Safe Haskell	None
Language	Haskell98

Algebra.RingUtils

Documentation

class AbelianGroup a where #

Minimal complete definition

Methods

zero :: a #

(+) :: a -> a -> a infixl 6 #

Instances

AbelianGroup Bool #
Methods zero :: Bool # (+) :: Bool -> Bool -> Bool #
AbelianGroup Int #
Methods zero :: Int # (+) :: Int -> Int -> Int #
AbelianGroup a => AbelianGroup (Pair a) #
Methods zero :: Pair a # (+) :: Pair a -> Pair a -> Pair a #
AbelianGroup a => AbelianGroup (Vec x a) #
Methods zero :: Vec x a # (+) :: Vec x a -> Vec x a -> Vec x a #
AbelianGroup (f (g a)) => AbelianGroup (O f g a) #
Methods zero :: O f g a # (+) :: O f g a -> O f g a -> O f g a #
AbelianGroupZ a => AbelianGroup (Mat x y a) #
Methods zero :: Mat x y a # (+) :: Mat x y a -> Mat x y a -> Mat x y a #

Minimal complete definition

Methods

Instances

AbelianGroupZ Int #
Methods isZero :: Int -> Bool #
AbelianGroupZ a => AbelianGroupZ (Pair a) #
Methods isZero :: Pair a -> Bool #
AbelianGroupZ (f (g a)) => AbelianGroupZ (O f g a) #
Methods isZero :: O f g a -> Bool #

class AbelianGroupZ a => Ring a where #

Minimal complete definition

Methods

(*) :: a -> a -> a infixl 7 #

Instances

Ring Int #
Methods (*) :: Int -> Int -> Int #

class AbelianGroupZ a => RingP a where #

Minimal complete definition

Methods

mul :: Bool -> a -> a -> Pair a #

data Pair a #

Constructors

(:/:) infixl 2
Fields leftOf :: a rightOf :: a

Instances

Functor Pair #
Methods fmap :: (a -> b) -> Pair a -> Pair b # (<$) :: a -> Pair b -> Pair a #
Applicative Pair #
Methods pure :: a -> Pair a # (<>) :: Pair (a -> b) -> Pair a -> Pair b # liftA2 :: (a -> b -> c) -> Pair a -> Pair b -> Pair c # (>) :: Pair a -> Pair b -> Pair b # (<*) :: Pair a -> Pair b -> Pair a #
Show a => Show (Pair a) #
Methods showsPrec :: Int -> Pair a -> ShowS # show :: Pair a -> String # showList :: [Pair a] -> ShowS #
AbelianGroupZ a => AbelianGroupZ (Pair a) #
Methods isZero :: Pair a -> Bool #
AbelianGroup a => AbelianGroup (Pair a) #
Methods zero :: Pair a # (+) :: Pair a -> Pair a -> Pair a #
Matrix m => Matrix (O Pair m) #
Methods at :: AbelianGroupZ a => Int -> Int -> O Pair m a -> a # extent :: O Pair m a -> Extent # singleton :: AbelianGroupZ a => a -> O Pair m a # glue :: AbelianGroup a => Dimension -> O Pair m a -> O Pair m a -> O Pair m a # split :: AbelianGroupZ a => Dimension -> Int -> O Pair m a -> (O Pair m a, O Pair m a) # zeroMatrix :: AbelianGroup a => Int -> Int -> O Pair m a #

select :: Bool -> [a] -> Pair [a] #

onlyLeft :: [a] -> Pair [a] #

onlyRight :: [a] -> Pair [a] #

newtype O f g a #

Constructors

O
Fields fromO :: f (g a)

Instances

(Functor f, Functor g) => Functor (O f g) #
Methods fmap :: (a -> b) -> O f g a -> O f g b # (<$) :: a -> O f g b -> O f g a #
Matrix m => Matrix (O Pair m) #
Methods at :: AbelianGroupZ a => Int -> Int -> O Pair m a -> a # extent :: O Pair m a -> Extent # singleton :: AbelianGroupZ a => a -> O Pair m a # glue :: AbelianGroup a => Dimension -> O Pair m a -> O Pair m a -> O Pair m a # split :: AbelianGroupZ a => Dimension -> Int -> O Pair m a -> (O Pair m a, O Pair m a) # zeroMatrix :: AbelianGroup a => Int -> Int -> O Pair m a #
Show (f (g a)) => Show (O f g a) #
Methods showsPrec :: Int -> O f g a -> ShowS # show :: O f g a -> String # showList :: [O f g a] -> ShowS #
AbelianGroupZ (f (g a)) => AbelianGroupZ (O f g a) #
Methods isZero :: O f g a -> Bool #
AbelianGroup (f (g a)) => AbelianGroup (O f g a) #
Methods zero :: O f g a # (+) :: O f g a -> O f g a -> O f g a #

sum :: AbelianGroup a => [a] -> a #

mulDefault :: RingP a => a -> a -> a #