Numeric.Algebra.Dual

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 t => Infinitesimal t where

Methods

d :: t

Instances

Infinitesimal DualBasis

Infinitesimal DualBasis'

Rig r => Infinitesimal (Dual r)

Rig r => Infinitesimal (Dual' r)

Rig r => Infinitesimal (DualBasis -> r)

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

Infinitesimal a => Infinitesimal (Covector r a)

data DualBasis

dual number basis, D^2 = 0. D /= 0.

Constructors

E

D

Instances

Bounded DualBasis

Enum DualBasis

Eq DualBasis

Data DualBasis

Ord DualBasis

Read DualBasis

Show DualBasis

Ix DualBasis

Typeable DualBasis

Distinguished DualBasis

Infinitesimal DualBasis

MonadReader DualBasis Dual

Rng k => Coalgebra k DualBasis

Rng k => Algebra k DualBasis

Rng k => Bialgebra k DualBasis

Rng k => CounitalCoalgebra k DualBasis

Rng k => UnitalAlgebra k DualBasis

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

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

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

Rig r => Distinguished (DualBasis -> r)

Rig r => Infinitesimal (DualBasis -> r)

data Dual a

Constructors

Dual a a

Instances

Monad Dual

Functor Dual

Typeable1 Dual

Applicative Dual

Foldable Dual

Traversable Dual

Distributive Dual

Representable Dual

Traversable1 Dual

Foldable1 Dual

Apply Dual

Bind Dual

MonadReader DualBasis Dual

RightModule r s => RightModule r (Dual s)

LeftModule r s => LeftModule r (Dual s)

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

Eq a => Eq (Dual a)

Data a => Data (Dual a)

Read a => Read (Dual a)

Show a => Show (Dual a)

Idempotent r => Idempotent (Dual r)

Abelian r => Abelian (Dual r)

Partitionable r => Partitionable (Dual r)

Additive r => Additive (Dual r)

Monoidal r => Monoidal (Dual r)

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

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

Group r => Group (Dual r)

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

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

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

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

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

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

(Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveMultiplication (Dual r)

Rig r => Distinguished (Dual r)

Rig r => Infinitesimal (Dual r)

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

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