algebra-4.3.1: Constructive abstract algebra

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LanguageHaskell98

Numeric.Algebra.Hyperbolic

Documentation

data HyperBasis' Source #

Constructors

Cosh' 
Sinh' 

Instances

Bounded HyperBasis' Source # 
Enum HyperBasis' Source # 
Eq HyperBasis' Source # 
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 # 
Read HyperBasis' Source # 
Show HyperBasis' Source # 
Ix HyperBasis' Source # 
Hyperbolic HyperBasis' Source # 
MonadReader HyperBasis' Hyper' Source # 
(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 # 

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 # 
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 # 
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 # 
(Commutative r, Ring r) => Ring (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 #