Data.Ratio

Standard functions on rational numbers

Documentation

data Ratio a

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

Instances

Typeable1 Ratio

Integral a ⇒ Enum (Ratio a)

Eq a ⇒ Eq (Ratio a)

Integral a ⇒ Fractional (Ratio a)

(Data a, Integral a) ⇒ Data (Ratio a)

Integral a ⇒ Num (Ratio a)

Integral a ⇒ Ord (Ratio a)

(Integral a, Read a) ⇒ Read (Ratio a)

Integral a ⇒ Real (Ratio a)

Integral a ⇒ RealFrac (Ratio a)

(Integral a, Show a) ⇒ Show (Ratio a)

Typeable (★ → ★) Ratio

type Rational = Ratio Integer

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

(%) ∷ Integral a ⇒ a → a → Ratio a infixl 7

Forms the ratio of two integral numbers.

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

• 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.