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Exponent Object","homepage":"https://github.com/davidryan59/Peo#readme","keywords":["add","big","binomial","coefficient","combinatorics","count","denominator","distinct","exponent","exponentiation","factorial","factorisation","factorization","factors","fraction","function","highest","huge","integer","liouville","logarithm","lowest","mobius","multiplication","number","numerator","object","power","prime","primorial","rational","small","split","tiny","vector"],"repository":{"type":"git","url":"git+ssh://git@github.com/davidryan59/Peo.git"},"author":{"name":"David Ryan","email":"davidryan1998@hotmail.com","url":"https://github.com/davidryan59"},"bugs":{"url":"https://github.com/davidryan59/Peo/issues"},"license":"ISC","readme":"# peo\nPrime Exponent Object module containing `Peo` class. Find [module on npm](https://www.npmjs.com/package/peo) and [code repo with examples on GitHub](https://github.com/davidryan59/Peo).\n\n[![npm version](https://badge.fury.io/js/peo.png)](https://badge.fury.io/js/peo)[![Build status](https://travis-ci.org/davidryan59/Peo.svg?master)](https://travis-ci.org/davidryan59)\n\nA **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}`.\n\nThis 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.\n\nThe class contains:\n- A central data store of these primes and exponents\n- Some cached data, e.g. numeric or text representations\n- An API with many functions to manipulate the Peo and return the result as a new Peo.\n\nTo 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.\n\n## API\n\n### General constructors using objects\n``` js\nnew Peo({num:a, denom:b, pow:c})    // Peo for rational number (a/b)^c\nnew Peo({p1:e1, ...,pk:ek})         // get Peo for p1^e1 * ... * pk^ek  (keys are prime numbers)\nnew Peo({p1:e1, ...,pk:ek}, n)      // get Peo for (p1^e1 * ... * pk^ek) ^ n\n```\n\n### Shorthand constructors\n``` js\nnew Peo(a)         // integer a\nnew Peo(a, b)      // integers a, b => fraction a/b\nnew Peo(a, b, n)   // integers a, b, n => fraction (a/b) ^ n\nnew Peo(d)         // decimal d (find a fraction that approximates d)\nnew Peo(d, n)      // decimal d^n\nnew Peo(txt)       // txt an integer or fraction in text form e.g. \"5\", \"3/2\"\nnew Peo(txt, n)    // txt ^ n\nnew Peo(peo)       // Copies prime information in a peo into a new peo. Also see instance method copy()\nnew Peo(peo, n)    // peo ^ n\n```\n\n### Static or Class methods\n``` js\nPeo.fact(n)          // returns n! = n * (n-1) * ... * 1        (Factorial function)\nPeo.perm(n, r)       // returns n * (n-1) * ... * (n-(r-1))     (Permutation function)\nPeo.binom(n, r)      // returns n choose r; perm(n, r)/fact(r)  (Binomial coefficient)\nPeo.multSeq(n, r, j) // returns n * (n+j) * ... * (n+j(r-1))    (Multiply r terms of a sequence with jump j)\nPeo.prim(a)          // returns product of primes from 1 and a  (Primorial function)\nPeo.multPrimes(a, b) // returns product of primes from a and b  (Primes in given range)\n```\n\n### Instance methods\n\n#### Accessing prime exponents\n``` js\npeo.checkPrimeExps({p1:e1,...})  // returns Boolean if these prime exponents agree\npeo.getPrimeExp(p)               // returns the exponent as a number\npeo.getPrimeExps()               // returns a copy of all prime info {p1:e1,...}\npeo.getPrimeExps([p1,...])       // returns a copy of prime info for specified primes only\n```\n\n#### General functions\n``` js\npeo.toString()  // returns a JSON object for the primes and exponents obtained via getPrimeExps()\npeo.compress()  // removes all cached information, reducing size of peo. Use if you've got millions of peos.\npeo.copy()      // returns a copy of the original peo. Cached information not transferred.\npeo.construct() // anyPeo.construct(...args) should return Peo instance equivalent to new Peo(...args).\n                // This allows any Peo instance to be used as a constructor.\n```\n\n#### Maths operations\n``` js\npeo.get1()               // returns a new identity Peo, e.g. new Peo(1)\npeo.mult(m)              // returns a new Peo which is this * integer m\npeo.mult(m, n)           // returns a new Peo which is this * integer m^n\npeo.mult(dec)            // returns a new Peo which is this * decimal\npeo.mult(dec, n)         // returns a new Peo which is this * decimal ^ power\npeo.mult(otherPeo)       // returns a new Peo which is this * otherPeo  \npeo.mult(otherPeo, n)    // returns a new Peo which is this * (otherPeo^n)\npeo.pow(n)               // returns a new Peo which is this^n\npeo.split(p1, [p2, p3])  // splits a Peo into an array of 3 components:\n                         // [{p1:e1}, {p2:e2, p3:e3}, {everything else}]\n                         // The argument list for .split is extensible and can contain\n                         // primes or arrays of primes in any order.\n// Unary comparisons\npeo.is1()                   // Return true if peo equivalent to 1/1, false otherwise\npeo.isNot1()                // Return false if peo equivalent to 1/1, true otherwise\npeo.lessThan1()             // Return true if peo has log value < 0, false otherwise\npeo.lessThanOrEqualTo1()    // Return true if peo has log value <= 0, false otherwise\npeo.greaterThan1()          // Return true if peo has log value > 0, false otherwise\npeo.greaterThanOrEqualTo1() // Return true if peo has log value >= 0, false otherwise\n// Comparing the log values, rather than original value, means that peos of any size are handled correctly.\n\n// Binary comparisons. Cases handled:\n// 1. input is a Peo\n// 2. input is a positive decimal number\npeo.equals(input)               // Return true if peo = input, false otherwise\npeo.notEquals(input)            // Return false if peo = input, true otherwise\npeo.lessThan(input)             // Return true if peo < input, false otherwise\npeo.lessThanOrEqualTo(input)    // Return true if peo <= input, false otherwise\npeo.greaterThan(input)          // Return true if peo > input, false otherwise\npeo.greaterThanOrEqualTo(input) // Return true if peo >= input, false otherwise\n```\n\n#### Numeric values\n``` js\npeo.getAsDecimal()       // returns a decimal representation of the Peo, if its not too big\npeo.getAsFractionText()  // returns fraction text if num, denom < around 1e15. Otherwise return NA.\npeo.getAsResultText()    // return fraction text, unless numbers are large, then return 10^NN.NN representation\npeo.getNum()             // returns integer numerator of the fraction\npeo.getDenom()           // returns integer denominator of the fraction\n```\n\n#### Logarithmic numeric values\n``` js\npeo.getLog(b)       // returns log of Peo to base b (if omitted, natural log)\npeo.getLogNum(b)    // returns log of Peo numerator\npeo.getLogDenom(b)  // returns log of Peo denominator\n```\n\n#### Numeric stats\n``` js\npeo.countUniquePrimeFactors() // returns the number of different prime factors of the Peo\npeo.countPrimeFactors()       // returns the number of prime factors, with multiplicity\npeo.countFactors()            // returns the total number of factors of the Peo\npeo.getLowestPrime()          // returns the lowest prime in the Peo (* null for 1)\npeo.getLowestExp()            // returns the lowest exponent in the Peo (*)\npeo.getHighestPrime()         // returns the highest prime in the Peo (*)\npeo.getHighestExp()           // returns the highest exponent in the Peo (*)\npeo.getHighestAbsExp()        // returns the highest abs(exponent) in the Peo (*)\npeo.getLiouville()            // returns the Liouville function on the Peo (-1 ^ countFactors)\npeo.getMobius()               // returns the Mobius function on the Peo (-1 ^ countFactors if square-free, 0 otherwise)\npeo.getBenedettiHeight()      // returns the Benedetti Height or the Complexity of the Peo; N x D when N/D is in lowest terms\n```\n","readmeFilename":"README.md"}