|Maintainer||Edward Kmett <firstname.lastname@example.org>|
Operations on free vector spaces.
- class Bind f => Additive f where
- negated :: (Functor f, Num a) => f a -> f a
- (^*) :: (Functor f, Num a) => f a -> a -> f a
- (*^) :: (Functor f, Num a) => a -> f a -> f a
- (^/) :: (Functor f, Fractional a) => f a -> a -> f a
- basis :: (Applicative t, Traversable t, Num a) => [t a]
- basisFor :: (Traversable t, Enum a, Num a) => t a -> [t a]
A vector is an additive group with additional structure.
The zero vector
Compute the sum of two vectors
V2 1 2 ^+^ V2 3 4V2 4 6
Compute the difference between two vectors
V2 4 5 - V2 3 1V2 1 4
Linearly interpolate between two vectors.
Compute the negation of a vector
negated (V2 2 4)V2 (-2) (-4)
Compute the right scalar product
V2 3 4 ^* 2V2 6 8
Compute the left scalar product
2 *^ V2 3 4V2 6 8
Compute division by a scalar on the right.
Produce a default basis for a vector space. If the dimensionality
of the vector space is not statically known, see