# publicfibo/algebra

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Vectors, matrices, tensors

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# algebra

Vectors, Matrices and more

# Installation

``````npm install algebra
``````

# 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);

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 a 2x2 invertible matrix.
var GL2R = new GLnR(2);

var m1 = new GL2R.Matrix(1, 2,
3, 4);
var m2 = new GL2R.Matrix(-1, 0,
0, 1);

m1.mul(m2);

console.log(m1.toString());
``````

# 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'd an intuition about a composition law for UTF-8 chars).

See the Wiki.

# 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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