algebra-4.2: Constructive abstract algebra

Numeric.Algebra.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 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 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