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

Language | Haskell98 |

# Documentation

numerator :: Integral a => Ratio a -> a

Extract the numerator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

denominator :: Integral a => Ratio a -> a

Extract the denominator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

approxRational :: RealFrac a => a -> a -> Rational

`approxRational`

, applied to two real fractional numbers `x`

and `epsilon`

,
returns the simplest rational number within `epsilon`

of `x`

.
A rational number `y`

is said to be *simpler* than another `y'`

if

, and`abs`

(`numerator`

y) <=`abs`

(`numerator`

y')

.`denominator`

y <=`denominator`

y'

Any real interval contains a unique simplest rational;
in particular, note that `0/1`

is the simplest rational of all.