Data.VectorSpace.Free

Documentation

class AdditiveGroup (Diff p) => AffineSpace p where

Associated Types

type Diff p :: *

Methods

(.-.) :: p -> p -> Diff p

(.+^) :: p -> Diff p -> p

Instances

AffineSpace Double

AffineSpace Float

AffineSpace Int

AffineSpace Integer

AffineSpace CSChar

AffineSpace CShort

AffineSpace CInt

AffineSpace CLong

AffineSpace CLLong

AffineSpace CFloat

AffineSpace CDouble

AffineSpace CIntMax

Integral a => AffineSpace (Ratio a)

AffineSpace p => AffineSpace (a -> p)

(AffineSpace p, AffineSpace q) => AffineSpace (p, q)

(AffineSpace p, AffineSpace q, AffineSpace r) => AffineSpace (p, q, r)

class AdditiveGroup v where

Minimal complete definition

zeroV, (^+^), negateV

Methods

zeroV :: v

(^+^) :: v -> v -> v

negateV :: v -> v

(^-^) :: v -> v -> v

Instances

AdditiveGroup Double

AdditiveGroup Float

AdditiveGroup Int

AdditiveGroup Integer

AdditiveGroup ()

AdditiveGroup CSChar

AdditiveGroup CShort

AdditiveGroup CInt

AdditiveGroup CLong

AdditiveGroup CLLong

AdditiveGroup CFloat

AdditiveGroup CDouble

AdditiveGroup CIntMax

Integral a => AdditiveGroup (Ratio a)

(RealFloat v, AdditiveGroup v) => AdditiveGroup (Complex v)

AdditiveGroup a => AdditiveGroup (Maybe a)

AdditiveGroup a => AdditiveGroup (Sum a)

AdditiveGroup v => AdditiveGroup (a -> v)

(AdditiveGroup u, AdditiveGroup v) => AdditiveGroup (u, v)

(HasTrie u, AdditiveGroup v) => AdditiveGroup ((:->:) u v)

(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w) => AdditiveGroup (u, v, w)

(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w, AdditiveGroup x) => AdditiveGroup (u, v, w, x)

class AdditiveGroup v => VectorSpace v where

Associated Types

type Scalar v :: *

Methods

(*^) :: Scalar v -> v -> v

Instances

VectorSpace Double

VectorSpace Float

VectorSpace Int

VectorSpace Integer

VectorSpace CSChar

VectorSpace CShort

VectorSpace CInt

VectorSpace CLong

VectorSpace CLLong

VectorSpace CFloat

VectorSpace CDouble

VectorSpace CIntMax

Integral a => VectorSpace (Ratio a)

(RealFloat v, VectorSpace v) => VectorSpace (Complex v)

VectorSpace v => VectorSpace (Maybe v)

VectorSpace v => VectorSpace (a -> v)

(VectorSpace u, (~) * s (Scalar u), VectorSpace v, (~) * s (Scalar v)) => VectorSpace (u, v)

(HasTrie a, VectorSpace v) => VectorSpace ((:->:) a v)

(VectorSpace u, (~) * s (Scalar u), VectorSpace v, (~) * s (Scalar v), VectorSpace w, (~) * s (Scalar w)) => VectorSpace (u, v, w)

(VectorSpace u, (~) * s (Scalar u), VectorSpace v, (~) * s (Scalar v), VectorSpace w, (~) * s (Scalar w), VectorSpace x, (~) * s (Scalar x)) => VectorSpace (u, v, w, x)

class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v where

Methods

(<.>) :: v -> v -> Scalar v

Instances

InnerSpace Double

InnerSpace Float

InnerSpace Int

InnerSpace Integer

InnerSpace CSChar

InnerSpace CShort

InnerSpace CInt

InnerSpace CLong

InnerSpace CLLong

InnerSpace CFloat

InnerSpace CDouble

InnerSpace CIntMax

Integral a => InnerSpace (Ratio a)

(RealFloat v, InnerSpace v) => InnerSpace (Complex v)

InnerSpace a => InnerSpace (Maybe a)

InnerSpace v => InnerSpace (a -> v)

(InnerSpace u, (~) * s (Scalar u), InnerSpace v, (~) * s (Scalar v)) => InnerSpace (u, v)

(InnerSpace u, (~) * s (Scalar u), InnerSpace v, (~) * s (Scalar v), InnerSpace w, (~) * s (Scalar w)) => InnerSpace (u, v, w)

(InnerSpace u, (~) * s (Scalar u), InnerSpace v, (~) * s (Scalar v), InnerSpace w, (~) * s (Scalar w), InnerSpace x, (~) * s (Scalar x)) => InnerSpace (u, v, w, x)