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)

Rig r => Distinguished (:->: ComplexBasis r)

Rig r => Distinguished (:->: QuaternionBasis 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

(Distinguished (Complex r), Rig r) => Complicated (Complex r)

(Distinguished (Quaternion r), Rig r) => Complicated (Quaternion r)

(Distinguished (Quaternion' r), Rig r) => Complicated (Quaternion' r)

(Distinguished (Trig r), Rig r) => Complicated (Trig r)

(Distinguished (ComplexBasis -> r), Rig r) => Complicated (ComplexBasis -> r)

(Distinguished (QuaternionBasis -> r), Rig r) => Complicated (QuaternionBasis -> r)

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

(Distinguished (TrigBasis -> r), Rig r) => Complicated (TrigBasis -> r)

(Distinguished (:->: ComplexBasis r), Rig r) => Complicated (:->: ComplexBasis r)

(Distinguished (:->: QuaternionBasis r), Rig r) => Complicated (:->: QuaternionBasis r)

(Distinguished (:->: QuaternionBasis' r), Rig r) => Complicated (:->: QuaternionBasis' r)

(Distinguished (:->: TrigBasis r), Rig r) => Complicated (:->: TrigBasis r)

(Distinguished (Covector r a), Complicated a) => Complicated (Covector r a)

class Complicated t => Hamiltonian t where

Methods

j :: t

k :: t

Instances

Hamiltonian QuaternionBasis

Hamiltonian QuaternionBasis'

(Complicated (Quaternion r), Rig r) => Hamiltonian (Quaternion r)

(Complicated (Quaternion' r), Rig r) => Hamiltonian (Quaternion' r)

(Complicated (QuaternionBasis -> r), Rig r) => Hamiltonian (QuaternionBasis -> r)

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

(Complicated (:->: QuaternionBasis r), Rig r) => Hamiltonian (:->: QuaternionBasis r)

(Complicated (:->: QuaternionBasis' r), Rig r) => Hamiltonian (:->: QuaternionBasis' r)

(Complicated (Covector r a), 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

Typeable QuaternionBasis

HasTrie QuaternionBasis

Distinguished QuaternionBasis

Complicated QuaternionBasis

Hamiltonian QuaternionBasis

MonadReader QuaternionBasis Quaternion

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

the trivial diagonal coalgebra

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

the quaternion algebra

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

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

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

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

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

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

Rig r => Distinguished (QuaternionBasis -> r)

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

(Distinguished (QuaternionBasis -> r), Rig r) => Complicated (QuaternionBasis -> r)

(Distinguished (:->: QuaternionBasis r), Rig r) => Complicated (:->: QuaternionBasis r)

(Complicated (QuaternionBasis -> r), Rig r) => Hamiltonian (QuaternionBasis -> r)

(Complicated (:->: QuaternionBasis r), Rig r) => Hamiltonian (:->: QuaternionBasis r)

data Quaternion a

Constructors

Quaternion a a a a

Instances

Monad Quaternion

Functor Quaternion

Typeable1 Quaternion

Applicative Quaternion

Foldable Quaternion

Traversable Quaternion

Distributive Quaternion

Keyed Quaternion

Zip Quaternion

ZipWithKey Quaternion

Indexable Quaternion

Lookup Quaternion

Adjustable Quaternion

FoldableWithKey Quaternion

FoldableWithKey1 Quaternion

TraversableWithKey Quaternion

TraversableWithKey1 Quaternion

Representable Quaternion

Traversable1 Quaternion

Foldable1 Quaternion

Apply Quaternion

Bind Quaternion

MonadReader QuaternionBasis Quaternion

(Semiring r, Additive (Quaternion s), RightModule r s) => RightModule r (Quaternion s)

(Semiring r, Additive (Quaternion s), LeftModule r s) => LeftModule r (Quaternion s)

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

Eq a => Eq (Quaternion a)

(Typeable (Quaternion a), Data a) => Data (Quaternion a)

Read a => Read (Quaternion a)

Show a => Show (Quaternion a)

(Additive (Quaternion r), Idempotent r) => Idempotent (Quaternion r)

(Additive (Quaternion r), Abelian r) => Abelian (Quaternion r)

(Additive (Quaternion r), Partitionable r) => Partitionable (Quaternion r)

Additive r => Additive (Quaternion r)

(LeftModule Natural (Quaternion r), RightModule Natural (Quaternion r), Monoidal r) => Monoidal (Quaternion r)

(Additive (Quaternion r), Abelian (Quaternion r), Multiplicative (Quaternion r), TriviallyInvolutive r, Rng r) => Semiring (Quaternion r)

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

(LeftModule Integer (Quaternion r), RightModule Integer (Quaternion r), Monoidal (Quaternion r), Group r) => Group (Quaternion r)

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

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

(Semiring (Quaternion r), Unital (Quaternion r), Monoidal (Quaternion r), TriviallyInvolutive r, Ring r) => Rig (Quaternion r)

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

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

Rig r => Distinguished (Quaternion r)

(Distinguished (Quaternion r), Rig r) => Complicated (Quaternion r)

(Complicated (Quaternion r), Rig r) => Hamiltonian (Quaternion r)

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

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

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

Cayley-Dickson quaternion isomorphism (one way)

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

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