algebra-cyclic

creates a space isomorphic to Zp: the cyclic ring of order p, where p is prime

Uroboro

Installation

With npm do

npm install algebra-cyclic

API

`algebraCyclic(elements)`

@param {Array|String} elements
@returns {Object} cyclic ring

`algebraCyclic.error`

An object exposing the following error messages:

numberOfElementsIsNotPrime
elementsAreNotUnique

Examples

All code in the examples below is intended to be contained into a single file.

var algebraCyclic = require('algebra-cyclic')

// Cyclic ring of vowels.
var vowel = algebraCyclic('aeiou')

vowel.contains('a') // true
vowel.contains('e') // true
vowel.contains('i') // true
vowel.contains('o') // true
vowel.contains('u') // true

vowel.contains('0') // false
vowel.contains('1') // false
vowel.contains('2') // false
vowel.contains('*') // false

vowel.addition('a', 'a') // 'a'
vowel.addition('a', 'e') // 'e'
vowel.addition('a', 'i') // 'i'
vowel.addition('a', 'o') // 'o'
vowel.addition('a', 'u') // 'u'
vowel.addition('e', 'e') // 'i'
vowel.addition('e', 'i') // 'o'
vowel.addition('e', 'o') // 'u'
vowel.addition('i', 'i') // 'u'
vowel.addition('i', 'o') // 'a'
vowel.addition('i', 'u') // 'e'
vowel.addition('o', 'o') // 'e'
vowel.addition('o', 'u') // 'i'
vowel.addition('u', 'u') // 'o'

vowel.subtraction('a', 'a') // 'a'
vowel.subtraction('a', 'e') // 'u'
vowel.subtraction('a', 'i') // 'o'
vowel.subtraction('a', 'o') // 'i'
vowel.subtraction('a', 'u') // 'e'
vowel.subtraction('e', 'e') // 'a'
vowel.subtraction('e', 'i') // 'u'
vowel.subtraction('e', 'o') // 'o'
vowel.subtraction('e', 'u') // 'i'
vowel.subtraction('i', 'i') // 'a'
vowel.subtraction('i', 'o') // 'u'
vowel.subtraction('i', 'u') // 'o'
vowel.subtraction('o', 'o') // 'a'
vowel.subtraction('o', 'u') // 'u'
vowel.subtraction('u', 'u') // 'a'

vowel.negation('a') // 'a'
vowel.negation('e') // 'u'
vowel.negation('i') // 'o'
vowel.negation('o') // 'i'
vowel.negation('u') // 'e'

// 'a' is considered as zero, and the following operation should throws
// cannotDivideByZero
vowel.inversion('a') // 'e'

vowel.inversion('e') // 'e'
vowel.inversion('i') // 'o'
vowel.inversion('o') // 'i'
vowel.inversion('u') // 'u'


// TODO complete operations (multiplication and divison)

The number of elements must be prime, and elements are required to be unique. The following snippets will throw.

// numberOfElementsIsNotPrime

algebraCyclic(['length', 'of', 'this', 'is', 'not', 'prime'])

// elementsAreNotUnique

algebraCyclic([1, 2, 1])

License

MIT