Safe Haskell	None

Numeric.Algebra.Dual

Synopsis

Documentation

Methods

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)

Methods

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)

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
Distinguished DualBasis
Infinitesimal 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)

Constructors

Instances

Monad Dual
Functor Dual
Typeable1 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)