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


-- | A lightweight Haskell implementation of Smith normal form over the integers.
--   
--   This package contains an implementation of Smith normal form for
--   arbitrary matrices over the integers. In particular, it does not
--   assume that the matrix is invertible or square.
@package SmithNormalForm
@version 0.1.0.0

module Data.Matrix.SmithNormalForm.Internal

-- | Main method that returns the Smith normal form of a given matrix.
smithNF :: Integral a => Matrix a -> Matrix a

-- | Given a diagonal matrix, outputs a list <math> that satisfies
--   <math> and represents the diagonal entries. Assumes input is a
--   diagonal matrix (not checked).
rectifyDiagonal :: Integral a => Matrix a -> [a]

-- | Given a matrix, returns a diagonal matrix obtained by applying
--   elementary row and column operations, but which does not necessarily
--   satisfy the divisibility property
diagonalize :: Integral a => Matrix a -> Matrix a

-- | Returns whether a matrix (not necessarily square) is diagonal
isDiagonalMatrix :: (Num a, Eq a) => Matrix a -> Bool

-- | Returns whether a <a>divides</a> b := &lt;math&gt; and handles the
--   special case of &lt;math&gt;
divides :: Integral a => a -> a -> Bool

module Data.Matrix.SmithNormalForm

-- | Returns the Smith normal form of an matrix, i.e. a diagonal matrix
--   obtained by applying elementary row and column operations whose
--   diagonal entries &lt;math&gt; are such that &lt;math&gt; (Does not
--   assume that the matrix is square.)
smithNormalForm :: Integral a => Matrix a -> Matrix a

-- | Given a matrix M, returns the invariant factors of M, i.e. the list of
--   diagonal entries of the Smith normal form of M.
invariantFactors :: Integral a => Matrix a -> [a]