Data.VectorSpace.Tuples

Vector space instances for small tuples of Fractional.

This module contains RModule, VectorSpace and InnerProductSpace for tuples of up to five elements.

Documentation

Orphan instances

((~) * (Groundfield a) (Groundfield b), InnerProductSpace a, InnerProductSpace b) => InnerProductSpace (a, b)

Inner Product Space instance for tuples.

Methods

dot :: (a, b) -> (a, b) -> Groundfield (a, b)

((~) * (Groundfield a) (Groundfield b), VectorSpace a, VectorSpace b) => VectorSpace (a, b)

Vector-space instance for tuples.

Methods

(^/) :: (a, b) -> Groundfield (a, b) -> (a, b)

((~) * (Groundring a) (Groundring b), RModule a, RModule b) => RModule (a, b)

R-module instance for tuples.

Associated Types

type Groundring (a, b) :: *

Methods

zeroVector :: (a, b)

(*^) :: Groundring (a, b) -> (a, b) -> (a, b)

(^*) :: (a, b) -> Groundring (a, b) -> (a, b)

negateVector :: (a, b) -> (a, b)

(^+^) :: (a, b) -> (a, b) -> (a, b)

(^-^) :: (a, b) -> (a, b) -> (a, b)

Num a => InnerProductSpace (a, a, a)

Inner Product Space instance for tuples with 3 elements.

Methods

dot :: (a, a, a) -> (a, a, a) -> Groundfield (a, a, a)

Fractional a => VectorSpace (a, a, a)

Vector-space instance for tuples with 3 elements.

Methods

(^/) :: (a, a, a) -> Groundfield (a, a, a) -> (a, a, a)

Num a => RModule (a, a, a)

R-module instance for tuples with 3 elements.

Associated Types

type Groundring (a, a, a) :: *

Methods

zeroVector :: (a, a, a)

(*^) :: Groundring (a, a, a) -> (a, a, a) -> (a, a, a)

(^*) :: (a, a, a) -> Groundring (a, a, a) -> (a, a, a)

negateVector :: (a, a, a) -> (a, a, a)

(^+^) :: (a, a, a) -> (a, a, a) -> (a, a, a)

(^-^) :: (a, a, a) -> (a, a, a) -> (a, a, a)

Num a => InnerProductSpace (a, a, a, a)

Inner Product Space instance for tuples with 4 elements.

Methods

dot :: (a, a, a, a) -> (a, a, a, a) -> Groundfield (a, a, a, a)

Fractional a => VectorSpace (a, a, a, a)

Vector-space instance for tuples with 4 elements.

Methods

(^/) :: (a, a, a, a) -> Groundfield (a, a, a, a) -> (a, a, a, a)

Num a => RModule (a, a, a, a)

R-module instance for tuples with 4 elements.

Associated Types

type Groundring (a, a, a, a) :: *

Methods

zeroVector :: (a, a, a, a)

(*^) :: Groundring (a, a, a, a) -> (a, a, a, a) -> (a, a, a, a)

(^*) :: (a, a, a, a) -> Groundring (a, a, a, a) -> (a, a, a, a)

negateVector :: (a, a, a, a) -> (a, a, a, a)

(^+^) :: (a, a, a, a) -> (a, a, a, a) -> (a, a, a, a)

(^-^) :: (a, a, a, a) -> (a, a, a, a) -> (a, a, a, a)

Num a => InnerProductSpace (a, a, a, a, a)

Inner Product Space instance for tuples with 5 elements.

Methods

dot :: (a, a, a, a, a) -> (a, a, a, a, a) -> Groundfield (a, a, a, a, a)

Fractional a => VectorSpace (a, a, a, a, a)

Vector-space instance for tuples with 5 elements.

Methods

(^/) :: (a, a, a, a, a) -> Groundfield (a, a, a, a, a) -> (a, a, a, a, a)

Num a => RModule (a, a, a, a, a)

R-module instance for tuples with 5 elements.

Associated Types

type Groundring (a, a, a, a, a) :: *

Methods

zeroVector :: (a, a, a, a, a)

(*^) :: Groundring (a, a, a, a, a) -> (a, a, a, a, a) -> (a, a, a, a, a)

(^*) :: (a, a, a, a, a) -> Groundring (a, a, a, a, a) -> (a, a, a, a, a)

negateVector :: (a, a, a, a, a) -> (a, a, a, a, a)

(^+^) :: (a, a, a, a, a) -> (a, a, a, a, a) -> (a, a, a, a, a)

(^-^) :: (a, a, a, a, a) -> (a, a, a, a, a) -> (a, a, a, a, a)