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


-- | Factorization of polynomials over finite field
--   
--   Factorization of polynomials over finite field
@package BerlekampAlgorithm
@version 0.1.0.0

module BerlekampAlgorithm

-- | Berlekamp's Factorization Algorithm over Fp[x] : computes the
--   factorization of a monic square-free polynomial P into irreducible
--   factor polynomials over F_{p}[x] , p is a prime number. This method is
--   based on linear algebra over finite field. | g
g :: (Eq a, Num a) => Maybe a -> a

-- | Frobenius automorphism : linear map V -&gt; V^p - V , V in Fp[x]<i>P
--   and Fp[x]</i>P as vector space over the field Fp.
frob :: Integer -> Integer -> [Integer] -> [Integer]

-- | pivotPos'
pivotPos' :: (Eq a, Num a, Num t) => t -> [[a]] -> (Int, t)

-- | lswap
lswap :: Int -> Int -> ([a], [a1]) -> ([a], [a1])

-- | triangulizedModIntegerMat triangulizedModIntegerMat p m: gives the
--   gauss triangular decomposition of an integeral matrix m in Fp. The
--   result is (r, u) where u is a unimodular matrix, r is an
--   upper-triangular matrix , and u.m = r.
triangulizedModIntegerMat :: Integer -> [[Integer]] -> ([[Integer]], [[Integer]])

-- | nullSpaceModIntegerMat p m : computes the null space of matrix m in Fp
nullSpaceModIntegerMat :: Integer -> [[Integer]] -> [[Integer]]

-- | mmultZ mmultZ p a b : compute the product of two integer matrices in
--   Fp.
mmultZ :: Integer -> [[Integer]] -> [[Integer]] -> [[Integer]]

-- | matrixBerl matrixBerl p f : is the matrix of the Frobenius
--   endomorphism over the canonical base {1,X,X^2..,X^(p-1)} ,
--   matrixBerl(i,j) = X^(pj)-X^j mod P.
matrixBerlTranspose :: Integer -> [Integer] -> [[Integer]]

-- | derivPolyZ : derivative of polynmial P over Fp[x]
derivPolyZ :: Integer -> [Integer] -> [Integer]

-- | squareFreePolyZ squareFreePolyZ p f : gives the euclidean quotient of
--   P and gcd(f,f'). That quotient is a square free polynomial.
squareFreePolyZ :: Integer -> [Integer] -> [Integer]

-- | irreducibilityTestPolyZ irreducibilityTestPolyZ : irreducibility test
--   of polynomials over Fp[x]
irreducibilityTestPolyZ :: Integer -> [Integer] -> Bool

-- | berlekamp berlekamp p P: gives a complete factorization of a polynom P
--   of irreducible polynoms over Fp[x].
berlekamp :: Integer -> [Integer] -> [[Integer]]

-- | multPoly multPoly : product of polynomials P1, .., Pk in Fp[x].
multPoly :: Integer -> [[Integer]] -> [Integer]