diff --git a/Data/Numbers.hs b/Data/Numbers.hs new file mode 100644 --- /dev/null +++ b/Data/Numbers.hs @@ -0,0 +1,48 @@ +-- | This is an assortment of number theorectic functions. As of now it's not very large or fast, but that should improve over time. +module Data.Numbers where + +import Data.List + +-- | An infinite list of prime numbers +primes :: [Integer] +primes = 2:3:primes' + where + 1:p:candidates = [6*k+r | k <- [0..], r <- [1,5]] + primes' = p : filter isPrime candidates + divides n p = n `mod` p == 0 + + +-- | Checks whether a number is prime +isPrime :: Integer -> Bool +isPrime n = all (not .(\p-> (n `mod` p) == 0)) $ takeWhile (\p -> p*p <= n) primes + +-- | Returns the prime factors for a given number +primeFactors :: Integer -> [Integer] +primeFactors n = primeFactors' n n [] primes where + -- die Ausgangszahl, der quotient vom letzten mal, die liste der primfaktoren, primzahlen + primeFactors' n m l (p:ps) + -- die nächste primzahl ist größer als wir? dann sind wir fertig + | p>n = l + -- wir sind teilbar durch p? p an die liste vorne dranhängen, quotient merken + | mo == 0 = primeFactors' n d (p:l) (p:ps) + -- nicht teilbar? mit der nächsten primzahl von vorne anfangen + | otherwise = primeFactors' n n l ps where + (d,mo) = divMod m p + +-- | Returns the number of divisors of a number. Uses +numOfFactors :: Integer -> Int +numOfFactors n = product (map ((+1).length) (group (primeFactors n))) + +-- | Returns the sum of the factors of a number +factorSum :: Integer -> Integer +factorSum = product.(map (\p@(x:xs) -> (product p * x -1) `div` (x-1))).(group.primeFactors) + +-- | Returns the factors of a number +factors :: Integer -> [Integer] +factors n = 1:factors' n [] [2..] where + factors' n l (m:ms) + | m*m==n= m:l + | m*m>n = l + | r == 0 = factors' n (d:m:l) ms + | otherwise = factors' n l ms where + (d,r) = divMod n m diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,3 @@ +Copyright 2009 Adrian Neumann + +You may use this library under the terms of the LGPL, which is included in the file lgpl-3.0.txt diff --git a/Numbers.cabal b/Numbers.cabal new file mode 100644 --- /dev/null +++ b/Numbers.cabal @@ -0,0 +1,19 @@ +Name: Numbers +Version: 0.0 +Cabal-Version: >= 1.2 +Synopsis: An assortment of number theoretic functions +Description: Functions for finding prime numbers, checking whether a number is prime, finding the factors of a number etc. +License: LGPL +License-file: LICENSE +Author: Adrian Neumann +Category: Algorithms, Number Theory +Maintainer: aneumann@inf.fu-berlin.de +stability: alpha +build-type: Simple +extra-source-files: README, test.hs, lgpl-3.0.txt + +Library + exposed-modules: Data.Numbers + build-depends: + base + GHC-Options: -O2 diff --git a/README b/README new file mode 100644 --- /dev/null +++ b/README @@ -0,0 +1,1 @@ +This is an assortment of number theorectic functions. As of now it's not very large or fast, but that should improve over time. diff --git a/Setup.lhs b/Setup.lhs new file mode 100644 --- /dev/null +++ b/Setup.lhs @@ -0,0 +1,4 @@ +#! /usr/bin/env runhaskell + +> import Distribution.Simple +> main = defaultMain diff --git a/lgpl-3.0.txt b/lgpl-3.0.txt new file mode 100644 --- /dev/null +++ b/lgpl-3.0.txt @@ -0,0 +1,165 @@ + GNU LESSER GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + + This version of the GNU Lesser General Public License incorporates +the terms and conditions of version 3 of the GNU General Public +License, supplemented by the additional permissions listed below. + + 0. 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