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.

License

Math-expressions is dual-licensed under GPLv3 and under Apache Version 2.0.