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


-- | Simple multivariate polynomials.
--   
--   Manipulation of multivariate polynomials on a ring.
@package mpolynomials
@version 0.1.1.0

module Math.Algebra.MultiPol
data Polynomial a
data Monomial a
Monomial :: a -> Seq Int -> Monomial a
[coefficient] :: Monomial a -> a
[powers] :: Monomial a -> Seq Int

-- | Polynomial x_n
lone :: (C a, Eq a) => Int -> Polynomial a

-- | Constant polynomial
constant :: (C a, Eq a) => a -> Polynomial a

-- | List of the terms of a polynomial
terms :: (C a, Eq a) => Polynomial a -> [Monomial a]

-- | Scale polynomial by a scalar
(*^) :: (C a, Eq a) => a -> Polynomial a -> Polynomial a
infixr 7 *^

-- | Addition of two polynomials
(^+^) :: (C a, Eq a) => Polynomial a -> Polynomial a -> Polynomial a
infixl 6 ^+^

-- | Substraction
(^-^) :: (C a, Eq a) => Polynomial a -> Polynomial a -> Polynomial a
infixl 6 ^-^

-- | Multiply two polynomials
(^*^) :: (C a, Eq a) => Polynomial a -> Polynomial a -> Polynomial a
infixl 7 ^*^

-- | Power of a polynomial
(^**^) :: (C a, Eq a) => Polynomial a -> Int -> Polynomial a
infixr 8 ^**^

-- | Evaluates a polynomial
evalPoly :: (C a, Eq a) => Polynomial a -> [a] -> a

-- | Pretty form of a polynomial
prettyPol :: (C a, Eq a) => (a -> String) -> String -> Polynomial a -> String
instance GHC.Classes.Eq a => GHC.Classes.Eq (Math.Algebra.MultiPol.Monomial a)
instance GHC.Show.Show a => GHC.Show.Show (Math.Algebra.MultiPol.Monomial a)
instance GHC.Show.Show a => GHC.Show.Show (Math.Algebra.MultiPol.Polynomial a)
instance (Algebra.Ring.C a, GHC.Classes.Eq a) => GHC.Classes.Eq (Math.Algebra.MultiPol.Polynomial a)
instance (Algebra.Ring.C a, GHC.Classes.Eq a) => Algebra.Additive.C (Math.Algebra.MultiPol.Polynomial a)
instance (Algebra.Ring.C a, GHC.Classes.Eq a) => Algebra.Module.C a (Math.Algebra.MultiPol.Polynomial a)
instance (Algebra.Ring.C a, GHC.Classes.Eq a) => Algebra.Ring.C (Math.Algebra.MultiPol.Polynomial a)