-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Fast functions on integers.
--   
--   Fast functions for number theory and combinatorics with a high level
--   of safety guaranteed by <a>ATS</a>.
@package fast-arithmetic
@version 0.6.4.0


-- | This provides facilities for working with common combinatorial
--   functions.
module Numeric.Combinatorics

-- | &lt;math&gt;
choose :: Int -> Int -> Integer

-- | &lt;math&gt;
doubleFactorial :: Int -> Integer

-- | The <tt>n</tt>th Catalan number, with indexing beginning at
--   <tt>0</tt>.
--   
--   <pre>
--   λ:&gt; catalan &lt;$&gt; [0..9]
--   [1,1,2,5,14,42,132,429,1430,4862]
--   </pre>
catalan :: Int -> Integer
factorial :: Int -> Integer

-- | \( !n \)
--   
--   <pre>
--   λ:&gt; derangement &lt;$&gt; [0..10]
--   [1,0,1,2,9,44,265,1854,14833,133496,1334961]
--   </pre>
derangement :: Int -> Integer
permutations :: Int -> Int -> Integer

-- | Compute the maximal number of regions obtained by joining \( n \)
--   points about a circle by straight lines. See <a>here</a>.
maxRegions :: Int -> Integer

-- | Stirling numbers of the second kind.
stirling2 :: Int -> Int -> Integer


-- | This module provides fast number theoretic functions.
module Numeric.NumberTheory

-- | Euler totient function.
totient :: Int -> Int

-- | Number of distinct divisors.
tau :: Int -> Int

-- | Number of distinct prime factors
littleOmega :: Int -> Int

-- | See <a>here</a>
isPerfect :: Int -> Bool

-- | Sum of proper divisors. May overflow.
sumDivisors :: Int -> Int

-- | &lt;math&gt;
isPrime :: Int -> Bool

-- | Radical of an integer
radical :: Int -> Int