Algebra.Morphism.Ratio

Documentation

divZeroError :: a

ratioZeroDenominatorError :: a

overflowError :: a

underflowError :: a

data Ratio a

Constructors

!a :% !a

Instances

Show a => Show (Ratio a)

instance (Integral a) => Real (Ratio a) where {-# SPECIALIZE instance Real Rational #-} toRational (x:%y) = toInteger x :% toInteger y

Since: 2.0.1

Defined in Algebra.Morphism.Ratio

Methods

showsPrec :: Int -> Ratio a -> ShowS

show :: Ratio a -> String

showList :: [Ratio a] -> ShowS

EuclideanDomain a => AbelianAdditive (Ratio a)

Defined in Algebra.Morphism.Ratio

EuclideanDomain a => Additive (Ratio a)

Since: 2.0.1

Defined in Algebra.Morphism.Ratio

Methods

(+) :: Ratio a -> Ratio a -> Ratio a

zero :: Ratio a

times :: Natural -> Ratio a -> Ratio a

EuclideanDomain a => Division (Ratio a)

Since: 2.0.1

Defined in Algebra.Morphism.Ratio

Methods

recip :: Ratio a -> Ratio a

(/) :: Ratio a -> Ratio a -> Ratio a

(^) :: Ratio a -> Integer -> Ratio a

EuclideanDomain a => Field (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

fromRational :: Rational -> Ratio a

EuclideanDomain a => Group (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

(-) :: Ratio a -> Ratio a -> Ratio a

subtract :: Ratio a -> Ratio a -> Ratio a

negate :: Ratio a -> Ratio a

mult :: Integer -> Ratio a -> Ratio a

EuclideanDomain a => Multiplicative (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

(*) :: Ratio a -> Ratio a -> Ratio a

one :: Ratio a

(^+) :: Ratio a -> Natural -> Ratio a

EuclideanDomain a => Ring (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

fromInteger :: Integer -> Ratio a

Eq a => Eq (Ratio a)

Since: 2.1

Defined in Algebra.Morphism.Ratio

Methods

(==) :: Ratio a -> Ratio a -> Bool

(/=) :: Ratio a -> Ratio a -> Bool

Integral a => Ord (Ratio a)

Since: 2.0.1

Defined in Algebra.Morphism.Ratio

Methods

compare :: Ratio a -> Ratio a -> Ordering

(<) :: Ratio a -> Ratio a -> Bool

(<=) :: Ratio a -> Ratio a -> Bool

(>) :: Ratio a -> Ratio a -> Bool

(>=) :: Ratio a -> Ratio a -> Bool

max :: Ratio a -> Ratio a -> Ratio a

min :: Ratio a -> Ratio a -> Ratio a

EuclideanDomain a => Scalable (Ratio a) (Ratio a)

Defined in Algebra.Morphism.Ratio

Methods

(*^) :: Ratio a -> Ratio a -> Ratio a

type Rational = Ratio Integer

reduce :: EuclideanDomain a => a -> a -> Ratio a

reduce is a subsidiary function used only in this module. It normalises a ratio by dividing both numerator and denominator by their greatest common divisor.

(%) :: EuclideanDomain a => a -> a -> Ratio a

ratioPrec :: Int

ratioPrec1 :: Int