algebra-4.3: Constructive abstract algebra

Numeric.Coalgebra.Quaternion

Synopsis

Documentation

class Distinguished t where Source #

Minimal complete definition

e

Methods

e :: t Source #

Instances

 Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Rig r => Distinguished (Complex r) Source # Methods Rig r => Distinguished (Dual r) Source # Methodse :: Dual r Source # Rig r => Distinguished (Quaternion r) Source # Methods Rig r => Distinguished (Dual' r) Source # Methods Rig r => Distinguished (Quaternion' r) Source # Methods Rig r => Distinguished (Trig r) Source # Methodse :: Trig r Source # Rig r => Distinguished (ComplexBasis -> r) Source # Methodse :: ComplexBasis -> r Source # Rig r => Distinguished (DualBasis -> r) Source # Methodse :: DualBasis -> r Source # Rig r => Distinguished (QuaternionBasis -> r) Source # Methodse :: QuaternionBasis -> r Source # Rig r => Distinguished (DualBasis' -> r) Source # Methodse :: DualBasis' -> r Source # Rig r => Distinguished (QuaternionBasis' -> r) Source # Methodse :: QuaternionBasis' -> r Source # Rig r => Distinguished (TrigBasis -> r) Source # Methodse :: TrigBasis -> r Source # Distinguished a => Distinguished (Covector r a) Source # Methodse :: Covector r a Source #

class Distinguished r => Complicated r where Source #

Minimal complete definition

i

Methods

i :: r Source #

Instances

 Source # Methods Source # Methods Source # Methods Source # Methods Rig r => Complicated (Complex r) Source # Methods Rig r => Complicated (Quaternion r) Source # Methods Rig r => Complicated (Quaternion' r) Source # Methods Rig r => Complicated (Trig r) Source # Methodsi :: Trig r Source # Rig r => Complicated (ComplexBasis -> r) Source # Methodsi :: ComplexBasis -> r Source # Rig r => Complicated (QuaternionBasis -> r) Source # Methodsi :: QuaternionBasis -> r Source # Rig r => Complicated (QuaternionBasis' -> r) Source # Methodsi :: QuaternionBasis' -> r Source # Rig r => Complicated (TrigBasis -> r) Source # Methodsi :: TrigBasis -> r Source # Complicated a => Complicated (Covector r a) Source # Methodsi :: Covector r a Source #

class Complicated t => Hamiltonian t where Source #

Minimal complete definition

j, k

Methods

j :: t Source #

k :: t Source #

Instances

 Source # Methods Source # Methods Rig r => Hamiltonian (Quaternion r) Source # Methods Rig r => Hamiltonian (Quaternion' r) Source # Methods Rig r => Hamiltonian (QuaternionBasis -> r) Source # Methodsj :: QuaternionBasis -> r Source #k :: QuaternionBasis -> r Source # Rig r => Hamiltonian (QuaternionBasis' -> r) Source # Methodsj :: QuaternionBasis' -> r Source #k :: QuaternionBasis' -> r Source # Hamiltonian a => Hamiltonian (Covector r a) Source # Methodsj :: Covector r a Source #k :: Covector r a Source #

Constructors

 E' I' J' K'

Instances

 Source # Methods Source # Methods Source # Methods Source # Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> QuaternionBasis' -> c QuaternionBasis' #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c QuaternionBasis' #dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c QuaternionBasis') #dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c QuaternionBasis') #gmapT :: (forall b. Data b => b -> b) -> QuaternionBasis' -> QuaternionBasis' #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> QuaternionBasis' -> r #gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> QuaternionBasis' -> r #gmapQ :: (forall d. Data d => d -> u) -> QuaternionBasis' -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> QuaternionBasis' -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> QuaternionBasis' -> m QuaternionBasis' #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> QuaternionBasis' -> m QuaternionBasis' #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> QuaternionBasis' -> m QuaternionBasis' # Source # Methods Source # Methods Source # MethodsshowList :: [QuaternionBasis'] -> ShowS # Source # Methods Source # Methods Source # Methods Source # Methods Source # Methodslocal :: (QuaternionBasis' -> QuaternionBasis') -> Quaternion' a -> Quaternion' a #reader :: (QuaternionBasis' -> a) -> Quaternion' a # Source # dual quaternion comultiplication Methodscomult :: (QuaternionBasis' -> r) -> QuaternionBasis' -> QuaternionBasis' -> r Source # Source # the trivial diagonal algebra Methodsmult :: (QuaternionBasis' -> QuaternionBasis' -> r) -> QuaternionBasis' -> r Source # Source # Source # Methodscounit :: (QuaternionBasis' -> r) -> r Source # Source # Methodsunit :: r -> QuaternionBasis' -> r Source # Source # Methodsantipode :: (QuaternionBasis' -> r) -> QuaternionBasis' -> r Source # Source # Methodscoinv :: (QuaternionBasis' -> r) -> QuaternionBasis' -> r Source # Source # Methodsinv :: (QuaternionBasis' -> r) -> QuaternionBasis' -> r Source # Rig r => Distinguished (QuaternionBasis' -> r) Source # Methodse :: QuaternionBasis' -> r Source # Rig r => Complicated (QuaternionBasis' -> r) Source # Methodsi :: QuaternionBasis' -> r Source # Rig r => Hamiltonian (QuaternionBasis' -> r) Source # Methodsj :: QuaternionBasis' -> r Source #k :: QuaternionBasis' -> r Source #

data Quaternion' a Source #

Constructors

 Quaternion' a a a a

Instances