Numeric.Covector

Documentation

newtype Covector r a

Linear functionals from elements of an (infinite) free module to a scalar

Constructors

Covector

Fields

($*) :: (a -> r) -> r

Instances

RightModule r s => RightModule r (Covector s m)

LeftModule r s => LeftModule r (Covector s m)

Monoidal r => Alternative (Covector r)

Monad (Covector r)

Functor (Covector r)

Monoidal r => MonadPlus (Covector r)

Applicative (Covector r)

Monoidal r => Plus (Covector r)

Additive r => Alt (Covector r)

Apply (Covector r)

Bind (Covector r)

Idempotent r => Idempotent (Covector r a)

Abelian s => Abelian (Covector s a)

Additive r => Additive (Covector r a)

Monoidal s => Monoidal (Covector s a)

Coalgebra r m => Semiring (Covector r m)

Coalgebra r m => Multiplicative (Covector r m)

Group s => Group (Covector s a)

CounitalCoalgebra r m => Unital (Covector r m)

(Idempotent r, IdempotentCoalgebra r a) => Band (Covector r a)

(Rig r, CounitalCoalgebra r m) => Rig (Covector r m)

(Ring r, CounitalCoalgebra r m) => Ring (Covector r m)

(Commutative m, Coalgebra r m) => Commutative (Covector r m)

Distinguished a => Distinguished (Covector r a)

Complicated a => Complicated (Covector r a)

Hamiltonian a => Hamiltonian (Covector r a)

Infinitesimal a => Infinitesimal (Covector r a)

Hyperbolic a => Hyperbolic (Covector r a)

Trigonometric a => Trigonometric (Covector r a)

Coalgebra r m => RightModule (Covector r m) (Covector r m)

Coalgebra r m => LeftModule (Covector r m) (Covector r m)

Covectors as linear functionals

counitM :: UnitalAlgebra r a => a -> Covector r ()

unitM :: CounitalCoalgebra r c => Covector r c

comultM :: Algebra r a => a -> Covector r (a, a)

multM :: Coalgebra r c => c -> c -> Covector r c

invM :: InvolutiveAlgebra r h => h -> Covector r h

coinvM :: InvolutiveCoalgebra r h => h -> Covector r h

antipodeM :: HopfAlgebra r h => h -> Covector r h

convolveM antipodeM return = convolveM return antipodeM = comultM >=> uncurry joinM

convolveM :: (Algebra r c, Coalgebra r a) => (c -> Covector r a) -> (c -> Covector r a) -> c -> Covector r a