website/content/blog/2017-03-09-simplifying-expressions-octave.md
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---
id: 2115
title: Simplifying Expressions with Octave
date: 2017-03-09T02:09:58+00:00
author: Brandon Rozek
layout: post
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---
Octave is a high level programming language intended for numerical computations. One of the cool features of this is that with symbolic expressions, you can then simplify mathematical expressions.
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## Setup
First install [Octave](https://www.gnu.org/software/octave/) and the [symbolic package](https://octave.sourceforge.io/symbolic/) using the website or your package manager of choice.
Then in octave type in the following code
pkg load symbolic
## Usage
For every variable not defined earlier in your expression, make sure to declare it as a symbolic data type
<pre class='language-MATLAB'><code class='language-MATLAB'>syms x y</code></pre>
Then make an expression
<pre class='language-MATLAB'><code class='language-MATLAB'>
expr = y + sin(x)^2 + cos(x)^2
</code></pre>
You can then ask Octave to simplify the expression for you
<pre class='language-MATLAB'><code class='language-MATLAB'>
simp_expr = simplify(expr)
</code></pre>
Displaying it shows it as
<pre class='language-MATLAB'><code class='language-MATLAB'>(sym) y + 1</code></pre>
Which is indeed a simplification using a trig identity 🙂