Numeric.Algebra.Complex

Documentation

class Distinguished t where

Methods

e :: t

Instances

Distinguished ComplexBasis

Distinguished QuaternionBasis

Distinguished DualBasis

Distinguished DualBasis'

Distinguished QuaternionBasis'

Distinguished TrigBasis

Rig r => Distinguished (Complex r)

Rig r => Distinguished (Quaternion r)

Rig r => Distinguished (Dual r)

Rig r => Distinguished (Dual' r)

Rig r => Distinguished (Quaternion' r)

Rig r => Distinguished (Trig r)

Rig r => Distinguished (ComplexBasis -> r)

Rig r => Distinguished (QuaternionBasis -> r)

Rig r => Distinguished (DualBasis -> r)

Rig r => Distinguished (DualBasis' -> r)

Rig r => Distinguished (QuaternionBasis' -> r)

Rig r => Distinguished (TrigBasis -> r)

Distinguished a => Distinguished (Covector r a)

class Distinguished r => Complicated r where

Methods

i :: r

Instances

Complicated ComplexBasis

Complicated QuaternionBasis

Complicated QuaternionBasis'

Complicated TrigBasis

Rig r => Complicated (Complex r)

Rig r => Complicated (Quaternion r)

Rig r => Complicated (Quaternion' r)

Rig r => Complicated (Trig r)

Rig r => Complicated (ComplexBasis -> r)

Rig r => Complicated (QuaternionBasis -> r)

Rig r => Complicated (QuaternionBasis' -> r)

Rig r => Complicated (TrigBasis -> r)

Complicated a => Complicated (Covector r a)

data ComplexBasis

Constructors

E

I

Instances

Bounded ComplexBasis

Enum ComplexBasis

Eq ComplexBasis

Data ComplexBasis

Ord ComplexBasis

Read ComplexBasis

Show ComplexBasis

Ix ComplexBasis

Distinguished ComplexBasis

Complicated ComplexBasis

Typeable * ComplexBasis

MonadReader ComplexBasis Complex

Rng k => Coalgebra k ComplexBasis

Rng k => Algebra k ComplexBasis

Rng k => Bialgebra k ComplexBasis

Rng k => CounitalCoalgebra k ComplexBasis

Rng k => UnitalAlgebra k ComplexBasis

(InvolutiveSemiring k, Rng k) => HopfAlgebra k ComplexBasis

(InvolutiveSemiring k, Rng k) => InvolutiveCoalgebra k ComplexBasis

(InvolutiveSemiring k, Rng k) => InvolutiveAlgebra k ComplexBasis

Rig r => Distinguished (ComplexBasis -> r)

Rig r => Complicated (ComplexBasis -> r)

data Complex a

Constructors

Complex a a

Instances

Monad Complex

Functor Complex

Applicative Complex

Foldable Complex

Traversable Complex

Distributive Complex

Representable Complex

Traversable1 Complex

Foldable1 Complex

Apply Complex

Bind Complex

MonadReader ComplexBasis Complex

RightModule r s => RightModule r (Complex s)

LeftModule r s => LeftModule r (Complex s)

(Commutative r, Rng r, InvolutiveSemiring r) => Quadrance r (Complex r)

Eq a => Eq (Complex a)

Data a => Data (Complex a)

Read a => Read (Complex a)

Show a => Show (Complex a)

Idempotent r => Idempotent (Complex r)

Abelian r => Abelian (Complex r)

Partitionable r => Partitionable (Complex r)

Additive r => Additive (Complex r)

Monoidal r => Monoidal (Complex r)

(Commutative r, Rng r) => Semiring (Complex r)

(Commutative r, Rng r) => Multiplicative (Complex r)

Group r => Group (Complex r)

(Commutative r, Ring r) => Unital (Complex r)

(Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Complex r)

(Commutative r, Ring r) => Rig (Complex r)

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

(TriviallyInvolutive r, Rng r) => Commutative (Complex r)

(Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveSemiring (Complex r)

(Commutative r, Rng r, InvolutiveMultiplication r) => InvolutiveMultiplication (Complex r)

Rig r => Distinguished (Complex r)

Rig r => Complicated (Complex r)

(Commutative r, Rng r) => RightModule (Complex r) (Complex r)

(Commutative r, Rng r) => LeftModule (Complex r) (Complex r)

Typeable (* -> *) Complex

type Rep Complex = ComplexBasis

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

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

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

half of the Cayley-Dickson quaternion isomorphism