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algebra-ring

0.6.4 • Public • Published

algebra-ring

defines an algebra ring structure

Installation | Example | API | License

NPM version Build Status JavaScript Style Guide

Installation

With npm do

npm install algebra-ring

Example

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

Real

Create a ring structure over real numbers.

const ring = require('algebra-ring')
 
// Define operators.
function contains (a) {
  // NaN, Infinity and -Infinity are not allowed
  return (typeof a === 'number' && isFinite(a))
}
 
function equality (a, b) { return a === b }
 
function addition (a, b) { return a + b }
 
function negation (a) { return -}
 
function multiplication (a, b) { return a * b }
 
function inversion (a) { return 1 / a }
 
// Create a ring by defining its identities and operators.
const R = ring([0, 1], {
  equality: equality,
  contains: contains,
  addition: addition,
  negation: negation,
  multiplication: multiplication,
  inversion: inversion
})

You get a Ring that is a Group with multiplication operator. The multiplication operator must be closed respect the underlying set; its inverse operator is division.

This is the list of ring operators:

  • contains
  • notContains
  • equality
  • disequality
  • addition
  • subtraction
  • negation
  • multiplication
  • division
  • inversion

The neutral element for addition and multiplication are, as usual, called zero and one respectively.

R.contains(10) // true
R.contains(-1, 0.5, Math.PI, 5) // true
R.notContains(Infinity) // true
 
R.addition(1, 2) // 3
R.addition(2, 3, 5, 7) // 17
 
R.equality(R.negation(2), -2) // true
 
R.subtraction(2, 3) // -1
 
R.multiplication(2, 5) // 10
R.multiplication(2, 2, 2, 2) // 16
 
R.equality(R.inversion(10), 0.1) // true
 
R.division(1, 2) // 0.5
 
R.equality(R.addition(2, R.zero), 2) // true
R.equality(R.subtraction(2, 2), R.zero) // true
 
R.equality(R.multiplication(2, R.one), 2) // true
R.equality(R.division(2, 2), R.one) // true
 
R.division(1, 0) // will complain
R.inversion(R.zero) // will complain too

Boolean

It is possible to create a ring over the booleans.

const Boole = ring([false, true], {
  equality: (a, b) => (=== b),
  contains: (a) => (typeof a === 'boolean'),
  addition: (a, b) => (|| b),
  negation: (a) => (a),
  multiplication: (a, b) => (&& b),
  inversion: (a) => (a)
})

There are only two elements, you know, true and false.

Boole.contains(true, false) // true

Check that false is the neutral element of addition and true is the neutral element of multiplication.

Boole.addition(true, Boole.zero) // true
Boole.multiplication(true, Boole.one) // true

As usual, it is not allowed to divide by zero: the following code will throw.

Boole.division(true, false)
Boole.inversion(Bool.zero)

API

ring(identities, operator)

  • @param {Array} identities
  • @param {*} identities[0] a.k.a zero
  • @param {*} identities1 a.k.a one
  • @param {Object} operator
  • @param {Function} operator.contains
  • @param {Function} operator.equality
  • @param {Function} operator.addition
  • @param {Function} operator.negation
  • @param {Function} operator.multiplication
  • @param {Function} operator.inversion
  • @returns {Object} ring

ring.error

An object exposing the following error messages:

  • cannotDivideByZero
  • doesNotContainIdentity
  • identityIsNotNeutral

License

MIT

Install

npm i algebra-ring

DownloadsWeekly Downloads

4

Version

0.6.4

License

MIT

Unpacked Size

11 kB

Total Files

7

Last publish

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