Package Exports

This package does not declare an exports field, so the exports above have been automatically detected and optimized by JSPM instead. If any package subpath is missing, it is recommended to post an issue to the original package (peo) to support the "exports" field. If that is not possible, create a JSPM override to customize the exports field for this package.

Readme

peo

Prime Exponent Object module, `Peo`

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 and return the result as a new 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(txt)                    // txt an integer or fraction in text form e.g. "5", "3/2"
new Peo(txt, n)                 // txt ^ 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

Accessing prime exponents

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

General functions

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

Maths operations

peo.get1()               // returns a new identity Peo, e.g. new Peo(1)
peo.mult(other)          // returns a new Peo which is this*other  
peo.mult(other, n)       // returns a new Peo which is this*(other^n)
peo.pow(n)               // returns a new Peo which is this^n
peo.split(p1, [p2, p3])  // splits a Peo into an array of 3 components:
                         // [{p1:e1}, {p2:e2, p3:e3}, {everything else}]
                         // The argument list for .split is extensible and can contain
                         // primes or arrays of primes in any order.

Numeric values

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

Logarithmic numeric values

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

Numeric stats

peo.countDistinctFactors()  // returns the number of distinct prime factors of the Peo
peo.countFactors()          // returns the total number of prime factors of the Peo
peo.getHighestAbsExp()      // returns the highest abs(exponent) in the Peo
peo.getHighestExp()         // returns the highest exponent in the Peo
peo.getHighestPrime()       // returns the highest prime in the Peo
peo.getLiouville()          // returns the Liouville function on the Peo
peo.getLowestExp()          // returns the lowest exponent in the Peo
peo.getLowestPrime()        // returns the lowest prime in the Peo
peo.getMobius()             // returns the Mobius function on the Peo

peo