algebra-4.1: Constructive abstract algebra

Safe Haskell	None

Numeric.Coalgebra.Hyperbolic

Documentation

class Hyperbolic r whereSource

Methods

cosh :: rSource

sinh :: rSource

Instances

Hyperbolic HyperBasis'
Hyperbolic HyperBasis
Rig r => Hyperbolic (Hyper' r)
Rig r => Hyperbolic (Hyper r)
Rig r => Hyperbolic (HyperBasis' -> r)
Rig r => Hyperbolic (HyperBasis -> r)
Hyperbolic a => Hyperbolic (Covector r a)

data HyperBasis Source

Constructors

Cosh
Sinh

Instances

Bounded HyperBasis
Enum HyperBasis
Eq HyperBasis
Data HyperBasis
Ord HyperBasis
Read HyperBasis
Show HyperBasis
Ix HyperBasis
Typeable HyperBasis
Hyperbolic HyperBasis
MonadReader HyperBasis Hyper
(Commutative k, Semiring k) => Coalgebra k HyperBasis	the hyperbolic trigonometric coalgebra
Semiring k => Algebra k HyperBasis	the trivial diagonal algebra
(Commutative k, Semiring k) => Bialgebra k HyperBasis
(Commutative k, Semiring k) => CounitalCoalgebra k HyperBasis
Semiring k => UnitalAlgebra k HyperBasis
(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis
(Commutative k, Group k, InvolutiveSemiring k) => InvolutiveCoalgebra k HyperBasis
(Commutative k, Group k, InvolutiveSemiring k) => InvolutiveAlgebra k HyperBasis
Rig r => Hyperbolic (HyperBasis -> r)

data Hyper a Source

Constructors

Instances

Monad Hyper
Functor Hyper
Typeable1 Hyper
Applicative Hyper
Foldable Hyper
Traversable Hyper
Distributive Hyper
Representable Hyper
Traversable1 Hyper
Foldable1 Hyper
Apply Hyper
Bind Hyper
MonadReader HyperBasis Hyper
RightModule r s => RightModule r (Hyper s)
LeftModule r s => LeftModule r (Hyper s)
Eq a => Eq (Hyper a)
Data a => Data (Hyper a)
Read a => Read (Hyper a)
Show a => Show (Hyper a)
Idempotent r => Idempotent (Hyper r)
Abelian r => Abelian (Hyper r)
Partitionable r => Partitionable (Hyper r)
Additive r => Additive (Hyper r)
Monoidal r => Monoidal (Hyper r)
(Commutative k, Semiring k) => Semiring (Hyper k)
(Commutative k, Semiring k) => Multiplicative (Hyper k)
Group r => Group (Hyper r)
(Commutative k, Rig k) => Unital (Hyper k)
(Commutative r, Rig r) => Rig (Hyper r)
(Commutative r, Ring r) => Ring (Hyper r)
(Commutative k, Semiring k) => Commutative (Hyper k)
(Commutative r, Group r, InvolutiveSemiring r) => InvolutiveSemiring (Hyper r)
(Commutative r, Group r, InvolutiveSemiring r) => InvolutiveMultiplication (Hyper r)
Rig r => Hyperbolic (Hyper r)
(Commutative r, Semiring r) => RightModule (Hyper r) (Hyper r)
(Commutative r, Semiring r) => LeftModule (Hyper r) (Hyper r)