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mathjs

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An extensive math library for JavaScript and Node.js. Includes an advanced expression parser. Supports numbers, complex numbers, units, strings, and matrices. Contains a large set of functions and constants.

Package Exports

  • mathjs

This package does not declare an exports field, so the exports above have been automatically detected and optimized by JSPM instead. If any package subpath is missing, it is recommended to post an issue to the original package (mathjs) to support the "exports" field. If that is not possible, create a JSPM override to customize the exports field for this package.

Readme

math.js

http://mathjs.org

Math.js is an extensive math library for JavaScript and Node.js, compatible with JavaScript's built-in Math library.

Features

  • A flexible expression parser.
  • Supports numbers, complex numbers, units, strings, arrays*, and matrices*.
  • A large set of built-in functions and constants.
  • Easily extensible with new functions and constants.
  • Powerful and easy to use.

* Note: arrays and matrices are to be implemented.

Install

Math.js can be installed with npm:

npm install mathjs

Alternatively, the latest stable version of math.js can be downloaded from github:

Load

Node.js

Math.js can be loaded in node.js using require, and similarly in the browser using require.js.

var math = require('mathjs');

var a = math.sqrt(-4);
console.log('a = ' + a);                // 'a = 2i'

Browser

Math.js can be loaded as a regular javascript file in the browser:

<!DOCTYPE HTML>
<html>
<head>
    <script src="math.js" type="text/javascript"></script>
</head>
<body>
    <script type="text/javascript">
        var a = math.sqrt(-4);
        document.write('a = ' + a);     // 'a = 2i'
    </script>
</body>
</html>

Use

Math.js can be used similar to Javascript's built-in Math library.

var math = require('mathjs'),
    Complex = math.Complex,
    Unit = math.Unit;

// use methods and types available in the math object
var a = math.sin(math.pi / 4);
var b = math.pow(a, 2);
console.log('b = ' + math.round(b, 3)); // 'b = 0.5'

var c = new Complex(3, -4);
var d = math.sqrt(c);
console.log('d = ' + d);                // 'd = 2 - i'

var e = math.sqrt(-4);
console.log('e = ' + e);                // 'e = 2i'

var f = new Unit(60, 'deg');
var g = math.cos(f);
console.log('g = ' + math.round(g, 3)); // 'g = 0.5'

Parser

Math.js contains a flexible and easy to use expression parser. The parser supports all data types, methods and constants available in math.js. It has a method eval to evaluate expressions, and parse to parse expressions and build a node tree from it. The parser supports variable and function definitions. Variables and functions can be manipulated using the methods get and put.

The following example code shows how to create and use a parser.

// load math.js
var math = require('mathjs');

// create a new parser
var parser = new math.parser.Parser();

// evaluate expressions
var a = parser.eval('sqrt(3^2 + 4^2)'); // 5
var b = parser.eval('sqrt(-4)');        // 2i
var c = parser.eval('2 inch in cm');    // 5.08 cm
var d = parser.eval('cos(45 deg)');     // 0.7071067811865476

// define variables and functions
parser.eval('x = 7 / 2');               // 3.5
parser.eval('x + 3');                   // 6.5
parser.eval('function f(x, y) = x^y');  // f(x, y)
parser.eval('f(2, 3)');                 // 8

// get and put variables and functions
var x = parser.get('x');                // 7
var f = parser.get('f');                // function
var g = f(3, 2);                        // 9
parser.put('h', 500);
var i = parser.eval('h / 2');           // 250
parser.put('hello', function (name) {
    return 'hello, ' + name + '!';
});
parser.eval('hello("user")');           // "hello, user!"

// clear defined functions and variables
parser.clear();

Available methods:

var result = parser.eval(expr);    // evaluate an expression
var value = parser.get(name);      // retrieve a variable from the parser
parser.put(name, value);           // put a variable in the parser

var node = parser.parse(expr);     // parse an expression into a node tree
var result = node.eval();          // evaluate a node

Workspace

Math.js features a workspace, which manages a set of expressions. Expressions can be added, replace, deleted, and inserted in the workspace. The workspace keeps track on the dependencies between the expressions, and automatically updates results of depending expressions when variables or function definitions are changed in the workspace.

// load math.js
var math = require('mathjs');

// create a new workspace
var workspace = new math.parser.Workspace();

// add expressions to the workspace
var id0 = workspace.append('a = 3/4');
var id1 = workspace.append('a + 2');
console.log('a + 2 = ' + workspace.getResult(id1));

// replace expressions in the workspace
workspace.replace('a=5/2', id0);
console.log('a + 2 = ' + workspace.getResult(id1));

Available methods:

var id = workspace.append(expr);
var id = workspace.insertBefore(expr, beforeId);
var id = workspace.insertAfter(expr, afterId);
workspace.replace(expr, id);
workspace.remove(id);
workspace.clear();
var expr    = workspace.getExpr(id);
var result  = workspace.getResult(id);
var deps    = workspace.getDependencies(id);
var changes = workspace.getChanges(updateSeq);

Data types

Math.js supports both native data types like Number, String, and Array, as well as advanced data types like Complex and Unit.

Number

The built-in type Number can be used in all methods.

var math = require('mathjs');

var a = math.subtract(7.1, 2.3);        // 4.8
var b = math.round(math.pi, 3);         // 3.142
var c = math.sqrt(new Number(4.41e2));  // 21

String

The built-in type String can be used in applicable methods.

var math = require('math.js');

var a = math.add('hello ', 'world');    // 'hello world'
var b = math.max('A', 'D', 'C');        // 'D'

Complex

Math.js supports complex numbers.

var math = require('math.js'),
    Complex = math.Complex;

var a = new Complex(2, 3);              // 2 + 3i
var b = new Complex('4 - 2i');          // 4 - 2i
var c = math.add(a, b);                 // 6 + i
var d = math.sqrt(-4);                  // 2i

Unit

Math.js supports units.

var math = require('math.js'),
    Unit = math.Unit;

var a = new Unit(55, 'cm');             // 550 mm
var b = new Unit(0.1, 'm');             // 100 mm
var c = math.add(a, b);                 // 650 mm

var parser = new math.parser.Parser();
var d = parser.eval('2 inch in cm');    // 5.08 cm

Constants

Math.js has the following built-in constants.

  • math.E, math.e
  • math.I, math.i
  • math.LN2
  • math.LN10
  • math.LOG2E
  • math.LOG10E
  • math.PI, math.pi
  • math.SQRT1_2
  • math.SQRT2

Methods

Math.js contains the following methods. The methods support all available data types (Number, String, Complex, and Unit) where applicable.

Arithmetic

  • math.abs(x)
  • math.add(x, y)
  • math.ceil(x)
  • math.cube(x)
  • math.divide(x, y)
  • math.equal(x)
  • math.exp(x)
  • math.fix(x)
  • math.floor(x)
  • math.larger(x, y)
  • math.largereq(x, y)
  • math.log(x [, base])
  • math.log10(x)
  • math.mod(x, y)
  • math.multiply(x, y)
  • math.pow(x, y)
  • math.round(x [, n])
  • math.sign()
  • math.smaller(x, y)
  • math.smallereq(x, y)
  • math.subtract(x, y)
  • math.sqrt(x)
  • math.square(x)
  • math.unaryminus(x)
  • math.unequal(x)

Complex

  • math.re(x)
  • math.im(x)
  • math.arg(x)
  • math.conj(x)

Probability

  • math.factorial(x)
  • math.random()

Statistics

  • math.max(a, b, c, ...)
  • math.min(a, b, c, ...)

Trigonometry

  • math.acos(x)
  • math.asin(x)
  • math.atan(x)
  • math.atan2(y, x)
  • math.cos(x)
  • math.cot(x)
  • math.csc(x)
  • math.sec(x)
  • math.sin(x)
  • math.tan(x)

Units

  • math.in(x, unit)

Utils

  • math.help(fn)
  • math.import(filename | object, override)
  • math.typeof(x)

Extend

The library can easily be extended with functions and variables using the import method. The method import accepts a filename or an object with functions and variables.

var math = require('mathjs');

// define new functions and variables
math.import({
    myvalue: 42,
    hello: function (name) {
        return 'hello, ' + name + '!';
    });
});

// defined methods can be used in both JavaScript as well as the parser
var a = math.myvalue * 2;               // 84
var b = math.hello('user');             // 'hello, user!'

var parser = new math.parser.Parser();
parser.eval('myvalue + 10');            // 52
parser.eval('hello("user")');           // 'hello, user!'

To import functions from a math library like numbers.js, the library must be installed using npm:

npm install numbers

And next, the library can be imported into math.js:

var math = require('mathjs'),
    parser = new math.parser.Parser();

// import the numbers.js library into math.js
math.import('numbers');

// use functions from numbers.js
math.fibonacci(7);                      // 7
parser.eval('fibonacci(7)');            // 7

Build

First clone the project from github:

git clone git://github.com/josdejong/mathjs.git

The project uses jake as build tool, which must be installed globally. After jake is installed, the project dependencies can be downloaded using npm. Then the project can be build by executing jake in the root of the project.

cd mathjs
sudo npm install -g jake
npm install
jake

When jake is executed, it will generate the library math.js and math.min.js from the source files, and will test the library.

Test

To execute tests for the library, run:

npm test

Roadmap

  • Version 0.1.0 (2013-02-18):
    • Implement all methods and constants available in the built-in Math library
    • Implement data types Complex and Unit
  • Version 0.2.0 (2013-02-25):
    • Implement Parser, Scope, Node tree
    • Implement more methods
  • Version 0.3.0:
    • Implement Workspace
    • Implement more methods
  • Build a website
  • Version 0.4.0:
    • Implement Arrays and Matrices
  • Version 1.0.0
    • Extensive testing

License

Copyright (C) 2013 Jos de Jong wjosdejong@gmail.com

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.