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mathjs

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Math.js is an extensive math library for JavaScript and Node.js. It features real and complex numbers, units, matrices, a large set of mathematical functions, and a flexible expression parser.

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  • 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. It features real and complex numbers, units, matrices, a large set of mathematical functions, and a flexible expression parser. Powerful and easy to use.

Features

  • Supports numbers, complex numbers, units, strings, arrays, and matrices.
  • Contains a large set of built-in functions and constants.
  • Contains a flexible expression parser.
  • Compatible with JavaScript’s built-in Math library.
  • No dependencies. Runs on any JavaScript engine.
  • Easily extensible.

Install

Math.js can be installed using npm:

npm install mathjs

Or the latest version of math.js can be downloaded from mathjs.org:

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');

math.sqrt(-4); // 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">
        math.sqrt(-4); // 2i
    </script>
</body>
</html>

Use

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

var math = require('mathjs');

// use methods and types available in the math object
var a = math.sin(math.pi / 4);  // 0.7071067811865476
var b = math.pow(a, 2);         // 0.5

var c = math.complex(3, -4);    // 3 - 4i
math.sqrt(c);                   // 2 - i

math.sqrt(-4);                  // 2i

var f = math.unit(60, 'deg');   // 60 deg
var g = math.cos(f);            // 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 set.

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

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

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

// evaluate expressions
var a = parser.eval('sqrt(3^2 + 4^2)'); // a = 5
var b = parser.eval('sqrt(-4)');        // b = 2i
var c = parser.eval('2 inch in cm');    // c = 5.08 cm
var d = parser.eval('cos(45 deg)');     // d = 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 set variables and functions
var x = parser.get('x');                // x = 7
var f = parser.get('f');                // f = function
var g = f(3, 3);                        // g = 27
parser.set('h', 500);
parser.eval('h / 2');                   // 250
parser.set('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.set(name, value);           // set 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 workspace
var workspace = math.workspace();

// add expressions to the workspace
var id0 = workspace.append('a = 3/4');
var id1 = workspace.append('a + 2');
workspace.getResult(id1); // 2.75

// replace expressions in the workspace
workspace.replace('a=5/2', id0);
workspace.getResult(id1); // 4.5

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.

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

String

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

math.add('hello ', 'world');    // 'hello world'
math.max('A', 'D', 'C');        // 'D'

Complex

Math.js supports complex numbers.

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

Unit

Math.js supports units.

var a = math.unit(55, 'cm');    // 550 mm
var b = math.unit('0.1m');      // 100 mm
math.add(a, b);                 // 0.65 m

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

Array and Matrix

Math.js supports n-dimensional arrays and matrices. Both regular JavaScript Array and the math.js Matrix can be used interchangeably in all math.js functions.

A Matrix is an object wrapped around a regular JavaScript Array, providing utility methods for easy matrix manipulation such as get, set, size, resize, clone, and more.

var matrix = math.matrix([1, 4, 9, 16, 25]);    // Matrix, [1, 4, 9, 16, 25]
math.sqrt(matrix);                              // Matrix, [1, 2, 3, 4, 5]

var array = [1, 2, 3, 4, 5];
math.factorial(array);                          // Array,  [1, 2, 6, 24, 120]

var a = [[1, 2], [3, 4]];                       // Array,  [[1, 2], [3, 4]]
var b = math.matrix([[5, 6], [1, 1]]);          // Matrix, [[5, 6], [1, 1]]
b.set([2, [1, 2]], [[7, 8]]);                   // Matrix, [[5, 6], [7, 8]]
var c = math.multiply(a, b);                    // Matrix, [[19, 22], [43, 50]]
var d = c.get([2, 1]);                          // 43

Matrices are supported by the parser:

parser = math.parser();

parser.eval('a = [1, 2; 3, 4]');                // Matrix, [[1, 2], [3, 4]]
parser.eval('b = [5, 6; 7, 8]');                // Matrix, [[5, 6], [1, 1]]
parser.eval('b(2, 1:2) = [7, 8]');              // Matrix, [[5, 6], [7, 8]]
parser.eval('c = a * b');                       // Matrix, [[19, 22], [43, 50]]
parser.eval('d = c(2, 1)');                     // 43

Range

A Range creates a range with a start, end, and optionally a step. A Range can be used to create indexes to get or set submatrices.

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

math.factorial(math.range(1,5));                // Array,  [1, 2, 6, 24, 120]

var a = math.matrix();                          // Matrix, []
a.set([math.range('2:5')], [7, 2, 1, 5]);       // Matrix, [0, 7, 2, 1, 5]

var b = math.range(2, -1, -2);                  // Range, 2👎-2
var c = b.valueOf();                            // Array,  [2, 1, 0, -1, -2]

var d = parser.eval('3:7');                     // Range, 3:7

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, Complex, Unit, String, and Array) 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)

Matrix

  • math.concat(a, b, c, ... [, dim])
  • math.det(x)
  • math.diag(x)
  • math.eye(m, n, p, ...)
  • math.inv(x)
  • math.ones(m, n, p, ...)
  • math.size(x)
  • math.squeeze(x)
  • math.transpose(x)
  • math.zeros(m, n, p, ...)

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.clone(x)
  • math.format([template, ] values)
  • 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
math.myvalue * 2;               // 84
math.hello('user');             // 'hello, user!'

var parser = math.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 = math.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. To be able to run jake from the command line, jake must be installed globally:

sudo npm install -g jake

Then, the project can be build by executing jake in the root of the project:

cd mathjs
jake

This will build the library math.js and math.min.js from the source files and execute tests.

Alternatively, when jake is not installed on your system, the project can be build by running npm install in the root of the project. npm will then use a local installation of jake to build the project.

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 (2013-03-09)
    • Implement Workspace
    • Implement more methods
  • Build a website (2013-03-11)
  • Version 0.4.0 (2013-03-16)
    • Implement Arrays
  • Version 0.5.0 (2013-04-06)
    • Implement Matrix and Range
  • Version 0.6.0
    • More on matrices
  • Version 1.0.0
    • Extensive testing
    • Examples and documentation

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.