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

Typeable HyperBasis

HasTrie 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

(UnitalAlgebra k HyperBasis, CounitalCoalgebra k HyperBasis, Commutative k, Semiring k) => Bialgebra k HyperBasis

(Coalgebra k HyperBasis, Commutative k, Semiring k) => CounitalCoalgebra k HyperBasis

(Algebra k HyperBasis, Semiring k) => UnitalAlgebra k HyperBasis

(Bialgebra k HyperBasis, Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis

(Coalgebra k HyperBasis, Commutative k, Group k, InvolutiveSemiring k) => InvolutiveCoalgebra k HyperBasis

(Algebra 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

Typeable1 Hyper

Applicative Hyper

Foldable Hyper

Traversable Hyper

Distributive Hyper

Keyed Hyper

Zip Hyper

ZipWithKey Hyper

Indexable Hyper

Lookup Hyper

Adjustable Hyper

FoldableWithKey Hyper

FoldableWithKey1 Hyper

TraversableWithKey Hyper

TraversableWithKey1 Hyper

Representable Hyper

Traversable1 Hyper

Foldable1 Hyper

Apply Hyper

Bind Hyper

MonadReader HyperBasis Hyper

(Semiring r, Additive (Hyper s), RightModule r s) => RightModule r (Hyper s)

(Semiring r, Additive (Hyper s), LeftModule r s) => LeftModule r (Hyper s)

Eq a => Eq (Hyper a)

(Typeable (Hyper a), Data a) => Data (Hyper a)

Read a => Read (Hyper a)

Show a => Show (Hyper a)

(Additive (Hyper r), Idempotent r) => Idempotent (Hyper r)

(Additive (Hyper r), Abelian r) => Abelian (Hyper r)

(Additive (Hyper r), Partitionable r) => Partitionable (Hyper r)

Additive r => Additive (Hyper r)

(LeftModule Natural (Hyper r), RightModule Natural (Hyper r), Monoidal r) => Monoidal (Hyper r)

(Additive (Hyper k), Abelian (Hyper k), Multiplicative (Hyper k), Commutative k, Semiring k) => Semiring (Hyper k)

(Commutative k, Semiring k) => Multiplicative (Hyper k)

(LeftModule Integer (Hyper r), RightModule Integer (Hyper r), Monoidal (Hyper r), Group r) => Group (Hyper r)

(Multiplicative (Hyper k), Commutative k, Rig k) => Unital (Hyper k)

(Semiring (Hyper r), Unital (Hyper r), Monoidal (Hyper r), Commutative r, Rig r) => Rig (Hyper r)

(Rig (Hyper r), Rng (Hyper r), Commutative r, Ring r) => Ring (Hyper r)

(Multiplicative (Hyper k), Commutative k, Semiring k) => Commutative (Hyper k)

(Semiring (Hyper r), InvolutiveMultiplication (Hyper r), Commutative r, Group r, InvolutiveSemiring r) => InvolutiveSemiring (Hyper r)

(Multiplicative (Hyper r), Commutative r, Group r, InvolutiveSemiring r) => InvolutiveMultiplication (Hyper r)

Rig r => Hyperbolic (Hyper r)

(Semiring (Hyper r), Additive (Hyper r), Commutative r, Semiring r) => RightModule (Hyper r) (Hyper r)

(Semiring (Hyper r), Additive (Hyper r), Commutative r, Semiring r) => LeftModule (Hyper r) (Hyper r)