Safe Haskell	None

Numeric.Coalgebra.Quaternion

Synopsis

Documentation

class Distinguished t whereSource

Methods

e :: tSource

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 whereSource

Methods

i :: rSource

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 whereSource

Methods

j :: tSource

k :: tSource

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' Source

Constructors

E'
I'
J'
K'

Instances

Bounded QuaternionBasis'
Enum QuaternionBasis'
Eq QuaternionBasis'
Data QuaternionBasis'
Ord QuaternionBasis'
Read QuaternionBasis'
Show QuaternionBasis'
Ix QuaternionBasis'
Typeable QuaternionBasis'
Distinguished QuaternionBasis'
Complicated QuaternionBasis'
Hamiltonian QuaternionBasis'
MonadReader QuaternionBasis' Quaternion'
(TriviallyInvolutive r, Rng r) => Coalgebra r QuaternionBasis'	dual quaternion comultiplication
(TriviallyInvolutive r, Semiring r) => Algebra r QuaternionBasis'	the trivial diagonal algebra
(TriviallyInvolutive r, Rng r) => Bialgebra r QuaternionBasis'
(TriviallyInvolutive r, Rng r) => CounitalCoalgebra r QuaternionBasis'
(TriviallyInvolutive r, Semiring 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 Source

Constructors

Quaternion' a a a a

Instances

Monad Quaternion'
Functor Quaternion'
Typeable1 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, Semiring r) => Semiring (Quaternion' r)
(TriviallyInvolutive r, Semiring 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)

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

Cayley-Dickson quaternion isomorphism (one way)

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

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