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 containing `Peo` class

A Prime Exponent Object (Peo) stores small or large rational numbers as an object of the form {p1:e1, p2:e2, ...}. A simple example would be 20/3 stored as {2:2, 3:-1, 5:1}.

This format aids multiplication and exponentiation of large numbers. Maximum prime factor size is approximately 10^15, so large factorial, primorial or combinatoric values can be made, e.g. factorial of 1000 or higher. Calculations on Peos via the API return new Peo objects in order to keep Peo instances immutable.

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.

To install, use npm i peo. To test, npm test. For examples of usage see Github examples directory, via npm run examples. Limits of both prime (key) and exponent (value) are around 10^15.

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 object 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})     // get Peo for p1^e1 * ... * pk^ek
new Peo({p1:e1, ...,pk:ek}, n)  // get Peo for (p1^e1 * ... * pk^ek) ^ n

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()               // returns all prime info {p1:e1,...}
peo.getPrimeExps([p1,...])       // returns specified prime info {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(m)              // returns a new Peo which is this * integer m
peo.mult(m, n)           // returns a new Peo which is this * integer m^n
peo.mult(otherPeo)       // returns a new Peo which is this * otherPeo  
peo.mult(otherPeo, n)    // returns a new Peo which is this * (otherPeo^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