Safe Haskell	None
Language	Haskell98

Numeric.Algebra.Hyperbolic

Documentation

class Hyperbolic r where Source #

Minimal complete definition

cosh, sinh

Methods

cosh :: r Source #

sinh :: r Source #

Instances

Hyperbolic HyperBasis Source #
Methods cosh :: HyperBasis Source # sinh :: HyperBasis Source #
Hyperbolic HyperBasis' Source #
Methods cosh :: HyperBasis' Source # sinh :: HyperBasis' Source #
Rig r => Hyperbolic (Hyper r) Source #
Methods cosh :: Hyper r Source # sinh :: Hyper r Source #
Rig r => Hyperbolic (Hyper' r) Source #
Methods cosh :: Hyper' r Source # sinh :: Hyper' r Source #
Rig r => Hyperbolic (HyperBasis -> r) Source #
Methods cosh :: HyperBasis -> r Source # sinh :: HyperBasis -> r Source #
Rig r => Hyperbolic (HyperBasis' -> r) Source #
Methods cosh :: HyperBasis' -> r Source # sinh :: HyperBasis' -> r Source #
Hyperbolic a => Hyperbolic (Covector r a) Source #
Methods cosh :: Covector r a Source # sinh :: Covector r a Source #

data HyperBasis' Source #

Constructors

Cosh'
Sinh'

Instances

Bounded HyperBasis' Source #
Methods minBound :: HyperBasis' # maxBound :: HyperBasis' #
Enum HyperBasis' Source #
Methods succ :: HyperBasis' -> HyperBasis' # pred :: HyperBasis' -> HyperBasis' # toEnum :: Int -> HyperBasis' # fromEnum :: HyperBasis' -> Int # enumFrom :: HyperBasis' -> [HyperBasis'] # enumFromThen :: HyperBasis' -> HyperBasis' -> [HyperBasis'] # enumFromTo :: HyperBasis' -> HyperBasis' -> [HyperBasis'] # enumFromThenTo :: HyperBasis' -> HyperBasis' -> HyperBasis' -> [HyperBasis'] #
Eq HyperBasis' Source #
Methods (==) :: HyperBasis' -> HyperBasis' -> Bool # (/=) :: HyperBasis' -> HyperBasis' -> Bool #
Data HyperBasis' Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HyperBasis' -> c HyperBasis' # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c HyperBasis' # toConstr :: HyperBasis' -> Constr # dataTypeOf :: HyperBasis' -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c HyperBasis') # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c HyperBasis') # gmapT :: (forall b. Data b => b -> b) -> HyperBasis' -> HyperBasis' # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HyperBasis' -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HyperBasis' -> r # gmapQ :: (forall d. Data d => d -> u) -> HyperBasis' -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> HyperBasis' -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> HyperBasis' -> m HyperBasis' # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HyperBasis' -> m HyperBasis' # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HyperBasis' -> m HyperBasis' #
Ord HyperBasis' Source #
Methods compare :: HyperBasis' -> HyperBasis' -> Ordering # (<) :: HyperBasis' -> HyperBasis' -> Bool # (<=) :: HyperBasis' -> HyperBasis' -> Bool # (>) :: HyperBasis' -> HyperBasis' -> Bool # (>=) :: HyperBasis' -> HyperBasis' -> Bool # max :: HyperBasis' -> HyperBasis' -> HyperBasis' # min :: HyperBasis' -> HyperBasis' -> HyperBasis' #
Read HyperBasis' Source #
Methods readsPrec :: Int -> ReadS HyperBasis' # readList :: ReadS [HyperBasis'] # readPrec :: ReadPrec HyperBasis' # readListPrec :: ReadPrec [HyperBasis'] #
Show HyperBasis' Source #
Methods showsPrec :: Int -> HyperBasis' -> ShowS # show :: HyperBasis' -> String # showList :: [HyperBasis'] -> ShowS #
Ix HyperBasis' Source #
Methods range :: (HyperBasis', HyperBasis') -> [HyperBasis'] # index :: (HyperBasis', HyperBasis') -> HyperBasis' -> Int # unsafeIndex :: (HyperBasis', HyperBasis') -> HyperBasis' -> Int inRange :: (HyperBasis', HyperBasis') -> HyperBasis' -> Bool # rangeSize :: (HyperBasis', HyperBasis') -> Int # unsafeRangeSize :: (HyperBasis', HyperBasis') -> Int
Hyperbolic HyperBasis' Source #
Methods cosh :: HyperBasis' Source # sinh :: HyperBasis' Source #
MonadReader HyperBasis' Hyper' Source #
Methods ask :: Hyper' HyperBasis' # local :: (HyperBasis' -> HyperBasis') -> Hyper' a -> Hyper' a # reader :: (HyperBasis' -> a) -> Hyper' a #
(Commutative k, Monoidal k, Semiring k) => Coalgebra k HyperBasis' Source #
Methods comult :: (HyperBasis' -> k) -> HyperBasis' -> HyperBasis' -> k Source #
(Commutative k, Semiring k) => Algebra k HyperBasis' Source #
Methods mult :: (HyperBasis' -> HyperBasis' -> k) -> HyperBasis' -> k Source #
(Commutative k, Monoidal k, Semiring k) => Bialgebra k HyperBasis' Source #

(Commutative k, Monoidal k, Semiring k) => CounitalCoalgebra k HyperBasis' Source #
Methods counit :: (HyperBasis' -> k) -> k Source #
(Commutative k, Monoidal k, Semiring k) => UnitalAlgebra k HyperBasis' Source #
Methods unit :: k -> HyperBasis' -> k Source #
(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis' Source #
Methods antipode :: (HyperBasis' -> k) -> HyperBasis' -> k Source #
(Commutative k, Group k, InvolutiveSemiring k) => InvolutiveCoalgebra k HyperBasis' Source #
Methods coinv :: (HyperBasis' -> k) -> HyperBasis' -> k Source #
(Commutative k, Group k, InvolutiveSemiring k) => InvolutiveAlgebra k HyperBasis' Source #
Methods inv :: (HyperBasis' -> k) -> HyperBasis' -> k Source #
Rig r => Hyperbolic (HyperBasis' -> r) Source #
Methods cosh :: HyperBasis' -> r Source # sinh :: HyperBasis' -> r Source #

data Hyper' a Source #

Constructors

Hyper' a a

Instances

Monad Hyper' Source #
Methods (>>=) :: Hyper' a -> (a -> Hyper' b) -> Hyper' b # (>>) :: Hyper' a -> Hyper' b -> Hyper' b # return :: a -> Hyper' a # fail :: String -> Hyper' a #
Functor Hyper' Source #
Methods fmap :: (a -> b) -> Hyper' a -> Hyper' b # (<$) :: a -> Hyper' b -> Hyper' a #
Applicative Hyper' Source #
Methods pure :: a -> Hyper' a # (<>) :: Hyper' (a -> b) -> Hyper' a -> Hyper' b # liftA2 :: (a -> b -> c) -> Hyper' a -> Hyper' b -> Hyper' c # (>) :: Hyper' a -> Hyper' b -> Hyper' b # (<*) :: Hyper' a -> Hyper' b -> Hyper' a #
Foldable Hyper' Source #
Methods fold :: Monoid m => Hyper' m -> m # foldMap :: Monoid m => (a -> m) -> Hyper' a -> m # foldr :: (a -> b -> b) -> b -> Hyper' a -> b # foldr' :: (a -> b -> b) -> b -> Hyper' a -> b # foldl :: (b -> a -> b) -> b -> Hyper' a -> b # foldl' :: (b -> a -> b) -> b -> Hyper' a -> b # foldr1 :: (a -> a -> a) -> Hyper' a -> a # foldl1 :: (a -> a -> a) -> Hyper' a -> a # toList :: Hyper' a -> [a] # null :: Hyper' a -> Bool # length :: Hyper' a -> Int # elem :: Eq a => a -> Hyper' a -> Bool # maximum :: Ord a => Hyper' a -> a # minimum :: Ord a => Hyper' a -> a # sum :: Num a => Hyper' a -> a # product :: Num a => Hyper' a -> a #
Traversable Hyper' Source #
Methods traverse :: Applicative f => (a -> f b) -> Hyper' a -> f (Hyper' b) # sequenceA :: Applicative f => Hyper' (f a) -> f (Hyper' a) # mapM :: Monad m => (a -> m b) -> Hyper' a -> m (Hyper' b) # sequence :: Monad m => Hyper' (m a) -> m (Hyper' a) #
Distributive Hyper' Source #
Methods distribute :: Functor f => f (Hyper' a) -> Hyper' (f a) # collect :: Functor f => (a -> Hyper' b) -> f a -> Hyper' (f b) # distributeM :: Monad m => m (Hyper' a) -> Hyper' (m a) # collectM :: Monad m => (a -> Hyper' b) -> m a -> Hyper' (m b) #
Representable Hyper' Source #
Associated Types type Rep (Hyper' :: * -> ) :: # Methods tabulate :: (Rep Hyper' -> a) -> Hyper' a # index :: Hyper' a -> Rep Hyper' -> a #
Traversable1 Hyper' Source #
Methods traverse1 :: Apply f => (a -> f b) -> Hyper' a -> f (Hyper' b) # sequence1 :: Apply f => Hyper' (f b) -> f (Hyper' b) #
Foldable1 Hyper' Source #
Methods fold1 :: Semigroup m => Hyper' m -> m # foldMap1 :: Semigroup m => (a -> m) -> Hyper' a -> m # toNonEmpty :: Hyper' a -> NonEmpty a #
Apply Hyper' Source #
Methods (<.>) :: Hyper' (a -> b) -> Hyper' a -> Hyper' b # (.>) :: Hyper' a -> Hyper' b -> Hyper' b # (<.) :: Hyper' a -> Hyper' b -> Hyper' a #
Bind Hyper' Source #
Methods (>>-) :: Hyper' a -> (a -> Hyper' b) -> Hyper' b # join :: Hyper' (Hyper' a) -> Hyper' a #
MonadReader HyperBasis' Hyper' Source #
Methods ask :: Hyper' HyperBasis' # local :: (HyperBasis' -> HyperBasis') -> Hyper' a -> Hyper' a # reader :: (HyperBasis' -> a) -> Hyper' a #
RightModule r s => RightModule r (Hyper' s) Source #
Methods (*.) :: Hyper' s -> r -> Hyper' s Source #
LeftModule r s => LeftModule r (Hyper' s) Source #
Methods (.*) :: r -> Hyper' s -> Hyper' s Source #
(Commutative r, InvolutiveSemiring r, Rng r) => Quadrance r (Hyper' r) Source #
Methods quadrance :: Hyper' r -> r Source #
Eq a => Eq (Hyper' a) Source #
Methods (==) :: Hyper' a -> Hyper' a -> Bool # (/=) :: Hyper' a -> Hyper' a -> Bool #
Data a => Data (Hyper' a) Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Hyper' a -> c (Hyper' a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Hyper' a) # toConstr :: Hyper' a -> Constr # dataTypeOf :: Hyper' a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Hyper' a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Hyper' a)) # gmapT :: (forall b. Data b => b -> b) -> Hyper' a -> Hyper' a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Hyper' a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Hyper' a -> r # gmapQ :: (forall d. Data d => d -> u) -> Hyper' a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Hyper' a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Hyper' a -> m (Hyper' a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Hyper' a -> m (Hyper' a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Hyper' a -> m (Hyper' a) #
Read a => Read (Hyper' a) Source #
Methods readsPrec :: Int -> ReadS (Hyper' a) # readList :: ReadS [Hyper' a] # readPrec :: ReadPrec (Hyper' a) # readListPrec :: ReadPrec [Hyper' a] #
Show a => Show (Hyper' a) Source #
Methods showsPrec :: Int -> Hyper' a -> ShowS # show :: Hyper' a -> String # showList :: [Hyper' a] -> ShowS #
Idempotent r => Idempotent (Hyper' r) Source #

Abelian r => Abelian (Hyper' r) Source #

Partitionable r => Partitionable (Hyper' r) Source #
Methods partitionWith :: (Hyper' r -> Hyper' r -> r) -> Hyper' r -> NonEmpty r Source #
Additive r => Additive (Hyper' r) Source #
Methods (+) :: Hyper' r -> Hyper' r -> Hyper' r Source # sinnum1p :: Natural -> Hyper' r -> Hyper' r Source # sumWith1 :: Foldable1 f => (a -> Hyper' r) -> f a -> Hyper' r Source #
Monoidal r => Monoidal (Hyper' r) Source #
Methods zero :: Hyper' r Source # sinnum :: Natural -> Hyper' r -> Hyper' r Source # sumWith :: Foldable f => (a -> Hyper' r) -> f a -> Hyper' r Source #
(Commutative k, Semiring k) => Semiring (Hyper' k) Source #

(Commutative k, Semiring k) => Multiplicative (Hyper' k) Source #
Methods (*) :: Hyper' k -> Hyper' k -> Hyper' k Source # pow1p :: Hyper' k -> Natural -> Hyper' k Source # productWith1 :: Foldable1 f => (a -> Hyper' k) -> f a -> Hyper' k Source #
Group r => Group (Hyper' r) Source #
Methods (-) :: Hyper' r -> Hyper' r -> Hyper' r Source # negate :: Hyper' r -> Hyper' r Source # subtract :: Hyper' r -> Hyper' r -> Hyper' r Source # times :: Integral n => n -> Hyper' r -> Hyper' r Source #
(Commutative k, Rig k) => Unital (Hyper' k) Source #
Methods one :: Hyper' k Source # pow :: Hyper' k -> Natural -> Hyper' k Source # productWith :: Foldable f => (a -> Hyper' k) -> f a -> Hyper' k Source #
(Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Hyper' r) Source #
Methods recip :: Hyper' r -> Hyper' r Source # (/) :: Hyper' r -> Hyper' r -> Hyper' r Source # (\\) :: Hyper' r -> Hyper' r -> Hyper' r Source # (^) :: Integral n => Hyper' r -> n -> Hyper' r Source #
(Commutative k, Semiring k) => Commutative (Hyper' k) Source #

(Commutative r, InvolutiveSemiring r, Rng r) => InvolutiveSemiring (Hyper' r) Source #

(Commutative r, InvolutiveSemiring r, Rng r) => InvolutiveMultiplication (Hyper' r) Source #
Methods adjoint :: Hyper' r -> Hyper' r Source #
(Commutative r, Rig r) => Rig (Hyper' r) Source #
Methods fromNatural :: Natural -> Hyper' r Source #
(Commutative r, Ring r) => Ring (Hyper' r) Source #
Methods fromInteger :: Integer -> Hyper' r Source #
Rig r => Hyperbolic (Hyper' r) Source #
Methods cosh :: Hyper' r Source # sinh :: Hyper' r Source #
(Commutative r, Semiring r) => RightModule (Hyper' r) (Hyper' r) Source #
Methods (*.) :: Hyper' r -> Hyper' r -> Hyper' r Source #
(Commutative r, Semiring r) => LeftModule (Hyper' r) (Hyper' r) Source #
Methods (.*) :: Hyper' r -> Hyper' r -> Hyper' r Source #
type Rep Hyper' Source #
type Rep Hyper' = HyperBasis'