TGroupAlgebra.hs

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

{-# LANGUAGE FlexibleInstances, TypeSynonymInstances #-}

module Math.Test.TAlgebras.TGroupAlgebra where

import Test.QuickCheck

import Math.Algebra.Group.PermutationGroup
import Math.Test.TPermutationGroup -- for instance Arbitrary (Permutation Int)

import Math.Algebras.VectorSpace
import Math.Algebras.TensorProduct
import Math.Algebras.Structures
import Math.Algebras.GroupAlgebra

import Math.Test.TAlgebras.TStructures

{-
instance Arbitrary (TensorAlgebra Integer) where
    arbitrary = do ts <- arbitrary :: Gen [([Int], Integer)]
                   return $ nf $ V ts
-}
instance Arbitrary (GroupAlgebra Integer) where
    arbitrary = do ts <- arbitrary :: Gen [(Permutation Int, Integer)]
                   return $ nf $ V ts


{-
prop_Algebra_TensorAlgebra (k,x,y,z) = prop_Algebra (k,x,y,z)
    where types = (k,x,y,z) :: (Integer, TensorAlgebra Integer, TensorAlgebra Integer, TensorAlgebra Integer)

prop_Coalgebra_TensorAlgebra x = prop_Coalgebra x
    where types = x :: TensorAlgebra Integer
-}

prop_Algebra_GroupAlgebra (k,x,y,z) = prop_Algebra (k,x,y,z)
    where types = (k,x,y,z) :: (Integer, GroupAlgebra Integer, GroupAlgebra Integer, GroupAlgebra Integer)

-- have to split the 8-tuple into two 4-tuples to avoid having to write Arbitrary instance
prop_Algebra_Linear_GroupAlgebra ((k,l,m,n),(x,y,z,w)) = prop_Algebra_Linear (k,l,m,n,x,y,z,w)
    where types = (k,l,m,n,x,y,z,w) :: (Integer, Integer, Integer, Integer,
                   GroupAlgebra Integer, GroupAlgebra Integer, GroupAlgebra Integer, GroupAlgebra Integer)

prop_Coalgebra_GroupAlgebra x = prop_Coalgebra x
    where types = x :: GroupAlgebra Integer

prop_Coalgebra_Linear_GroupAlgebra (k,l,x,y) = prop_Coalgebra_Linear (k,l,x,y)
    where types = (k,l,x,y) :: (Integer, Integer, GroupAlgebra Integer, GroupAlgebra Integer)

prop_Bialgebra_GroupAlgebra (k,x,y) = prop_Bialgebra (k,x,y)
    where types = (k,x,y) :: (Integer, GroupAlgebra Integer, GroupAlgebra Integer)

prop_HopfAlgebra_GroupAlgebra x = prop_HopfAlgebra x
    where types = x :: GroupAlgebra Integer