php-math

Collection of mathematical and math related functions

FACTORS - DIVISORS (array)

* Get all divisors of $x * if $all==true return the other half * Output #1 (default): factors(10) => array(1=>10,2=>5) * Output #2 : factors(10,true) => array(1=>10,2=>5,5=>2,10=>1)

function factors($x,$all=false,$onlyCount=false)

sum all proper divisors (1 included, N excluded)

function sumFactors($x)

get the first factor (v2)

* return: array(0,1)

function firstFactor($x)

LCD: LOWEST COMMON DIVISOR

* Input: A < B !!!

function lcd($a,$b)

LCM: LOWEST COMMON MULTIPLE

* Input: array() !!!

function lcm($a)

PRIME FACTORS

* Needs a prime slieve !!! with primes as keys !!! * Will return all primes that factor in the number (and their powers) unless $howMany is set over 1 * Will return false is $howMany is set and prime factors differ from $howMany (except value 1) * - using this with a prime number will just waste time

function primeFactors($x,&$primeList,$howMany=0)

PRIMES

* Output: array() | eg. prime=>Nth (2=>1,3=>2,5=>3,7=>4,11=>5,13=>6,17=>7,19=>8...)

function primes($max)

IS PRIME

* Output: bool (true/false)

function is_prime($x)

UN-POWER

* Default: Return lowest base at highest power * Backwards: Return highest base -at least squared- * Fallback: Return the number itself at power 1 * eg. unpow(1024) => array(2,10) * eg. unpow(1024,true) => array(32,2)

function unpow($n,$backwards=false)

BC FACTORIAL

* n! = n * (n-1) * (n-2) .. 1 [eg. 5! = 5 * 4 * 3 * 2 * 1 = 120]

function bcfact($n)

SIGMA - SUM (int)

* Sum all numbers 1...$n * Output : sigma(10) => 55 * Output : sigma(100) => 5050

function sigma($n)

BC SIGMA big numbers

function bcsigma($n)

SIGMA^2 - SUM^2 (int)

* Sum all numbers 1^2...$n^2 * Output : sigma2(4) => 30 * Output : sigma2(10) => 385

function sigma2($n)

BC SIGMA^2 big numbers

function bcsigma2($n)

GRADED

* Find out individual grade posibilities when graded by $no Prof.s * $grade (float); grades (int) base10! range 1..10 !

function graded($grade,$no,$min=1,$max=10)

Kaprekar

* Input: (string) !!!! * Unknown effects for sting length other than 3 or 4 !!! MIGHT LOOP 4ever

function kaprekar($x,$c=0)

Kaprekar BASE b = 6t+3, t>1 (15,21...) (constant length will be 5)

* Input: (array) !!!! * Output: (int) number of stages to get to the constant * Unknown effects for Base != ^above^ !!! MIGHT LOOP 4ever

function kaprekarB($x,$base,$c=0,$orig=array())

Collatz Sequence

* Return NEXT Collatz number in Sequence ! * Input: (string/int)

function Collatz($n)

ADD a+b (in base $base)

* Input: $a, $b (array) !!! A>B ! * Output: (array) !!!

function add($a,$b,$base)

SUBSTRACT a-b (in base $base)

* Input: $a, $b (array) !!! A>B !!! * Output: (array) !!!

function sub($a,$b,$base)

PERMUTE

* Return next lexicographic permutation of the array

function permute($array)

INCREASE UNIQUE

* Make unique sets for given $base

function inc_uniq($a,$base,$autoExpand=false)

STRIP ZEROES (string)

* Strip leading zeroes * Output : strip0('00009') => 9

function strip0($n)

REPEATING SUB STRING

* Get the first (shortest) repeating substring * Useful with fractions::repeating decimals

function repeatingSubString($s)

SUB STRINGS (array)

* Get all posible substrings from (string) $s * Output : subStrings('1234') => array('1234','123','234','12','23','34','1','2','3','4') * Output : subStrings('abc') => array('abc','ab','bc','a','b','c')

function subStrings($s)

WORD SCORE

* score a word (eg. 'Bay'=2+1+25=28)

function wordScore($word)

ADD DIGITS

* Add up all digits in a number

function addDigits($stringNumber)

SPELL NUMBER

* Up to 999 in English (translate for more langs)

function spellNumber($number,$separator=' ',$useAND=true)

DIVISOR OF 1 (bool)

* Dummy function * Output : true !!!

function divisor1($n)

function divisor2($n)

DIVISOR OF 3 (bool)

* Evaluate if very big integer is divisible * Fallback on engine math if it can handle it //(Slower)??? * Input: (string) !!! * Output : true/false

function divisor3($n)

DIVISOR OF 4 (bool)

* Evaluate if very big integer is divisible * Fallback on engine math if it can handle it * Input: (string) !!! * Output : true/false

function divisor4($n)

DIVISOR OF 5 (bool)

* Evaluate if very big integer is divisible * Input: (string) !!! * Output : true/false

function divisor5($n)

DIVISOR OF 6 (bool)

* Evaluate if very big integer is divisible * Input: (string) !!! * Output : true/false

function divisor6($n)

DIVISOR OF 7 (bool)

* Evaluate if very big integer is divisible * Input: (string) !!! * Output : true/false

function divisor7($n)

Licensed to the Public Domain