Data.Ratio

Rational numbers, with numerator and denominator of some Integral type.

Note that Ratio's instances inherit the deficiencies from the type parameter's. For example, Ratio Natural's Num instance has similar problems to Numeric.Natural.Natural's.

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

• abs (numerator y) <= abs (numerator y'), and

• denominator y <= denominator y'.

Any real interval contains a unique simplest rational; in particular, note that 0/1 is the simplest rational of all.

Forms the ratio of two integral numbers.

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

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

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.