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fibo committed Jan 3, 2017
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17 changes: 9 additions & 8 deletions _data/package.json
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Expand Up @@ -10,14 +10,13 @@
"license": "MIT",
"main": "index.js",
"scripts": {
"build": "npm test && npm run browserify && npm run tex && npm run jekyll; git status",
"build": "npm test && npm run browserify && npm run minify && npm run tex && npm run jekyll; git status",
"browserify": "npm run browserify:dist; npm run browserify:test",
"browserify:dist": "browserify -r ./index.js:${npm_package_name} -o dist/${npm_package_name}.js",
"browserify:test": "browserify test/*.js -o gh-pages/test/bundle.js",
"check-deps": "npm outdated",
"coverage": "npm run istanbul && npm run coveralls",
"coveralls": "cat ./coverage/lcov.info | coveralls --verbose",
"decrypt:.coveralls.yml": "keybase decrypt -o .coveralls.yml .coveralls.yml.asc",
"gh-pages:_data": "for x in package.json tags.json; do npm run gh-pages:_data:$x; done",
"gh-pages:_data:package.json": "cp package.json gh-pages/_data/",
"gh-pages:_data:tags.json": "wget https://api.github.com/repos/fibo/${npm_package_name}/tags -O gh-pages/_data/tags.json",
Expand All @@ -30,6 +29,7 @@
"lint": "npm run lint_src; npm run lint_test",
"lint_src": "standard src/*.js",
"lint_test": "cd test; standard --global describe --global it; cd -",
"minify": "cd dist; uglifyjs ${npm_package_name}.js --source-map ${npm_package_name}.map --output ${npm_package_name}.min.js --compress --mangle --preamble \"// Software: ${npm_package_name}\n// Homepage: ${npm_package_homepage}\n// License: ${npm_package_license}\"; cd -",
"tex": "npm run tex:display; npm run tex:inline",
"tex:display": "ls gh-pages/tex-snippets/display/*.tex | while read texfile; do cat $texfile | katex --display-mode > gh-pages/_includes/display/$(basename ${texfile%.tex}).html; done",
"tex:inline": "ls gh-pages/tex-snippets/inline/*.tex | while read texfile; do cat $texfile | katex > gh-pages/_includes/inline/$(basename ${texfile%.tex}).html; done",
Expand Down Expand Up @@ -64,26 +64,27 @@
],
"devDependencies": {
"browserify": "^13.1.1",
"coveralls": "^2.11.14",
"coveralls": "2.x",
"istanbul": "^0.4.1",
"katex": "^0.6.0",
"mocha": "^3.1.2",
"mocha": "3.x",
"mocha-lcov-reporter": "1.2.0",
"pre-commit": "^1.1.2",
"should": "^11.1.1",
"standard": "^8.5.0"
"standard": "^8.6.0",
"uglify-js": "github:mishoo/UglifyJS2#harmony"
},
"dependencies": {
"algebra-cyclic": "^0.2.0",
"cayley-dickson": "^0.4.2",
"indices-permutations": "^0.2.0",
"inherits": "^2.0.1",
"laplace-determinant": "^0.1.0",
"matrix-multiplication": "^0.4.0",
"matrix-multiplication": "^0.5.0",
"multidim-array-index": "^0.5.0",
"not-defined": "^1.0.0",
"static-props": "^1.0.0",
"strict-mode": "^1.0.0",
"static-props": "1.x",
"strict-mode": "1.x",
"tensor-contraction": "^0.1.1",
"tensor-product": "^0.2.0"
}
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4 changes: 4 additions & 0 deletions changelog.md
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Expand Up @@ -15,6 +15,10 @@ Changelog format adheres to [Keep a Changelog](http://keepachangelog.com/)</sub>

## [Unreleased]

### Added

UglifyJS with harmony branch.

## [v0.12.0] - 2016-11-05

### Removed
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115 changes: 85 additions & 30 deletions index.md
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Expand Up @@ -9,7 +9,7 @@ title: algebra
**NOTA BENE** Immagine all code examples below as written in some REPL where expected output is documented as a comment.

[![NPM version](https://badge.fury.io/js/algebra.svg)](http://badge.fury.io/js/algebra) [![Badge size](https://badge-size.herokuapp.com/fibo/algebra/master/dist/algebra.min.js)](https://github.com/fibo/algebra/blob/master/dist/algebra.min.js) [![Build Status](https://travis-ci.org/fibo/algebra.svg?branch=master)](https://travis-ci.org/fibo/algebra?branch=master) [![Dependency Status](https://david-dm.org/fibo/algebra.svg)](https://david-dm.org/fibo/algebra) [![Coverage Status](https://coveralls.io/repos/fibo/algebra/badge.svg?branch=master)](https://coveralls.io/r/fibo/algebra?branch=master) [![Test page](https://img.shields.io/badge/test-page-blue.svg)](http://g14n.info/algebra/test) [![Change log](https://img.shields.io/badge/change-log-blue.svg)](http://g14n.info/algebra/changelog)
[![NPM version](https://badge.fury.io/js/algebra.svg)](http://badge.fury.io/js/algebra) [![Badge size](https://badge-size.herokuapp.com/fibo/algebra/master/dist/algebra.js)](https://github.com/fibo/algebra/blob/master/dist/algebra.js) [![Build Status](https://travis-ci.org/fibo/algebra.svg?branch=master)](https://travis-ci.org/fibo/algebra?branch=master) [![Dependency Status](https://david-dm.org/fibo/algebra.svg)](https://david-dm.org/fibo/algebra) [![Coverage Status](https://coveralls.io/repos/fibo/algebra/badge.svg?branch=master)](https://coveralls.io/r/fibo/algebra?branch=master) [![Test page](https://img.shields.io/badge/test-page-blue.svg)](http://g14n.info/algebra/test) [![Change log](https://img.shields.io/badge/change-log-blue.svg)](http://g14n.info/algebra/changelog)

[![Whatchers](https://g14n.info/svg/github/watchers/algebra.svg)](https://github.com/fibo/algebra/watchers) [![Stargazers](https://g14n.info/svg/github/stars/algebra.svg)](https://github.com/fibo/algebra/stargazers) [![Forks](https://g14n.info/svg/github/forks/algebra.svg)](https://github.com/fibo/algebra/network/members)

Expand Down Expand Up @@ -218,8 +218,8 @@ Create a matrix.
// | 1 0 |
//
const m1 = new R3x2([1, 1,
0, 1,
1, 0])
0, 1,
1, 0])
```

Multiply m1 by v1, the result is a vector v3 with dimension 3.
Expand Down Expand Up @@ -379,7 +379,7 @@ A generic function is provided to iterate the [Cayley-Dickson construction][Cayl

#### `CompositionAlgebra(field[, num])`

* num can be 1, 2, 4 or 8
* *num* can be 1, 2, 4 or 8

Let's use for example the [src/binaryField][binaryField] which exports an object with all the stuff needed by [algebra-ring npm package][algebra-ring].

Expand Down Expand Up @@ -628,31 +628,82 @@ const H = algebra.H

### Vector

Inherits everything from [Tensor](#tensor).
A *Vector* extends the concept of number, since it is defined as a tuple
of numbers.
For example, the [Cartesian plane](https://en.wikipedia.org/wiki/Cartesian_coordinate_system)
is a set where every point has two coordinates, the famous `(x, y)` that
is in fact a *vector* of dimension 2.
A [Scalar](#scalar) itself can be identified with a vector of dimension 1.

We have already seen an implementation of the plain: [R2](#r2).

If you want to find the position of an airplain, you need *latitute*, *longitude*
but also *altitude*, hence three coordinates. That is a 3-ple, a tuple with
three numbers, a vector of dimension 3.

An implementation of the vector space of dimension 3 over reals is given
by [R3](#r3).

##### `VectorSpace(Scalar)(dimension)`
A *Vector* class inherits everything from [Tensor](#tensor).

### Vector attributes
#### `VectorSpace(Scalar)(dimension)`

#### Vector dimension

Strictly speaking, dimension of a Vector is the number of its elements.

##### `Vector.dimension`

It is a static class attribute.

```javascript
R2.dimension // 2
R3.dimension // 3
```

##### `vector.dimension`

It is also defined as a static instance attribute.

```javascript
const vector = new R2([1, 1])

vector.dimension // 2
```

### Vector operators
### Vector norm

The *norm*, at the end, is the square of the length of vector.
The good old [Pythagorean theorem](https://en.wikipedia.org/wiki/Pythagorean_theorem).
It is usually defined as the sum of the squares of the coordinates.
Anyway, it must be a function that, given an element, returns a positive real number.
For example in [Complex](#complex) numbers it is defined as the multiplication of
an element and its conjugate: it works as a norm.
It is a really important property since it shapes a metric space.
In the Euclidean topology gives us the common sense of space,
but it is also important in other spaces even not so exotic, like a functional space.
In fact a *norm* gives us a *distance* defined as its square root, thus it
defines a metric space and hence a topology: a lot of good stuff.

#### Addition
#### `Vector.norm()`

Is a static operator that returns the square of the lenght of the vector.

```javascript
R2.norm([3, 4]).data // 25
```

#### `vector.norm`

This implements a static attribute that returns the square of the length of the vector instance.

```javascript
const vector = new R2([1, 2])

vector.norm.data // 5
```

#### Vector addition

##### `Vector.addition(vector1, vector2)`

Expand All @@ -671,7 +722,7 @@ const vector3 = vector1.addition(vector2)
vector3 // Vector { data: [4, 3] }
```

#### Cross product
#### Vector cross product

It is defined only in dimension three. See [Cross product on wikipedia](https://en.wikipedia.org/wiki/Cross_product).

Expand All @@ -694,19 +745,15 @@ vector3 // Vector { data: [-15, 2, 39] }

### Matrix

Inherits everything from [Tensor](#tensor).
A *Matrix* class inherits everything from [Tensor](#tensor).

##### `MatrixSpace(Scalar)(numRows[, numCols])`
#### `MatrixSpace(Scalar)(numRows[, numCols])`

#### Matrix attributes
#### `Matrix.isSquare`

##### `Matrix.isSquare`
#### `Matrix.numCols`

##### `Matrix.numCols`

##### `Matrix.numRows`

#### Matrix operators
#### `Matrix.numRows`

#### Matrix multiplication

Expand Down Expand Up @@ -738,15 +785,13 @@ It is defined only for square matrices.

### Tensor

##### `TensorSpace(Scalar)(indices)`

### Tensor attributes
#### `TensorSpace(Scalar)(indices)`

##### `Tensor.one`
#### `Tensor.one`

##### `Tensor.zero`
#### `Tensor.zero`

##### `tensor.data`
#### `tensor.data`

#### Tensor indices

Expand All @@ -766,9 +811,7 @@ It represents the number of varying indices.

##### `tensor.order`

### Tensor operators

##### `Tensor.contains(tensor1, tensor2[, tensor3, … ])`
#### `Tensor.contains(tensor1, tensor2[, tensor3, … ])`

#### Tensor equality

Expand All @@ -793,31 +836,43 @@ tensor1.equality(tensor1) // true
tensor2.equality(tensor2) // false
```

##### `Tensor.disequality(tensor1, tensor2)`
#### Tensor disequality

#### `Tensor.disequality(tensor1, tensor2)`

##### `tensor1.disequality(tensor2)`

#### Tensor addition

##### `Tensor.addition(tensor1, tensor2[, tensor3, … ])`

##### `tensor1.addition(tensor2[, tensor3, … ])`

#### Tensor subtraction

##### `Tensor.subtraction(tensor1, tensor2[, tensor3, … ])`

##### `tensor1.subtraction(tensor2[, tensor3, … ])`

#### Tensor product

##### `Tensor.product(tensor1, tensor2)`

##### `tensor1.product(tensor2)`

#### Tensor contraction

##### `Tensor.contraction()`

##### `tensor.contraction()`

#### Tensor negation

##### `Tensor.negation(tensor1)`

##### `tensor.negation()`

#### Tensor multiplication
#### Tensor scalar multiplication

##### `Tensor.scalarMultiplication(tensor, scalar)`

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