Safe Haskell	Safe-Inferred
Language	Haskell2010

Algebra.Morphism.Ratio

Synopsis

divZeroError :: a
ratioZeroDenominatorError :: a
overflowError :: a
underflowError :: a
data Ratio a = !a :% !a
type Rational = Ratio Integer
reduce :: EuclideanDomain a => a -> a -> Ratio a
(%) :: EuclideanDomain a => a -> a -> Ratio a
ratioPrec :: Int
ratioPrec1 :: Int

Documentation

divZeroError :: a Source #

ratioZeroDenominatorError :: a Source #

overflowError :: a Source #

underflowError :: a Source #

data Ratio a Source #

Constructors

!a :% !a

Instances

Instances details

Show a => Show (Ratio a) Source #	instance (Integral a) => Real (Ratio a) where {-# SPECIALIZE instance Real Rational #-} toRational (x:%y) = toInteger x :% toInteger y Since: 2.0.1
Instance details Defined in Algebra.Morphism.Ratio Methods showsPrec :: Int -> Ratio a -> ShowS # show :: Ratio a -> String # showList :: [Ratio a] -> ShowS #
EuclideanDomain a => AbelianAdditive (Ratio a) Source #
Instance details Defined in Algebra.Morphism.Ratio
EuclideanDomain a => Additive (Ratio a) Source #	Since: 2.0.1
Instance details Defined in Algebra.Morphism.Ratio Methods (+) :: Ratio a -> Ratio a -> Ratio a Source # zero :: Ratio a Source # times :: Natural -> Ratio a -> Ratio a Source #
EuclideanDomain a => Division (Ratio a) Source #	Since: 2.0.1
Instance details Defined in Algebra.Morphism.Ratio Methods recip :: Ratio a -> Ratio a Source # (/) :: Ratio a -> Ratio a -> Ratio a Source # (^) :: Ratio a -> Integer -> Ratio a Source #
EuclideanDomain a => Field (Ratio a) Source #
Instance details Defined in Algebra.Morphism.Ratio Methods fromRational :: Rational -> Ratio a Source #
EuclideanDomain a => Group (Ratio a) Source #
Instance details Defined in Algebra.Morphism.Ratio Methods (-) :: Ratio a -> Ratio a -> Ratio a Source # subtract :: Ratio a -> Ratio a -> Ratio a Source # negate :: Ratio a -> Ratio a Source # mult :: Integer -> Ratio a -> Ratio a Source #
EuclideanDomain a => Multiplicative (Ratio a) Source #
Instance details Defined in Algebra.Morphism.Ratio Methods (*) :: Ratio a -> Ratio a -> Ratio a Source # one :: Ratio a Source # (^+) :: Ratio a -> Natural -> Ratio a Source #
EuclideanDomain a => Ring (Ratio a) Source #
Instance details Defined in Algebra.Morphism.Ratio Methods fromInteger :: Integer -> Ratio a Source #
Eq a => Eq (Ratio a) Source #	Since: 2.1
Instance details Defined in Algebra.Morphism.Ratio Methods (==) :: Ratio a -> Ratio a -> Bool # (/=) :: Ratio a -> Ratio a -> Bool #
Integral a => Ord (Ratio a) Source #	Since: 2.0.1
Instance details 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) Source #
Instance details Defined in Algebra.Morphism.Ratio Methods (*^) :: Ratio a -> Ratio a -> Ratio a Source #

type Rational = Ratio Integer Source #

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

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 Source #

ratioPrec :: Int Source #

ratioPrec1 :: Int Source #