-- Copyright (c) 2010, David Amos. All rights reserved.

{-# LANGUAGE FlexibleInstances, TypeSynonymInstances #-}

module Math.Test.TAlgebras.TQuaternions where

import Test.QuickCheck

import Math.Algebras.VectorSpace
import Math.Algebras.TensorProduct
import Math.Algebras.Quaternions

import Math.Test.TAlgebras.TStructures

instance Arbitrary HBasis where
    arbitrary = elements [One,I,J,K]

instance Arbitrary (Quaternion Integer) where
    arbitrary = do ts <- arbitrary :: Gen [(HBasis, Integer)]
                   return $ nf $ V ts



prop_Algebra_Quaternion (k,x,y,z) = prop_Algebra (k,x,y,z)
    where types = (k,x,y,z) :: (Integer, Quaternion Integer, Quaternion Integer, Quaternion Integer)

prop_Coalgebra_Quaternion x = prop_Coalgebra x
    where types = x :: Quaternion Integer

-- Fails - the algebra and coalgebra structures I've given are not compatible
prop_Bialgebra_Quaternion (k,x,y) = prop_Bialgebra (k,x,y)
    where types = (k,x,y) :: (Integer, Quaternion Integer, Quaternion Integer)

{-
prop_FrobeniusRelation_Quaternion (x,y) = prop_FrobeniusRelation (x,y)
    where types = (x,y) :: (Quaternion Integer, Quaternion Integer)
-- !! fails, because the counit we have given is not a Frobenius form
-}