Numeric.Coalgebra.Hyperbolic

Documentation

class Hyperbolic r where

Methods

cosh :: r

sinh :: r

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

Constructors

Cosh

Sinh

Instances

Bounded HyperBasis

Enum HyperBasis

Eq HyperBasis

Data HyperBasis

Ord HyperBasis

Read HyperBasis

Show HyperBasis

Ix HyperBasis

Hyperbolic HyperBasis

Typeable * 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

Constructors

Hyper a a

Instances

Monad Hyper

Functor 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)

Typeable (* -> *) Hyper

type Rep Hyper = HyperBasis