Numeric.Algebra.Quaternion

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)

class Complicated t => Hamiltonian t where

Methods

j :: t

k :: t

Instances

Hamiltonian QuaternionBasis

Hamiltonian QuaternionBasis'

Rig r => Hamiltonian (Quaternion r)

Rig r => Hamiltonian (Quaternion' r)

Rig r => Hamiltonian (QuaternionBasis -> r)

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

Hamiltonian a => Hamiltonian (Covector r a)

data QuaternionBasis

Constructors

E

I

J

K

Instances

Bounded QuaternionBasis

Enum QuaternionBasis

Eq QuaternionBasis

Data QuaternionBasis

Ord QuaternionBasis

Read QuaternionBasis

Show QuaternionBasis

Ix QuaternionBasis

Distinguished QuaternionBasis

Complicated QuaternionBasis

Hamiltonian QuaternionBasis

Typeable * QuaternionBasis

MonadReader QuaternionBasis Quaternion

(TriviallyInvolutive r, Rng r) => Coalgebra r QuaternionBasis

the trivial diagonal coalgebra

(TriviallyInvolutive r, Rng r) => Algebra r QuaternionBasis

the quaternion algebra

(TriviallyInvolutive r, Rng r) => Bialgebra r QuaternionBasis

(TriviallyInvolutive r, Rng r) => CounitalCoalgebra r QuaternionBasis

(TriviallyInvolutive r, Rng r) => UnitalAlgebra r QuaternionBasis

(TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => HopfAlgebra r QuaternionBasis

(TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => InvolutiveCoalgebra r QuaternionBasis

(TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => InvolutiveAlgebra r QuaternionBasis

Rig r => Distinguished (QuaternionBasis -> r)

Rig r => Complicated (QuaternionBasis -> r)

Rig r => Hamiltonian (QuaternionBasis -> r)

data Quaternion a

Constructors

Quaternion a a a a

Instances

Monad Quaternion

Functor Quaternion

Applicative Quaternion

Foldable Quaternion

Traversable Quaternion

Distributive Quaternion

Representable Quaternion

Traversable1 Quaternion

Foldable1 Quaternion

Apply Quaternion

Bind Quaternion

MonadReader QuaternionBasis Quaternion

RightModule r s => RightModule r (Quaternion s)

LeftModule r s => LeftModule r (Quaternion s)

(TriviallyInvolutive r, Rng r) => Quadrance r (Quaternion r)

Eq a => Eq (Quaternion a)

Data a => Data (Quaternion a)

Read a => Read (Quaternion a)

Show a => Show (Quaternion a)

Idempotent r => Idempotent (Quaternion r)

Abelian r => Abelian (Quaternion r)

Partitionable r => Partitionable (Quaternion r)

Additive r => Additive (Quaternion r)

Monoidal r => Monoidal (Quaternion r)

(TriviallyInvolutive r, Rng r) => Semiring (Quaternion r)

(TriviallyInvolutive r, Rng r) => Multiplicative (Quaternion r)

Group r => Group (Quaternion r)

(TriviallyInvolutive r, Ring r) => Unital (Quaternion r)

(TriviallyInvolutive r, Ring r, Division r) => Division (Quaternion r)

(TriviallyInvolutive r, Ring r) => Rig (Quaternion r)

(TriviallyInvolutive r, Ring r) => Ring (Quaternion r)

(TriviallyInvolutive r, Rng r) => InvolutiveMultiplication (Quaternion r)

Rig r => Distinguished (Quaternion r)

Rig r => Complicated (Quaternion r)

Rig r => Hamiltonian (Quaternion r)

(TriviallyInvolutive r, Rng r) => RightModule (Quaternion r) (Quaternion r)

(TriviallyInvolutive r, Rng r) => LeftModule (Quaternion r) (Quaternion r)

Typeable (* -> *) Quaternion

type Rep Quaternion = QuaternionBasis

complicate :: Complicated c => QuaternionBasis -> (c, c)

Cayley-Dickson quaternion isomorphism (one way)

vectorPart :: (Representable f, Rep f ~ QuaternionBasis) => f r -> (r, r, r)

scalarPart :: (Representable f, Rep f ~ QuaternionBasis) => f r -> r