algebra-4.2: Constructive abstract algebra

Numeric.Coalgebra.Dual

Synopsis

# Documentation

class Distinguished t where Source

Methods

e :: t Source

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 Source

Methods

d :: t Source

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' Source

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' Distinguished DualBasis' Infinitesimal DualBasis' Typeable * 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 Source

Constructors

 Dual' a a

Instances

 Monad Dual' Functor 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) Typeable (* -> *) Dual' type Rep Dual' = DualBasis'