Safe Haskell | None |
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Numeric.Algebra.Dual
- class Distinguished t where
- e :: t
- class Distinguished t => Infinitesimal t where
- d :: t
- data DualBasis
- data Dual a = Dual a a
Documentation
class Distinguished t whereSource
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
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) |
dual number basis, D^2 = 0. D /= 0.
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) |
Constructors
Dual a a |
Instances