Numeric.Algebra.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, Rng 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, Rng 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)