Prime Exponent Object

(PEO, Peo class)

A Prime Exponent Object (Peo) is a JavaScript object which stores small or large rational numbers as an object of the form {2:1000, 3:-567, 65536:-1} = 2^1000 * 3^-567 * 65537^-1, i.e. as an object with keys equal to primes, and values equal to the exponent of that prime.

The class contains:

• A central data store of these primes and exponents
• Some cached data, e.g. numeric, textual or fractional representation (the latter using Fraction class from fraction.js)
• An API with many functions to manipulate the Peo.

Note that the Peo is designed to be immutable, i.e. all the API functions return a new Peo when any modification has taken place.

Install

npm install peo

Usage

var Peo = require('peo')
var peo = new Peo(80, 14)
console.log(peo.getText()) // "40/7"
console.log(peo.getNum()) // 40
console.log(peo.getDenom()) // 7
console.log(peo.getVal()) // 5.7142857142857135

Test

npm test
npm run examples

API

Constructors

new Peo(a) // integer a
new Peo(a, b) // fraction a/b
new Peo(a, b, n) // fraction (a/b)^n
new Peo(fr) // fr a Fraction from fraction.js
new Peo(fr, n) // fr^n
new Peo({p1:e1, ...,pk:ek}) // equivalent to p1^e1 * ... * pk^ek
new Peo({p1:e1, ...,pk:ek}, n) // equivalent to p1^(n*e1) * ... * pk^(n*ek)

These constructors have been tested up to (11/2)^1000000000 = new Peo(11, 2, 10^9)
Peo can handle large numbers! (With small-ish prime factors.)

Static or Class methods

Peo.binom(n, r) // returns 'n choose r', e.g. binomial coefficient
Peo.fact(a) // returns a! = a * (a-1) * ... * 1 (Factorial function)
Peo.fact(a, b) // returns a * (a-1) * ... * (a-(b-1))
Peo.fact(a, b, c) // returns a * (a+c) * ... * (a+c(b-1))
Peo.prim(a) // returns product of primes between 1 and a
Peo.prim(a, b) // returns product of primes between a and b

Instance methods

(The underscore _ represents your own instance of Peo class)

Accessing prime exponents

_.checkPrimeExps({p1:e1,...}) // returns Boolean
_.getPrimeExp(p) // returns numeric, the exponent
_.getPrimeExps([p1,...]) // returns {p1:e1,...}

General functions

_.copy() // returns a copy of the original peo
_.toString() // returns a text representation of the Peo (same as .getText()

Maths operations

_.get1() // returns a new identity Peo, e.g. new Peo(1)
_.mult(other) // returns a new Peo which is this*other
_.mult(other, n) // returns a new Peo which is this*(other^n)
_.pow(n) // returns a new Peo which is this^n

Numeric values

_.getDenom() // returns the denominator of the fraction
_.getFraction() // returns relevant Fraction object from fraction.js
_.getNum() // returns the numerator of the fraction
_.getText() // returns a text representation of the Peo
_.getVal() // returns a decimal representation of the Peo

Logarithmic numeric values

_.getLog(b) // returns log of Peo to base b (if omitted, natural log)
_.getLogDenom(b) // returns log of Peo denominator
_.getLogNum(b) // returns log of Peo numerator

Numeric stats

_.countDistinctFactors() // returns the number of distinct prime factors of the Peo
_.countFactors() // returns the total number of prime factors of the Peo
_.getHighestPrime() // returns the highest prime in the Peo
_.getLowestPrime() // returns the lowest prime in the Peo