algebra-4.2: Constructive abstract algebra

Safe HaskellNone
LanguageHaskell98

Numeric.Coalgebra.Dual

Synopsis

Documentation

class Distinguished t where Source

Methods

e :: t Source

Instances

class Distinguished t => Infinitesimal t where Source

Methods

d :: t Source

Instances

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'