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<html><head><meta charset="UTF-8" /><title>propeller.tools.calculus documentation</title><link rel="stylesheet" type="text/css" href="css/default.css" /><link rel="stylesheet" type="text/css" href="css/highlight.css" /><script type="text/javascript" src="js/highlight.min.js"></script><script type="text/javascript" src="js/jquery.min.js"></script><script type="text/javascript" src="js/page_effects.js"></script><script>hljs.initHighlightingOnLoad();</script></head><body><div id="header"><h2>Generated by <a href="https://github.com/weavejester/codox">Codox</a></h2><h1><a href="index.html"><span class="project-title"><span class="project-name">Propeller</span> <span class="project-version">0.3.0</span></span></a></h1></div><div class="sidebar primary"><h3 class="no-link"><span class="inner">Project</span></h3><ul class="index-link"><li class="depth-1 "><a href="index.html"><div class="inner">Index</div></a></li></ul><h3 class="no-link"><span class="inner">Topics</span></h3><ul><li class="depth-1 "><a href="A_Guide_To_Propeller.html"><div class="inner"><span>A Guide to Propeller</span></div></a></li><li class="depth-1 "><a href="Adding_Genetic_Operators.html"><div class="inner"><span>Adding Genetic Operators</span></div></a></li><li class="depth-1 "><a href="Adding_Problem.html"><div class="inner"><span>Adding a Problem</span></div></a></li><li class="depth-1 "><a href="Adding_Selection_Method.html"><div class="inner"><span>Adding a Selection Method</span></div></a></li><li class="depth-1 "><a href="Additional_Instructions.html"><div class="inner"><span>Additional Instructions</span></div></a></li><li class="depth-1 "><a href="Generating_Documentation.html"><div class="inner"><span>Generating Documentation for Propeller</span></div></a></li></ul><h3 class="no-link"><span class="inner">Namespaces</span></h3><ul><li class="depth-1"><div class="no-link"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>propeller</span></div></div></li><li class="depth-2 branch"><a href="propeller.genome.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>genome</span></div></a></li><li class="depth-2 branch"><a href="propeller.gp.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>gp</span></div></a></li><li class="depth-2"><div class="no-link"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>problems</span></div></div></li><li class="depth-3"><div class="no-link"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>PSB2</span></div></div></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.basement.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>basement</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.bouncing-balls.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>bouncing-balls</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.bowling.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>bowling</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.camel-case.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>camel-case</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.dice-game.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>dice-game</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.fizz-buzz.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>fizz-buzz</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.fuel-cost.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>fuel-cost</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.gcd.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>gcd</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.luhn.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>luhn</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.middle-character.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>middle-character</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.paired-digits.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>paired-digits</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.shopping-list.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>shopping-list</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.snow-day.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>snow-day</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.solve-boolean.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>solve-boolean</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.spin-words.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>spin-words</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.square-digits.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>square-digits</span></div></a></li><li class="depth-4 branch"><a href="propeller.problems.PSB2.substitution-cipher.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>substitution-cipher</span></div></a></li><li class="depth-4"><a href="propeller.problems.PSB2.twitter.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>twitter</span></div></a></li><li class="depth-3 branch"><a href="propeller.problems.simple-regression.html"><div class="inner"><span class="tree" style="top: -579px;"><span class="top" style="height: 588px;"></span><span class="bottom"></span></span><span>simple-regression</span></div></a></li><li class="depth-3"><div class="no-link"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>software</span></div></div></li><li class="depth-4 branch"><a href="propeller.problems.software.number-io.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>number-io</span></div></a></li><li class="depth-4"><a href="propeller.problems.software.smallest.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>smallest</span></div></a></li><li class="depth-3 branch"><a href="propeller.problems.string-classification.html"><div class="inner"><span class="tree" style="top: -83px;"><span class="top" style="height: 92px;"></span><span class="bottom"></span></span><span>string-classification</span></div></a></li><li class="depth-3"><a href="propeller.problems.valiant.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>valiant</span></div></a></li><li class="depth-2"><div class="no-link"><div class="inner"><span class="tree" style="top: -796px;"><span class="top" style="height: 805px;"></span><span class="bottom"></span></span><span>push</span></div></div></li><li class="depth-3"><a href="propeller.push.instructions.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>instructions</span></div></a></li><li class="depth-4 branch"><a href="propeller.push.instructions.bool.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>bool</span></div></a></li><li class="depth-4 branch"><a href="propeller.push.instructions.character.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>character</span></div></a></li><li class="depth-4 branch"><a href="propeller.push.instructions.code.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>code</span></div></a></li><li class="depth-4 branch"><a href="propeller.push.instructions.input-output.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>input-output</span></div></a></li><li class="depth-4 branch"><a href="propeller.push.instructions.numeric.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>numeric</span></div></a></li><li class="depth-4 branch"><a href="propeller.push.instructions.polymorphic.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>polymorphic</span></div></a></li><li class="depth-4 branch"><a href="propeller.push.instructions.string.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>string</span></div></a></li><li class="depth-4"><a href="propeller.push.instructions.vector.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>vector</span></div></a></li><li class="depth-3 branch"><a href="propeller.push.interpreter.html"><div class="inner"><span class="tree" style="top: -269px;"><span class="top" style="height: 278px;"></span><span class="bottom"></span></span><span>interpreter</span></div></a></li><li class="depth-3 branch"><a href="propeller.push.limits.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>limits</span></div></a></li><li class="depth-3"><a href="propeller.push.state.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>state</span></div></a></li><li class="depth-2 branch"><a href="propeller.selection.html"><div class="inner"><span class="tree" style="top: -393px;"><span class="top" style="height: 402px;"></span><span class="bottom"></span></span><span>selection</span></div></a></li><li class="depth-2 branch"><a href="propeller.simplification.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>simplification</span></div></a></li><li class="depth-2"><div class="no-link"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>tools</span></div></div></li><li class="depth-3 branch current"><a href="propeller.tools.calculus.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>calculus</span></div></a></li><li class="depth-3 branch"><a href="propeller.tools.character.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>character</span></div></a></li><li class="depth-3 branch"><a href="propeller.tools.distributions.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>distributions</span></div></a></li><li class="depth-3 branch"><a href="propeller.tools.math.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>math</span></div></a></li><li class="depth-3"><a href="propeller.tools.metrics.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>metrics</span></div></a></li><li class="depth-2 branch"><a href="propeller.utils.html"><div class="inner"><span class="tree" style="top: -176px;"><span class="top" style="height: 185px;"></span><span class="bottom"></span></span><span>utils</span></div></a></li><li class="depth-2"><a href="propeller.variation.html"><div class="inner"><span class="tree"><span class="top"></span><span class="bottom"></span></span><span>variation</span></div></a></li></ul></div><div class="sidebar secondary"><h3><a href="#top"><span class="inner">Public Vars</span></a></h3><ul><li class="depth-1"><a href="propeller.tools.calculus.html#var-deriv"><div class="inner"><span>deriv</span></div></a></li><li class="depth-1"><a href="propeller.tools.calculus.html#var-integrate"><div class="inner"><span>integrate</span></div></a></li></ul></div><div class="namespace-docs" id="content"><h1 class="anchor" id="top">propeller.tools.calculus</h1><div class="doc"><div class="markdown"><p>Functions for calculus operations</p>
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</div></div><div class="public anchor" id="var-deriv"><h3>deriv</h3><div class="usage"><code>(deriv f c)</code><code>(deriv f)</code></div><div class="doc"><div class="markdown"><p>Returns the derivative of f evaluated at c. If called with only one argument, it returns the derivative function.</p>
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</div></div></div><div class="public anchor" id="var-integrate"><h3>integrate</h3><div class="usage"><code>(integrate f)</code><code>(integrate f a b)</code></div><div class="doc"><div class="markdown"><p>Returns the definite integral of f over <a href="a, b">a, b</a> using Simpson’s method. If called with only one argument (the function), returns the indefinite integral, which takes as input a value x and (optionally) a constant c.</p>
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