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# Documentation

class Applicative f => Metric f whereSource

A free inner product/metric space

dot :: Num a => f a -> f a -> aSource

Compute the inner product of two vectors or (equivalently)
convert a vector `f a`

into a covector `f a -> a`

.

quadrance :: Num a => f a -> aSource

Compute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.

qd :: Num a => f a -> f a -> aSource

Compute the quadrance of the difference

distance :: Floating a => f a -> f a -> aSource

Compute the distance between two vectors in a metric space

norm :: Floating a => f a -> aSource

Compute the norm of a vector in a metric space

signorm :: Floating a => f a -> f aSource

Convert a non-zero vector to unit vector.