algebra-2.1: Constructive abstract algebra

Numeric.Coalgebra.Dual

Synopsis

# Documentation

class Distinguished t whereSource

Methods

e :: tSource

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 t => Infinitesimal t whereSource

Methods

d :: tSource

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' Typeable DualBasis' HasTrie 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 Source

Constructors

 Dual' a a

Instances

 Monad Dual' Functor Dual' Typeable1 Dual' Applicative Dual' Foldable Dual' Traversable Dual' Distributive Dual' Keyed Dual' Zip Dual' ZipWithKey Dual' Indexable Dual' Lookup Dual' Adjustable Dual' FoldableWithKey Dual' FoldableWithKey1 Dual' TraversableWithKey Dual' TraversableWithKey1 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)