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)

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 where

Methods

d :: t

Instances

Infinitesimal DualBasis

Infinitesimal DualBasis'

(Distinguished (Dual r), Rig r) => Infinitesimal (Dual r)

(Distinguished (Dual' r), Rig r) => Infinitesimal (Dual' r)

(Distinguished (DualBasis -> r), Rig r) => Infinitesimal (DualBasis -> r)

(Distinguished (DualBasis' -> r), Rig r) => Infinitesimal (DualBasis' -> r)

(Distinguished (Covector r a), 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'

HasTrie DualBasis'

Distinguished DualBasis'

Infinitesimal DualBasis'

MonadReader DualBasis' Dual'

(Semiring k, Rng k) => Coalgebra k DualBasis'

Semiring k => Algebra k DualBasis'

(UnitalAlgebra k DualBasis', CounitalCoalgebra k DualBasis', Rng k) => Bialgebra k DualBasis'

(Coalgebra k DualBasis', Rng k) => CounitalCoalgebra k DualBasis'

(Algebra k DualBasis', Semiring k) => UnitalAlgebra k DualBasis'

(Bialgebra k DualBasis', InvolutiveSemiring k, Rng k) => HopfAlgebra k DualBasis'

(Coalgebra k DualBasis', InvolutiveSemiring k, Rng k) => InvolutiveCoalgebra k DualBasis'

(Algebra k DualBasis', InvolutiveSemiring k, Rng k) => InvolutiveAlgebra k DualBasis'

Rig r => Distinguished (DualBasis' -> 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'

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'

(Semiring r, Additive (Dual' s), RightModule r s) => RightModule r (Dual' s)

(Semiring r, Additive (Dual' s), LeftModule r s) => LeftModule r (Dual' s)

(Additive r, Commutative r, Rng r, InvolutiveSemiring r) => Quadrance r (Dual' r)

Eq a => Eq (Dual' a)

(Typeable (Dual' a), Data a) => Data (Dual' a)

Read a => Read (Dual' a)

Show a => Show (Dual' a)

(Additive (Dual' r), Idempotent r) => Idempotent (Dual' r)

(Additive (Dual' r), Abelian r) => Abelian (Dual' r)

(Additive (Dual' r), Partitionable r) => Partitionable (Dual' r)

Additive r => Additive (Dual' r)

(LeftModule Natural (Dual' r), RightModule Natural (Dual' r), Monoidal r) => Monoidal (Dual' r)

(Additive (Dual' r), Abelian (Dual' r), Multiplicative (Dual' r), Commutative r, Rng r) => Semiring (Dual' r)

(Commutative r, Rng r) => Multiplicative (Dual' r)

(LeftModule Integer (Dual' r), RightModule Integer (Dual' r), Monoidal (Dual' r), Group r) => Group (Dual' r)

(Multiplicative (Dual' r), Commutative r, Ring r) => Unital (Dual' r)

(Unital (Dual' r), Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Dual' r)

(Semiring (Dual' r), Unital (Dual' r), Monoidal (Dual' r), Commutative r, Ring r) => Rig (Dual' r)

(Rig (Dual' r), Rng (Dual' r), Commutative r, Ring r) => Ring (Dual' r)

(Multiplicative (Dual' r), TriviallyInvolutive r, Rng r) => Commutative (Dual' r)

(Semiring (Dual' r), InvolutiveMultiplication (Dual' r), Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveSemiring (Dual' r)

(Multiplicative (Dual' r), Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveMultiplication (Dual' r)

Rig r => Distinguished (Dual' r)

(Distinguished (Dual' r), Rig r) => Infinitesimal (Dual' r)

(Semiring (Dual' r), Additive (Dual' r), Commutative r, Rng r) => RightModule (Dual' r) (Dual' r)

(Semiring (Dual' r), Additive (Dual' r), Commutative r, Rng r) => LeftModule (Dual' r) (Dual' r)