algebra-3.1: Constructive abstract algebra

Numeric.Algebra.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' (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 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 (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 Source

Constructors

 Dual a a

Instances