Numeric.Coalgebra.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'

Semiring k => Algebra k DualBasis'

Rng k => Bialgebra k DualBasis'

Rng k => CounitalCoalgebra k DualBasis'

Semiring 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)