l2"><a class="reference internal" href="random#discrete-distributions">Discrete distributions</a></li> <li class="toctree-l2"><a class="reference internal" href="random#real-valued-distributions">Real-valued distributions</a></li> <li class="toctree-l2"><a class="reference internal" href="random#alternative-generator">Alternative Generator</a></li> <li class="toctree-l2"><a class="reference internal" href="random#notes-on-reproducibility">Notes on Reproducibility</a></li> <li class="toctree-l2"><a class="reference internal" href="random#examples">Examples</a></li> <li class="toctree-l2"><a class="reference internal" href="random#recipes">Recipes</a></li> </ul> </li> <li class="toctree-l1">
+<a class="reference internal" href="statistics"><code>statistics</code> — Mathematical statistics functions</a><ul> <li class="toctree-l2"><a class="reference internal" href="statistics#averages-and-measures-of-central-location">Averages and measures of central location</a></li> <li class="toctree-l2"><a class="reference internal" href="statistics#measures-of-spread">Measures of spread</a></li> <li class="toctree-l2"><a class="reference internal" href="statistics#statistics-for-relations-between-two-inputs">Statistics for relations between two inputs</a></li> <li class="toctree-l2"><a class="reference internal" href="statistics#function-details">Function details</a></li> <li class="toctree-l2"><a class="reference internal" href="statistics#exceptions">Exceptions</a></li> <li class="toctree-l2">
+<a class="reference internal" href="statistics#normaldist-objects"><code>NormalDist</code> objects</a><ul> <li class="toctree-l3">
+<a class="reference internal" href="statistics#normaldist-examples-and-recipes"><code>NormalDist</code> Examples and Recipes</a><ul> <li class="toctree-l4"><a class="reference internal" href="statistics#classic-probability-problems">Classic probability problems</a></li> <li class="toctree-l4"><a class="reference internal" href="statistics#monte-carlo-inputs-for-simulations">Monte Carlo inputs for simulations</a></li> <li class="toctree-l4"><a class="reference internal" href="statistics#approximating-binomial-distributions">Approximating binomial distributions</a></li> <li class="toctree-l4"><a class="reference internal" href="statistics#naive-bayesian-classifier">Naive bayesian classifier</a></li> <li class="toctree-l4"><a class="reference internal" href="statistics#kernel-density-estimation">Kernel density estimation</a></li> </ul> </li> </ul> </li> </ul> </li> </ul>  <div class="_attribution">
+  <p class="_attribution-p">
+    &copy; 2001&ndash;2023 Python Software Foundation<br>Licensed under the PSF License.<br>
+    <a href="https://docs.python.org/3.12/library/numeric.html" class="_attribution-link">https://docs.python.org/3.12/library/numeric.html</a>
+  </p>
+</div>