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Vectors, matrices, tensors
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README.md

algebra

Vectors, Matrices, Tensors.

DISCLAIMER : this is a developer release, Tensors are not implemented yet. Every feedback is welcome!

on-quaternions-and-octonions!

Installation

npm install algebra

Description

I'm implementing matrices and vectors on few algebra fields (Reals, Complexes etc.) following Micheal Artin's "Algebra", which was my book at Universita' Degli Studi di Genova.

My goal is to provide users with the feature of creating their own algebra field and building vector spaces and matrices on it.

Suppose for example the set of strings with the concatenation operator, it could be extended to a group and maybe to a field and build "matrices of strings" or probably in the future ... "strings of matrices" (I had an intuition about a composition law for UTF-8 chars).

Quick start

This is a 60 seconds tutorial to get your hands dirty with algebra.

Complex numbers

var algebra = require('algebra');

var Complex = algebra.Complex.Element;

// Create two complex numbers
// z1 = 1 + 2i
// z2 = 3 + 4i
var z1 = new Complex(1, 2);
var z2 = new Complex(3, 4);

// Multiply z1 by z2.
z1.mul(z2); // (1 + 2i) * (3 + 4i) = -5 + 10i

console.log(z1.xy()); // [-5, 10]

Vectors

var algebra = require('algebra');

// Rn is a class representing a real vector space of dimension = n.
var Rn = algebra.Real.VectorSpace;

// Create a real vector space with dimension = 2, a.k.a. the cartesian plane.
var R2 = new Rn(2);

// Create two vectors
// v1 = (1, 1)
// v2 = (2, 4)
var v1 = new R2.Vector(1, 1);
var v2 = new R2.Vector(2, 4);

// Add v2 to v1.
v1.add(v2); // (1, 1) + (2, 4) = (3, 5)

console.log(v1.getCoordinates()); // [3, 5]

Matrices

var algebra = require('algebra');

// GLnR is the Real General Linear Group of invertible matrices of order n.
var GLnR = algebra.Real.GeneralLinearGroup;

// Create the group of 2x2 invertible matrices.
var GL2R = new GLnR(2);

// Create two invertible matrices:
//
//       | 1 2 |         | -1 0 |
//       | 3 4 |   and   |  0 1 |
//
var m1 = new GL2R.Matrix(1, 2, 
                         3, 4);

var m2 = new GL2R.Matrix(-1, 0, 
                          0, 1);

// Multiply m1 by m2 at right side.
m1.mul(m2);

console.log(m1.toString()); //  | -1 2 |
                            //  | -3 4 |

// Check out m1 determinant, should be 2 = (1 * 4 - 3 * 2) * (-1 * 1 - 0 * 0)
console.log(m1.determinant().num()); // 2

Documentation

See the Wiki.

Support

Issues

Please use algebra's bug tracker on github: patches welcome.

Human contact

My skype and gtalk is casati.gianluca, contact me if you can give me some advice about coding this lib or if you have passion for math. I'm located in Milan and Genoa, it could be possible to have a pizza or a beer :)

Development

Coding style

This project coding style refers to Felix's Node.js Style Guide.

Testing

Say hello to the nyan cat :)

npm test

Browserify

Install browserify globally

npm install browserify -g

Build algebra client lib

browserify index.js -o algebra.js
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