algebra-4.3: Constructive abstract algebra

Numeric.Coalgebra.Dual

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 t => Infinitesimal t where Source #

Minimal complete definition

d

Methods

d :: t Source #

Instances

 Source # Methods Source # Methods Rig r => Infinitesimal (Dual r) Source # Methodsd :: Dual r Source # Rig r => Infinitesimal (Dual' r) Source # Methods Rig r => Infinitesimal (DualBasis -> r) Source # Methodsd :: DualBasis -> r Source # Rig r => Infinitesimal (DualBasis' -> r) Source # Methodsd :: DualBasis' -> r Source # Infinitesimal a => Infinitesimal (Covector r a) Source # Methodsd :: Covector r a Source #

dual number basis, D^2 = 0. D /= 0.

Constructors

 E D

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) -> DualBasis' -> c DualBasis' #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c DualBasis' #dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c DualBasis') #dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c DualBasis') #gmapT :: (forall b. Data b => b -> b) -> DualBasis' -> DualBasis' #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> DualBasis' -> r #gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> DualBasis' -> r #gmapQ :: (forall d. Data d => d -> u) -> DualBasis' -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> DualBasis' -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> DualBasis' -> m DualBasis' #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> DualBasis' -> m DualBasis' #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> DualBasis' -> m DualBasis' # Source # Methods Source # Methods Source # MethodsshowList :: [DualBasis'] -> ShowS # Source # Methodsrange :: (DualBasis', DualBasis') -> [DualBasis'] #index :: (DualBasis', DualBasis') -> DualBasis' -> Int #unsafeIndex :: (DualBasis', DualBasis') -> DualBasis' -> IntinRange :: (DualBasis', DualBasis') -> DualBasis' -> Bool #rangeSize :: (DualBasis', DualBasis') -> Int # Source # Methods Source # Methods Source # Methodslocal :: (DualBasis' -> DualBasis') -> Dual' a -> Dual' a #reader :: (DualBasis' -> a) -> Dual' a # Source # Methodscomult :: (DualBasis' -> k) -> DualBasis' -> DualBasis' -> k Source # Source # Methodsmult :: (DualBasis' -> DualBasis' -> k) -> DualBasis' -> k Source # Source # Source # Methodscounit :: (DualBasis' -> k) -> k Source # Source # Methodsunit :: k -> DualBasis' -> k Source # Source # Methodsantipode :: (DualBasis' -> k) -> DualBasis' -> k Source # Source # Methodscoinv :: (DualBasis' -> k) -> DualBasis' -> k Source # Source # Methodsinv :: (DualBasis' -> k) -> DualBasis' -> k Source # Rig r => Distinguished (DualBasis' -> r) Source # Methodse :: DualBasis' -> r Source # Rig r => Infinitesimal (DualBasis' -> r) Source # Methodsd :: DualBasis' -> r Source #

data Dual' a Source #

Constructors

 Dual' a a

Instances