algebra-4.3.1: Constructive abstract algebra
Safe HaskellSafe-Inferred
LanguageHaskell98

Numeric.Algebra.Complex

Synopsis

Documentation

class Distinguished t where Source #

Methods

e :: t Source #

Instances

Instances details
Distinguished ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

e :: ComplexBasis Source #

Distinguished DualBasis Source # 
Instance details

Defined in Numeric.Algebra.Dual

Methods

e :: DualBasis Source #

Distinguished QuaternionBasis Source # 
Instance details

Defined in Numeric.Algebra.Quaternion

Methods

e :: QuaternionBasis Source #

Distinguished DualBasis' Source # 
Instance details

Defined in Numeric.Coalgebra.Dual

Methods

e :: DualBasis' Source #

Distinguished QuaternionBasis' Source # 
Instance details

Defined in Numeric.Coalgebra.Quaternion

Methods

e :: QuaternionBasis' Source #

Distinguished TrigBasis Source # 
Instance details

Defined in Numeric.Coalgebra.Trigonometric

Methods

e :: TrigBasis Source #

Rig r => Distinguished (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

e :: Complex r Source #

Rig r => Distinguished (Dual r) Source # 
Instance details

Defined in Numeric.Algebra.Dual

Methods

e :: Dual r Source #

Rig r => Distinguished (Quaternion r) Source # 
Instance details

Defined in Numeric.Algebra.Quaternion

Methods

e :: Quaternion r Source #

Rig r => Distinguished (Dual' r) Source # 
Instance details

Defined in Numeric.Coalgebra.Dual

Methods

e :: Dual' r Source #

Rig r => Distinguished (Quaternion' r) Source # 
Instance details

Defined in Numeric.Coalgebra.Quaternion

Methods

e :: Quaternion' r Source #

Rig r => Distinguished (Trig r) Source # 
Instance details

Defined in Numeric.Coalgebra.Trigonometric

Methods

e :: Trig r Source #

Distinguished a => Distinguished (Covector r a) Source # 
Instance details

Defined in Numeric.Algebra.Distinguished.Class

Methods

e :: Covector r a Source #

Rig r => Distinguished (ComplexBasis -> r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

e :: ComplexBasis -> r Source #

Rig r => Distinguished (DualBasis -> r) Source # 
Instance details

Defined in Numeric.Algebra.Dual

Methods

e :: DualBasis -> r Source #

Rig r => Distinguished (QuaternionBasis -> r) Source # 
Instance details

Defined in Numeric.Algebra.Quaternion

Methods

e :: QuaternionBasis -> r Source #

Rig r => Distinguished (DualBasis' -> r) Source # 
Instance details

Defined in Numeric.Coalgebra.Dual

Methods

e :: DualBasis' -> r Source #

Rig r => Distinguished (QuaternionBasis' -> r) Source # 
Instance details

Defined in Numeric.Coalgebra.Quaternion

Methods

e :: QuaternionBasis' -> r Source #

Rig r => Distinguished (TrigBasis -> r) Source # 
Instance details

Defined in Numeric.Coalgebra.Trigonometric

Methods

e :: TrigBasis -> r Source #

class Distinguished r => Complicated r where Source #

Methods

i :: r Source #

Instances

Instances details
Complicated ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

i :: ComplexBasis Source #

Complicated QuaternionBasis Source # 
Instance details

Defined in Numeric.Algebra.Quaternion

Methods

i :: QuaternionBasis Source #

Complicated QuaternionBasis' Source # 
Instance details

Defined in Numeric.Coalgebra.Quaternion

Methods

i :: QuaternionBasis' Source #

Complicated TrigBasis Source # 
Instance details

Defined in Numeric.Coalgebra.Trigonometric

Methods

i :: TrigBasis Source #

Rig r => Complicated (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

i :: Complex r Source #

Rig r => Complicated (Quaternion r) Source # 
Instance details

Defined in Numeric.Algebra.Quaternion

Methods

i :: Quaternion r Source #

Rig r => Complicated (Quaternion' r) Source # 
Instance details

Defined in Numeric.Coalgebra.Quaternion

Methods

i :: Quaternion' r Source #

Rig r => Complicated (Trig r) Source # 
Instance details

Defined in Numeric.Coalgebra.Trigonometric

Methods

i :: Trig r Source #

Complicated a => Complicated (Covector r a) Source # 
Instance details

Defined in Numeric.Algebra.Complex.Class

Methods

i :: Covector r a Source #

Rig r => Complicated (ComplexBasis -> r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

i :: ComplexBasis -> r Source #

Rig r => Complicated (QuaternionBasis -> r) Source # 
Instance details

Defined in Numeric.Algebra.Quaternion

Methods

i :: QuaternionBasis -> r Source #

Rig r => Complicated (QuaternionBasis' -> r) Source # 
Instance details

Defined in Numeric.Coalgebra.Quaternion

Methods

i :: QuaternionBasis' -> r Source #

Rig r => Complicated (TrigBasis -> r) Source # 
Instance details

Defined in Numeric.Coalgebra.Trigonometric

Methods

i :: TrigBasis -> r Source #

data ComplexBasis Source #

Constructors

E 
I 

Instances

Instances details
Complicated ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

i :: ComplexBasis Source #

Distinguished ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

e :: ComplexBasis Source #

Data ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ComplexBasis -> c ComplexBasis #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ComplexBasis #

toConstr :: ComplexBasis -> Constr #

dataTypeOf :: ComplexBasis -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c ComplexBasis) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ComplexBasis) #

gmapT :: (forall b. Data b => b -> b) -> ComplexBasis -> ComplexBasis #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ComplexBasis -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ComplexBasis -> r #

gmapQ :: (forall d. Data d => d -> u) -> ComplexBasis -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> ComplexBasis -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> ComplexBasis -> m ComplexBasis #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ComplexBasis -> m ComplexBasis #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ComplexBasis -> m ComplexBasis #

Bounded ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

minBound :: ComplexBasis #

maxBound :: ComplexBasis #

Enum ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

succ :: ComplexBasis -> ComplexBasis #

pred :: ComplexBasis -> ComplexBasis #

toEnum :: Int -> ComplexBasis #

fromEnum :: ComplexBasis -> Int #

enumFrom :: ComplexBasis -> [ComplexBasis] #

enumFromThen :: ComplexBasis -> ComplexBasis -> [ComplexBasis] #

enumFromTo :: ComplexBasis -> ComplexBasis -> [ComplexBasis] #

enumFromThenTo :: ComplexBasis -> ComplexBasis -> ComplexBasis -> [ComplexBasis] #

Ix ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

range :: (ComplexBasis, ComplexBasis) -> [ComplexBasis] #

index :: (ComplexBasis, ComplexBasis) -> ComplexBasis -> Int #

unsafeIndex :: (ComplexBasis, ComplexBasis) -> ComplexBasis -> Int #

inRange :: (ComplexBasis, ComplexBasis) -> ComplexBasis -> Bool #

rangeSize :: (ComplexBasis, ComplexBasis) -> Int #

unsafeRangeSize :: (ComplexBasis, ComplexBasis) -> Int #

Read ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

readsPrec :: Int -> ReadS ComplexBasis #

readList :: ReadS [ComplexBasis] #

readPrec :: ReadPrec ComplexBasis #

readListPrec :: ReadPrec [ComplexBasis] #

Show ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

showsPrec :: Int -> ComplexBasis -> ShowS #

show :: ComplexBasis -> String #

showList :: [ComplexBasis] -> ShowS #

Eq ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(==) :: ComplexBasis -> ComplexBasis -> Bool #

(/=) :: ComplexBasis -> ComplexBasis -> Bool #

Ord ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

compare :: ComplexBasis -> ComplexBasis -> Ordering #

(<) :: ComplexBasis -> ComplexBasis -> Bool #

(<=) :: ComplexBasis -> ComplexBasis -> Bool #

(>) :: ComplexBasis -> ComplexBasis -> Bool #

(>=) :: ComplexBasis -> ComplexBasis -> Bool #

max :: ComplexBasis -> ComplexBasis -> ComplexBasis #

min :: ComplexBasis -> ComplexBasis -> ComplexBasis #

Rng k => Algebra k ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

mult :: (ComplexBasis -> ComplexBasis -> k) -> ComplexBasis -> k Source #

Rng k => Coalgebra k ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

comult :: (ComplexBasis -> k) -> ComplexBasis -> ComplexBasis -> k Source #

(InvolutiveSemiring k, Rng k) => HopfAlgebra k ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

antipode :: (ComplexBasis -> k) -> ComplexBasis -> k Source #

(InvolutiveSemiring k, Rng k) => InvolutiveAlgebra k ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

inv :: (ComplexBasis -> k) -> ComplexBasis -> k Source #

(InvolutiveSemiring k, Rng k) => InvolutiveCoalgebra k ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

coinv :: (ComplexBasis -> k) -> ComplexBasis -> k Source #

Rng k => Bialgebra k ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Rng k => CounitalCoalgebra k ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

counit :: (ComplexBasis -> k) -> k Source #

Rng k => UnitalAlgebra k ComplexBasis Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

unit :: k -> ComplexBasis -> k Source #

MonadReader ComplexBasis Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

ask :: Complex ComplexBasis #

local :: (ComplexBasis -> ComplexBasis) -> Complex a -> Complex a #

reader :: (ComplexBasis -> a) -> Complex a #

Rig r => Complicated (ComplexBasis -> r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

i :: ComplexBasis -> r Source #

Rig r => Distinguished (ComplexBasis -> r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

e :: ComplexBasis -> r Source #

data Complex a Source #

Constructors

Complex a a 

Instances

Instances details
Representable Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Associated Types

type Rep Complex 
Instance details

Defined in Numeric.Algebra.Complex

type Rep Complex = ComplexBasis

Methods

tabulate :: (Rep Complex -> a) -> Complex a #

index :: Complex a -> Rep Complex -> a #

Foldable1 Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

fold1 :: Semigroup m => Complex m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Complex a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Complex a -> m #

toNonEmpty :: Complex a -> NonEmpty a #

maximum :: Ord a => Complex a -> a #

minimum :: Ord a => Complex a -> a #

head :: Complex a -> a #

last :: Complex a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Complex a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Complex a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Complex a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Complex a -> b #

Distributive Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

distribute :: Functor f => f (Complex a) -> Complex (f a) #

collect :: Functor f => (a -> Complex b) -> f a -> Complex (f b) #

distributeM :: Monad m => m (Complex a) -> Complex (m a) #

collectM :: Monad m => (a -> Complex b) -> m a -> Complex (m b) #

Applicative Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

pure :: a -> Complex a #

(<*>) :: Complex (a -> b) -> Complex a -> Complex b #

liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c #

(*>) :: Complex a -> Complex b -> Complex b #

(<*) :: Complex a -> Complex b -> Complex a #

Functor Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b #

(<$) :: a -> Complex b -> Complex a #

Monad Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(>>=) :: Complex a -> (a -> Complex b) -> Complex b #

(>>) :: Complex a -> Complex b -> Complex b #

return :: a -> Complex a #

Foldable Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

fold :: Monoid m => Complex m -> m #

foldMap :: Monoid m => (a -> m) -> Complex a -> m #

foldMap' :: Monoid m => (a -> m) -> Complex a -> m #

foldr :: (a -> b -> b) -> b -> Complex a -> b #

foldr' :: (a -> b -> b) -> b -> Complex a -> b #

foldl :: (b -> a -> b) -> b -> Complex a -> b #

foldl' :: (b -> a -> b) -> b -> Complex a -> b #

foldr1 :: (a -> a -> a) -> Complex a -> a #

foldl1 :: (a -> a -> a) -> Complex a -> a #

toList :: Complex a -> [a] #

null :: Complex a -> Bool #

length :: Complex a -> Int #

elem :: Eq a => a -> Complex a -> Bool #

maximum :: Ord a => Complex a -> a #

minimum :: Ord a => Complex a -> a #

sum :: Num a => Complex a -> a #

product :: Num a => Complex a -> a #

Traversable Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) #

sequenceA :: Applicative f => Complex (f a) -> f (Complex a) #

mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) #

sequence :: Monad m => Complex (m a) -> m (Complex a) #

Apply Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(<.>) :: Complex (a -> b) -> Complex a -> Complex b #

(.>) :: Complex a -> Complex b -> Complex b #

(<.) :: Complex a -> Complex b -> Complex a #

liftF2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c #

Bind Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(>>-) :: Complex a -> (a -> Complex b) -> Complex b #

join :: Complex (Complex a) -> Complex a #

Traversable1 Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

traverse1 :: Apply f => (a -> f b) -> Complex a -> f (Complex b) #

sequence1 :: Apply f => Complex (f b) -> f (Complex b) #

MonadReader ComplexBasis Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

ask :: Complex ComplexBasis #

local :: (ComplexBasis -> ComplexBasis) -> Complex a -> Complex a #

reader :: (ComplexBasis -> a) -> Complex a #

LeftModule r s => LeftModule r (Complex s) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(.*) :: r -> Complex s -> Complex s Source #

RightModule r s => RightModule r (Complex s) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(*.) :: Complex s -> r -> Complex s Source #

(Commutative r, Rng r, InvolutiveSemiring r) => Quadrance r (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

quadrance :: Complex r -> r Source #

Abelian r => Abelian (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Additive r => Additive (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(+) :: Complex r -> Complex r -> Complex r Source #

sinnum1p :: Natural -> Complex r -> Complex r Source #

sumWith1 :: Foldable1 f => (a -> Complex r) -> f a -> Complex r Source #

Idempotent r => Idempotent (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Partitionable r => Partitionable (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

partitionWith :: (Complex r -> Complex r -> r0) -> Complex r -> NonEmpty r0 Source #

Group r => Group (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(-) :: Complex r -> Complex r -> Complex r Source #

negate :: Complex r -> Complex r Source #

subtract :: Complex r -> Complex r -> Complex r Source #

times :: Integral n => n -> Complex r -> Complex r Source #

Monoidal r => Monoidal (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

zero :: Complex r Source #

sinnum :: Natural -> Complex r -> Complex r Source #

sumWith :: Foldable f => (a -> Complex r) -> f a -> Complex r Source #

(Commutative r, Rng r) => Multiplicative (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(*) :: Complex r -> Complex r -> Complex r Source #

pow1p :: Complex r -> Natural -> Complex r Source #

productWith1 :: Foldable1 f => (a -> Complex r) -> f a -> Complex r Source #

(Commutative r, Rng r) => Semiring (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

(TriviallyInvolutive r, Rng r) => Commutative (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Rig r => Complicated (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

i :: Complex r Source #

Rig r => Distinguished (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

e :: Complex r Source #

(Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

recip :: Complex r -> Complex r Source #

(/) :: Complex r -> Complex r -> Complex r Source #

(\\) :: Complex r -> Complex r -> Complex r Source #

(^) :: Integral n => Complex r -> n -> Complex r Source #

(Commutative r, Rng r, InvolutiveMultiplication r) => InvolutiveMultiplication (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

adjoint :: Complex r -> Complex r Source #

(Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveSemiring (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

(Commutative r, Ring r) => Unital (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

one :: Complex r Source #

pow :: Complex r -> Natural -> Complex r Source #

productWith :: Foldable f => (a -> Complex r) -> f a -> Complex r Source #

(Commutative r, Ring r) => Rig (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

fromNatural :: Natural -> Complex r Source #

(Commutative r, Ring r) => Ring (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

fromInteger :: Integer -> Complex r Source #

Data a => Data (Complex a) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Complex a -> c (Complex a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Complex a) #

toConstr :: Complex a -> Constr #

dataTypeOf :: Complex a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Complex a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Complex a)) #

gmapT :: (forall b. Data b => b -> b) -> Complex a -> Complex a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Complex a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Complex a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) #

Read a => Read (Complex a) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

readsPrec :: Int -> ReadS (Complex a) #

readList :: ReadS [Complex a] #

readPrec :: ReadPrec (Complex a) #

readListPrec :: ReadPrec [Complex a] #

Show a => Show (Complex a) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

showsPrec :: Int -> Complex a -> ShowS #

show :: Complex a -> String #

showList :: [Complex a] -> ShowS #

Eq a => Eq (Complex a) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(==) :: Complex a -> Complex a -> Bool #

(/=) :: Complex a -> Complex a -> Bool #

(Commutative r, Rng r) => LeftModule (Complex r) (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(.*) :: Complex r -> Complex r -> Complex r Source #

(Commutative r, Rng r) => RightModule (Complex r) (Complex r) Source # 
Instance details

Defined in Numeric.Algebra.Complex

Methods

(*.) :: Complex r -> Complex r -> Complex r Source #

type Rep Complex Source # 
Instance details

Defined in Numeric.Algebra.Complex

type Rep Complex = ComplexBasis

realPart :: (Representable f, Rep f ~ ComplexBasis) => f a -> a Source #

imagPart :: (Representable f, Rep f ~ ComplexBasis) => f a -> a Source #

uncomplicate :: Hamiltonian q => ComplexBasis -> ComplexBasis -> q Source #

half of the Cayley-Dickson quaternion isomorphism