# kisonecat/math-expressions

Javascript library handling mathematical expressions involving transcendental functions
JavaScript
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# math-expressions

Math-expressions is client- or server-side JavaScript library for parse expressions like sin^2 (x^3) and do some basic computer algebra with them, like symbolic differentiation and numerically identifying equivalent expressions.

# Demo of client-side use

There is a demo available which focuses on the equality testing.

# Code Example

Include the script in build/math-expressions.js on your page.

<script type="text/javascript" src="math-expressions.js"></script>

This adds MathExpression to the global namespace, so you can then perform the following parsing and equality-testing.

var f = MathExpression.fromText("sin^2 (x^3)");

console.log(f.tex());

var g = MathExpression.fromText("sin^2 x + cos^2 x");
var h = MathExpression.fromText("1");

console.log( g.equals(h) );

var g = MathExpression.fromText("x + x^2");
var h = MathExpression.fromText("x + x^3");

console.log( g.equals(h) );

For server-side use, you can load the package as usual via var MathExpression = require('math-expressions');.

# Installation

The pre-built library is stored in build/math-expressions.js. This is packaged in a "unified" module format, so it can be treated as an AMD-style or a CommonJS-style module (and imported via a module loader like RequireJS). If you are not using a module loader, you can import it via

<script type="text/javascript" src="math-expressions.js"></script>

to add MathExpression to the global namespace.

# API Reference

## Expression constructors

### MathExpression.fromText(string)

Convert string to expression through the text parser. For example, var f = MathExpression.fromText('x^2'); will result in f representing the expression x^2. Then f.evaluate({x:3}) is 9.

This is often used for student-facing text, considering that even MathExpression.fromText('sin^2 x') does the right thing and produces the square of the sine function. Exceptions are thrown when string does not parse.

### MathExpression.fromLatex(string)

Convert string to an expression through the LaTeX parser. For example, var f = MathExpression.fromLatex('\\frac{x+1}{2}'); will result in f representing the expression (x+1)/2. Then f.evaluate({x:3}) is 2.

## Expression methods

### expression.toString()

Produce a textual representation of expression. For example, MathExpression.fromText( f.toString() ) recreates f.

### expression.toLatex()

Produce a LaTeX representation of expression. For example, if f is MathExpression.fromText('x^10'), then f.toLatex() is x^{10} since LaTeX requires braces for exponents.

### expression.variables()

Return the list of variables used in expression. For example, if f is MathExpression.fromText('x + cos(y)'), then f.variables() is ['x','y'].

### expression.equals(another)

Determine whether expression and another represent the "same" expression.

The current algorithm randomly samples the two expressions in a neighborhood of the real line of the complex plane and demands approximate numeric equality most of the time for random assignments to the variables. This is, quite admittedly, not a perfect algorithm, and it is likely to be replaced in a future version of this library.

### expression.derivative(variable)

Symbolically differentiate expression with respect to the given variable. For example, if f is MathExpression.fromText('x^10'), then f.derivative('x') is 10 x^9.

# Tests

Assuming you have git cloneed the repository and npm installed to populate node_modules with jasmine, you can then run the tests with npm test.

Most of the tests are used to determine if expression.equals(another) does the expected thing on student input.