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.
- Supports numbers, complex numbers, units, strings, arrays, and matrices.
- Is compatible with JavaScript’s built-in Math library.
- Contains a flexible expression parser.
- Supports chained operations.
- Comes with a large set of built-in functions and constants.
- Has no dependencies. Runs on any JavaScript engine.
- Can be used as a command line application as well.
- Is easily extensible.
Math.js can be installed using npm:
npm install mathjs
Note: when installed globally (using the -g option), math.js is available as
a command line application mathjs, see section
command line interface.
Or using bower:
bower install mathjs
Or by downloading the latest version from mathjs.org:
- math.js (Development version)
- math.min.js (Production version)
Load math.js in node.js:
var math = require('mathjs');
math.sqrt(-4); // 2iMath.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>Load math.js in the browser using require.js:
require.config({
paths: {
mathjs: 'path/to/mathjs',
}
});
require(['mathjs'], function (math) {
math.sqrt(-4); // 2i
});Math.js can be used similar to JavaScript's built-in Math library. Besides that, math.js can evaluate expressions (see Expressions) and supports chained operations (see Chained operations).
The example code below shows how to use math.js. More examples can be found in the examples directory.
// load math.js
var math = require('mathjs');
// functions and constants
math.round(math.e, 3); // 2.718
math.atan2(3, -3) / math.pi; // 0.75
math.log(1000, 10); // 3
math.sqrt(-4); // 2i
math.pow([[-1, 2], [3, 1]], 2); // [[7, 0], [0, 7]]
// expressions
math.eval('12 / (2.3 + 0.7)'); // 4
math.eval('5.08 cm in inch'); // 2 inch
math.eval('sin(45 deg) ^ 2'); // 0.5
math.eval('9 / 3 + 2i'); // 3 + 2i
math.eval('det([-1, 2; 3, 1])'); // -7
// chained operations
math.select(3)
.add(4)
.multiply(2)
.done(); // 14Math.js contains a flexible and easy to use expression parser. The parser supports all data types, methods and constants available in math.js. Expressions can be evaluated in various ways:
- Using the function
math.eval(expr [,scope]). - Using the function
math.parse(expr [,scope]). - By creating a parser,
math.parser(), which contains functionseval,parse, and keeps a scope with assigned variables in memory.
Math.js comes with a function math.eval to evaluate expressions. Syntax:
math.eval(expr)
math.eval(expr, scope)
math.eval([expr1, expr2, expr3, ...])
math.eval([expr1, expr2, expr3, ...], scope)Function eval accepts a single expression or an array with
expressions as first argument, and has an optional second argument
containing a scope with variables and functions. The scope is a regular
JavaScript Object. The scope will be used to resolve symbols, and to write
assigned variables or function.
The following code demonstrates how to evaluate expressions.
// load math.js
var math = require('mathjs');
// evaluate expressions
math.eval('sqrt(3^2 + 4^2)'); // 5
math.eval('sqrt(-4)'); // 2i
math.eval('2 inch in cm'); // 5.08 cm
math.eval('cos(45 deg)'); // 0.7071067811865476
// provide a scope
var scope = {
a: 3,
b: 4
};
math.eval('a * b', scope); // 12
math.eval('c = 2.3 + 4.5', scope); // 6.8
scope.c; // 6.8Math.js contains a function math.parse to parse expressions into a node
tree. The syntax is similar to math.eval:
math.parse(expr)
math.parse(expr, scope)
math.parse([expr1, expr2, expr3, ...])
math.parse([expr1, expr2, expr3, ...], scope)Function parse accepts a single expression or an array with
expressions as first argument, and has an optional second argument
containing a scope with variables and functions. The scope is a regular
JavaScript Object. The scope will be used to resolve symbols, and to write
assigned variables or function. Variables are linked dynamically to the
provided scope.
Example usage:
// load math.js
var math = require('mathjs');
// parse an expression into a node, and evaluate the node
var node1 = math.parse('sqrt(3^2 + 4^2)');
node1.eval(); // 5
// provide a scope
var scope = {
x: 3,
a: 2
};
var node2 = math.parse('x^a', scope);
node2.eval(); // 9
// change a value in the scope and re-evaluate the node
scope.a = 3;
node2.eval(); // 27In addition to the static functions math.eval and
math.parse, math.js contains a parser with functions eval and
parse, which automatically keeps a scope with assigned variables in memory.
The parser also contains some convenience methods to get, set, and remove
variables from memory.
A parser can be created by:
var parser = math.parser();The parser contains the following methods:
clear()Completely clear the parsers scope.eval(expr)Evaluate an expression.get(name)Retrieve a variable or function from the parsers scope.parse(expr)Parse an expression into a node tree.remove(name)Remove a variable or function from the parsers scope.set(name, value)Set a variable or function in the parsers scope. A node can be evaluated asnode.eval().
The following 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
parser.eval('sqrt(3^2 + 4^2)'); // 5
parser.eval('sqrt(-4)'); // 2i
parser.eval('2 inch in cm'); // 5.08 cm
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 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();Math.js supports chaining operations by wrapping a value into a Selector.
A selector can be created with the function math.select(value).
All methods available in the math namespace can be executed via the selector.
The methods will be executed with the selectors value as first argument,
followed by extra arguments provided by the function call itself.
math.select(3)
.add(4)
.subtract(2)
.done(); // 5
math.select( [[1, 2], [3, 4]] )
.set([1, 1], 8)
.multiply(3)
.done(); // [[24, 6], [9, 12]]The Selector has a number of special functions:
done()Finalize the chained operation and return the selectors value.valueOf()The same asdone(), returns the selectors value.toString()Executesmath.format(value)onto the selectors value, returning a string representation of the value.get(index)Get a subselection of the selectors value. Only applicable when the value has a function get, for example when value is a Matrix or Array.set(index, replacement)Replace a subselection of the selectors value. Only applicable when the value has a function get, for example when value is a Matrix or Array.
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); // 4.5Available 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);
Math.js supports both native data types like Number, String, and Array, as well as advanced data types like Complex and Unit.
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)); // 21The built-in type String can be used in applicable methods.
math.add('hello ', 'world'); // 'hello world'
math.max('A', 'D', 'C'); // 'D'Math.js supports complex numbers. Most methods can be executed with complex numbers as arguments.
var a = math.complex(2, 3); // 2 + 3i
a.re; // 2
a.im; // 3
var b = math.complex('4 - 2i'); // 4 - 2i
math.add(a, b); // 6 + i
math.sqrt(-4); // 2iMath.js supports units. Basic operations add, subtract, multiply,
and divide can be performed on units.
Trigonometric methods like sin support units with an angle as argument.
Units can be converted from one to another using function in,
an the value of a unit can be retrieved using toNumber.
var a = math.unit(55, 'cm'); // 550 mm
var b = math.unit('0.1m'); // 100 mm
math.add(a, b); // 0.65 m
b.in('cm'); // 10 cm Alternatively: math.in(b, 'cm')
b.toNumber('cm'); // 10
math.eval('2 inch in cm'); // 5.08 cm
math.eval('cos(45 deg)'); // 0.7071067811865476Math.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]); // 43Matrices are supported by the parser:
parser = math.parser();
parser.eval('a = [1, 2; 3, 4]'); // Matrix, [[1, 2], [3, 4]]
parser.eval('b = zeros(2, 2)'); // Matrix, [[0, 0], [0, 0]]
parser.eval('b(1, 1:2) = [5, 6]'); // Matrix, [[5, 6], [0, 0]]
parser.eval('b(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
parser.eval('e = c(2, 1:end)'); // Matrix, [[43, 50]]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');
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:-1:-2
var c = b.valueOf(); // Array, [2, 1, 0, -1, -2]
var d = math.eval('3:7'); // Range, 3:7Math.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
Math.js contains the following methods. The methods support all available data types (Number, Complex, Unit, String, and Array) where applicable.
- 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.gcd(a, b, c, ...)
- math.larger(x, y)
- math.largereq(x, y)
- math.lcm(a, b, c, ...)
- 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)
- math.xgcd(a, b)
- math.re(x)
- math.im(x)
- math.arg(x)
- math.conj(x)
- math.complex(re, im)
- math.matrix(x)
- math.number(x)
- math.parser()
- math.range(start [, step] , end)
- math.string(x)
- math.unit(x)
- math.workspace()
- 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.subset(x, index [, replacement])
- math.transpose(x)
- math.zeros(m, n, p, ...)
- math.factorial(x)
- math.random()
- math.max(a, b, c, ...)
- math.min(a, b, c, ...)
- 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)
- math.in(x, unit)
- math.clone(x)
- math.eval(expr [, scope])
- math.format([template, ] values)
- math.import(filename | object, override)
- math.select([x])
- math.parse(expr [, scope])
- math.typeof(x)
The library can easily be extended with functions and variables using the
import function. The function 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!'External libraries like numbers.js and numeric.js can be imported as well. The libraries must be installed using npm:
npm install numbers
npm install numeric
The libraries can be easily imported into math.js using import. By default,
existing functions will not be overwritten, and math.js will create a wrapper
function around the imported functions which converts data types like Matrix
to primitive types like Array.
var math = require('mathjs');
// import the numbers.js and numeric.js libraries into math.js
math.import('numbers');
math.import('numeric');
// use functions from numbers.js
math.fibonacci(7); // 13
math.eval('fibonacci(7)'); // 13
// use functions from numeric.js
math.eval('eig([1, 2; 4, 3])').lambda.x; // [5, -1]When math.js is installed globally using npm, its expression parser can be used from the command line. To install math.js globally:
npm install -g mathjs
Normally, a global installation must be run with admin rights (precede the
command with sudo). After installation, the application mathjs is available:
$ mathjs
> 12 / (2.3 + 0.7)
4
> 5.08 cm in inch
2 inch
> sin(45 deg) ^ 2
0.5
> 9 / 3 + 2i
3 + 2i
> det([-1, 2; 3, 1])
-7The command line interface can be used open a prompt, to execute a script, or to pipe input and output streams:
$ mathjs # Open a command prompt
$ mathjs script.txt # Run a script file, output to console
$ mathjs script.txt > results.txt # Run a script file, output to file
$ cat script.txt | mathjs # Run input stream, output to console
$ cat script.txt | mathjs > results.txt # Run input stream, output to fileFirst 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.
To execute tests for the library, run:
npm test
Version 1.0:
- An expression parser.
- A basic set of functions and constants.
- Data types Number, Complex, Matrix, Unit, String.
- Examples and documentation.
- Extensive testing.
Version 2.0:
- A basic set of functions covering all common mathematical areas.
- Functions and data types for numeral systems: Bin, Oct, Hex, Dec.
- Arbitrary precision calculations with a BigNumber data type.
- Support for derived units (like km/h, kg*m/s2, etc).
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.