Safe Haskell | Safe |
---|---|

Language | Haskell2010 |

Metric classes

- class MultiplicativeUnital a => Signed a where
- class Normed a b where
- class Metric a b where
- class AdditiveGroup a => Epsilon a where
- (≈) :: Epsilon a => a -> a -> Bool

# Documentation

class MultiplicativeUnital a => Signed a where Source #

`signum`

from base is not an operator replicated in numhask, being such a very silly name, and preferred is the much more obvious `sign`

. Compare with `Norm`

and `Banach`

where there is a change in codomain

abs a * sign a == a

Generalising this class tends towards size and direction (abs is the size on the one-dim number line of a vector with its tail at zero, and sign is the direction, right?).

class Metric a b where Source #

distance between numbers

distance a b >= zero distance a a == zero \a b c -> distance a c + distance b c - distance a b >= zero && distance a b + distance b c - distance a c >= zero && distance a b + distance a c - distance b c >= zero &&

class AdditiveGroup a => Epsilon a where Source #

todo: This should probably be split off into some sort of alternative Equality logic, but to what end?