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)

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)

data ComplexBasis

Constructors

E

I

Instances

Bounded ComplexBasis

Enum ComplexBasis

Eq ComplexBasis

Data ComplexBasis

Ord ComplexBasis

Read ComplexBasis

Show ComplexBasis

Ix ComplexBasis

Typeable ComplexBasis

HasTrie ComplexBasis

Distinguished ComplexBasis

Complicated ComplexBasis

MonadReader ComplexBasis Complex

(Semiring k, Rng k) => Coalgebra k ComplexBasis

(Semiring k, Rng k) => Algebra k ComplexBasis

(UnitalAlgebra k ComplexBasis, CounitalCoalgebra k ComplexBasis, Rng k) => Bialgebra k ComplexBasis

(Coalgebra k ComplexBasis, Rng k) => CounitalCoalgebra k ComplexBasis

(Algebra k ComplexBasis, Rng k) => UnitalAlgebra k ComplexBasis

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

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

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

Rig r => Distinguished (ComplexBasis -> r)

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

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

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

data Complex a

Constructors

Complex a a

Instances

Monad Complex

Functor Complex

Typeable1 Complex

Applicative Complex

Foldable Complex

Traversable Complex

Distributive Complex

Keyed Complex

Zip Complex

ZipWithKey Complex

Indexable Complex

Lookup Complex

Adjustable Complex

FoldableWithKey Complex

FoldableWithKey1 Complex

TraversableWithKey Complex

TraversableWithKey1 Complex

Representable Complex

Traversable1 Complex

Foldable1 Complex

Apply Complex

Bind Complex

MonadReader ComplexBasis Complex

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

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

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

Eq a => Eq (Complex a)

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

Read a => Read (Complex a)

Show a => Show (Complex a)

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

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

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

Additive r => Additive (Complex r)

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

(Additive (Complex r), Abelian (Complex r), Multiplicative (Complex r), Commutative r, Rng r) => Semiring (Complex r)

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

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

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

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

(Semiring (Complex r), Unital (Complex r), Monoidal (Complex r), Commutative r, Ring r) => Rig (Complex r)

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

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

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

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

Rig r => Distinguished (Complex r)

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

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

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

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

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

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

half of the Cayley-Dickson quaternion isomorphism