Numeric.MixedTypes.Field

Field

type CanAddSubMulDivCNBy t s = (CanAddSubMulBy t s, CanAddSubMulBy (EnsureCN t) s, CanDivCNBy t s)

class (Ring t, CanDivCNSameType t, CanRecipCNSameType t, CanAddSubMulDivCNBy t Rational, CanAddSubMulDivCNBy t Integer, CanAddSubMulDivCNBy t Int) => Field t

Instances

Field Rational

Field (CN Rational)

class (Field t, OrderedRing t, HasOrder t Rational, HasOrder (EnsureCN t) Rational) => OrderedField t

Instances

OrderedField Rational

OrderedField (CN Rational)

class (Field t, OrderedCertainlyRing t, HasOrderCertainly t Rational, HasOrderCertainly (EnsureCN t) Rational) => OrderedCertainlyField t

Instances

OrderedCertainlyField Rational

OrderedCertainlyField (CN Rational)

Division

class CanDiv t1 t2 where

A replacement for Prelude's binary /. If t1 = t2 and Fractional t1, then one can use the default implementation to mirror Prelude's /.

Minimal complete definition

divideNoCN

Associated Types

type DivTypeNoCN t1 t2

type DivType t1 t2

Methods

divideNoCN :: t1 -> t2 -> DivTypeNoCN t1 t2

divide :: t1 -> t2 -> DivType t1 t2

divide :: (CanTestZero t2, CanEnsureCN (DivTypeNoCN t1 t2), DivType t1 t2 ~ EnsureCN (DivTypeNoCN t1 t2)) => t1 -> t2 -> DivType t1 t2

Instances

CanDiv Double Double

Associated Types

type DivTypeNoCN Double Double :: *

type DivType Double Double :: *

Methods

divideNoCN :: Double -> Double -> DivTypeNoCN Double Double

divide :: Double -> Double -> DivType Double Double

CanDiv Double Int

Associated Types

type DivTypeNoCN Double Int :: *

type DivType Double Int :: *

Methods

divideNoCN :: Double -> Int -> DivTypeNoCN Double Int

divide :: Double -> Int -> DivType Double Int

CanDiv Double Integer

Associated Types

type DivTypeNoCN Double Integer :: *

type DivType Double Integer :: *

Methods

divideNoCN :: Double -> Integer -> DivTypeNoCN Double Integer

divide :: Double -> Integer -> DivType Double Integer

CanDiv Double Rational

Associated Types

type DivTypeNoCN Double Rational :: *

type DivType Double Rational :: *

Methods

divideNoCN :: Double -> Rational -> DivTypeNoCN Double Rational

divide :: Double -> Rational -> DivType Double Rational

CanDiv Int Double

Associated Types

type DivTypeNoCN Int Double :: *

type DivType Int Double :: *

Methods

divideNoCN :: Int -> Double -> DivTypeNoCN Int Double

divide :: Int -> Double -> DivType Int Double

CanDiv Int Int

Associated Types

type DivTypeNoCN Int Int :: *

type DivType Int Int :: *

Methods

divideNoCN :: Int -> Int -> DivTypeNoCN Int Int

divide :: Int -> Int -> DivType Int Int

CanDiv Int Integer

Associated Types

type DivTypeNoCN Int Integer :: *

type DivType Int Integer :: *

Methods

divideNoCN :: Int -> Integer -> DivTypeNoCN Int Integer

divide :: Int -> Integer -> DivType Int Integer

CanDiv Int Rational

Associated Types

type DivTypeNoCN Int Rational :: *

type DivType Int Rational :: *

Methods

divideNoCN :: Int -> Rational -> DivTypeNoCN Int Rational

divide :: Int -> Rational -> DivType Int Rational

CanDiv Integer Double

Associated Types

type DivTypeNoCN Integer Double :: *

type DivType Integer Double :: *

Methods

divideNoCN :: Integer -> Double -> DivTypeNoCN Integer Double

divide :: Integer -> Double -> DivType Integer Double

CanDiv Integer Int

Associated Types

type DivTypeNoCN Integer Int :: *

type DivType Integer Int :: *

Methods

divideNoCN :: Integer -> Int -> DivTypeNoCN Integer Int

divide :: Integer -> Int -> DivType Integer Int

CanDiv Integer Integer

Associated Types

type DivTypeNoCN Integer Integer :: *

type DivType Integer Integer :: *

Methods

divideNoCN :: Integer -> Integer -> DivTypeNoCN Integer Integer

divide :: Integer -> Integer -> DivType Integer Integer

CanDiv Integer Rational

Associated Types

type DivTypeNoCN Integer Rational :: *

type DivType Integer Rational :: *

Methods

divideNoCN :: Integer -> Rational -> DivTypeNoCN Integer Rational

divide :: Integer -> Rational -> DivType Integer Rational

CanDiv Rational Double

Associated Types

type DivTypeNoCN Rational Double :: *

type DivType Rational Double :: *

Methods

divideNoCN :: Rational -> Double -> DivTypeNoCN Rational Double

divide :: Rational -> Double -> DivType Rational Double

CanDiv Rational Int

Associated Types

type DivTypeNoCN Rational Int :: *

type DivType Rational Int :: *

Methods

divideNoCN :: Rational -> Int -> DivTypeNoCN Rational Int

divide :: Rational -> Int -> DivType Rational Int

CanDiv Rational Integer

Associated Types

type DivTypeNoCN Rational Integer :: *

type DivType Rational Integer :: *

Methods

divideNoCN :: Rational -> Integer -> DivTypeNoCN Rational Integer

divide :: Rational -> Integer -> DivType Rational Integer

CanDiv Rational Rational

Associated Types

type DivTypeNoCN Rational Rational :: *

type DivType Rational Rational :: *

Methods

divideNoCN :: Rational -> Rational -> DivTypeNoCN Rational Rational

divide :: Rational -> Rational -> DivType Rational Rational

(CanDiv Double b0, CanEnsureCE es0 b0, CanEnsureCE es0 (DivType Double b0), CanEnsureCE es0 (DivTypeNoCN Double b0), SuitableForCE es0) => CanDiv Double (CollectErrors es0 b0)

Associated Types

type DivTypeNoCN Double (CollectErrors es0 b0) :: *

type DivType Double (CollectErrors es0 b0) :: *

Methods

divideNoCN :: Double -> CollectErrors es0 b0 -> DivTypeNoCN Double (CollectErrors es0 b0)

divide :: Double -> CollectErrors es0 b0 -> DivType Double (CollectErrors es0 b0)

(CanDiv Int b0, CanEnsureCE es0 b0, CanEnsureCE es0 (DivType Int b0), CanEnsureCE es0 (DivTypeNoCN Int b0), SuitableForCE es0) => CanDiv Int (CollectErrors es0 b0)

Associated Types

type DivTypeNoCN Int (CollectErrors es0 b0) :: *

type DivType Int (CollectErrors es0 b0) :: *

Methods

divideNoCN :: Int -> CollectErrors es0 b0 -> DivTypeNoCN Int (CollectErrors es0 b0)

divide :: Int -> CollectErrors es0 b0 -> DivType Int (CollectErrors es0 b0)

(CanDiv Integer b0, CanEnsureCE es0 b0, CanEnsureCE es0 (DivType Integer b0), CanEnsureCE es0 (DivTypeNoCN Integer b0), SuitableForCE es0) => CanDiv Integer (CollectErrors es0 b0)

Associated Types

type DivTypeNoCN Integer (CollectErrors es0 b0) :: *

type DivType Integer (CollectErrors es0 b0) :: *

Methods

divideNoCN :: Integer -> CollectErrors es0 b0 -> DivTypeNoCN Integer (CollectErrors es0 b0)

divide :: Integer -> CollectErrors es0 b0 -> DivType Integer (CollectErrors es0 b0)

(CanDiv Rational b0, CanEnsureCE es0 b0, CanEnsureCE es0 (DivType Rational b0), CanEnsureCE es0 (DivTypeNoCN Rational b0), SuitableForCE es0) => CanDiv Rational (CollectErrors es0 b0)

Associated Types

type DivTypeNoCN Rational (CollectErrors es0 b0) :: *

type DivType Rational (CollectErrors es0 b0) :: *

Methods

divideNoCN :: Rational -> CollectErrors es0 b0 -> DivTypeNoCN Rational (CollectErrors es0 b0)

divide :: Rational -> CollectErrors es0 b0 -> DivType Rational (CollectErrors es0 b0)

CanDiv a b => CanDiv [a] [b]

Associated Types

type DivTypeNoCN [a] [b] :: *

type DivType [a] [b] :: *

Methods

divideNoCN :: [a] -> [b] -> DivTypeNoCN [a] [b]

divide :: [a] -> [b] -> DivType [a] [b]

CanDiv a b => CanDiv (Maybe a) (Maybe b)

Associated Types

type DivTypeNoCN (Maybe a) (Maybe b) :: *

type DivType (Maybe a) (Maybe b) :: *

Methods

divideNoCN :: Maybe a -> Maybe b -> DivTypeNoCN (Maybe a) (Maybe b)

divide :: Maybe a -> Maybe b -> DivType (Maybe a) (Maybe b)

(CanDiv a0 Double, CanEnsureCE es0 a0, CanEnsureCE es0 (DivType a0 Double), CanEnsureCE es0 (DivTypeNoCN a0 Double), SuitableForCE es0) => CanDiv (CollectErrors es0 a0) Double

Associated Types

type DivTypeNoCN (CollectErrors es0 a0) Double :: *

type DivType (CollectErrors es0 a0) Double :: *

Methods

divideNoCN :: CollectErrors es0 a0 -> Double -> DivTypeNoCN (CollectErrors es0 a0) Double

divide :: CollectErrors es0 a0 -> Double -> DivType (CollectErrors es0 a0) Double

(CanDiv a0 Rational, CanEnsureCE es0 a0, CanEnsureCE es0 (DivType a0 Rational), CanEnsureCE es0 (DivTypeNoCN a0 Rational), SuitableForCE es0) => CanDiv (CollectErrors es0 a0) Rational

Associated Types

type DivTypeNoCN (CollectErrors es0 a0) Rational :: *

type DivType (CollectErrors es0 a0) Rational :: *

Methods

divideNoCN :: CollectErrors es0 a0 -> Rational -> DivTypeNoCN (CollectErrors es0 a0) Rational

divide :: CollectErrors es0 a0 -> Rational -> DivType (CollectErrors es0 a0) Rational

(CanDiv a0 Int, CanEnsureCE es0 a0, CanEnsureCE es0 (DivType a0 Int), CanEnsureCE es0 (DivTypeNoCN a0 Int), SuitableForCE es0) => CanDiv (CollectErrors es0 a0) Int

Associated Types

type DivTypeNoCN (CollectErrors es0 a0) Int :: *

type DivType (CollectErrors es0 a0) Int :: *

Methods

divideNoCN :: CollectErrors es0 a0 -> Int -> DivTypeNoCN (CollectErrors es0 a0) Int

divide :: CollectErrors es0 a0 -> Int -> DivType (CollectErrors es0 a0) Int

(CanDiv a0 Integer, CanEnsureCE es0 a0, CanEnsureCE es0 (DivType a0 Integer), CanEnsureCE es0 (DivTypeNoCN a0 Integer), SuitableForCE es0) => CanDiv (CollectErrors es0 a0) Integer

Associated Types

type DivTypeNoCN (CollectErrors es0 a0) Integer :: *

type DivType (CollectErrors es0 a0) Integer :: *

Methods

divideNoCN :: CollectErrors es0 a0 -> Integer -> DivTypeNoCN (CollectErrors es0 a0) Integer

divide :: CollectErrors es0 a0 -> Integer -> DivType (CollectErrors es0 a0) Integer

(CanDiv a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (DivType a b), CanEnsureCE es (DivTypeNoCN a b), SuitableForCE es) => CanDiv (CollectErrors es a) (CollectErrors es b)

Associated Types

type DivTypeNoCN (CollectErrors es a) (CollectErrors es b) :: *

type DivType (CollectErrors es a) (CollectErrors es b) :: *

Methods

divideNoCN :: CollectErrors es a -> CollectErrors es b -> DivTypeNoCN (CollectErrors es a) (CollectErrors es b)

divide :: CollectErrors es a -> CollectErrors es b -> DivType (CollectErrors es a) (CollectErrors es b)

type CanDivBy t1 t2 = (CanDiv t1 t2, DivType t1 t2 ~ t1, DivTypeNoCN t1 t2 ~ t1)

type CanDivCNBy t1 t2 = (CanDiv t1 t2, DivType t1 t2 ~ EnsureCN t1, DivTypeNoCN t1 t2 ~ t1, CanEnsureCN t1, CanDiv (EnsureCN t1) t2, DivType (EnsureCN t1) t2 ~ EnsureCN t1, DivTypeNoCN (EnsureCN t1) t2 ~ EnsureCN t1)

type CanDivSameType t = CanDivBy t t

type CanDivCNSameType t = (CanDivCNBy t t, CanDiv (EnsureCN t) (EnsureCN t), DivType (EnsureCN t) (EnsureCN t) ~ EnsureCN t, DivTypeNoCN (EnsureCN t) (EnsureCN t) ~ EnsureCN t)

type CanRecip t = CanDiv Integer t

type CanRecipSameType t = (CanDiv Integer t, DivType Integer t ~ t, DivTypeNoCN Integer t ~ t)

type CanRecipCNSameType t = (CanDiv Integer t, DivType Integer t ~ EnsureCN t, DivTypeNoCN Integer t ~ t, CanEnsureCN t, CanDiv Integer (EnsureCN t), DivType Integer (EnsureCN t) ~ EnsureCN t, DivTypeNoCN Integer (EnsureCN t) ~ EnsureCN t)

(/) :: CanDiv t1 t2 => t1 -> t2 -> DivType t1 t2 infixl 7

(/!) :: CanDiv t1 t2 => t1 -> t2 -> DivTypeNoCN t1 t2 infixl 7

recip :: CanRecip t => t -> DivType Integer t

powUsingMulRecip :: (CanBeInteger e, CanRecipCNSameType t, CanMulSameType t, CanEnsureCN t) => t -> t -> e -> EnsureCN t

Tests

specCanDiv :: (Show t1, Show t2, Show (DivType Integer (DivType Integer t1)), Show (DivType t1 t2), Show (DivType t1 t1), Show (MulType t1 (DivType t1 t2)), Arbitrary t1, Arbitrary t2, ConvertibleExactly Integer t1, ConvertibleExactly Integer t2, CanTestCertainly (EqCompareType (DivType Integer (DivType Integer t1)) t1), CanTestCertainly (EqCompareType (DivType t1 t2) t1), CanTestCertainly (EqCompareType (DivType t1 t1) t1), CanTestCertainly (EqCompareType (DivType t1 t2) (MulType t1 (DivType t1 t2))), HasEqAsymmetric (DivType Integer (DivType Integer t1)) t1, HasEqAsymmetric (DivType t1 t2) t1, HasEqAsymmetric (DivType t1 t2) (MulType t1 (DivType t1 t2)), HasEqAsymmetric (DivType t1 t1) t1, CanTestZero t1, CanTestZero t2, CanTestZero (DivType Integer t1), CanMulAsymmetric t1 (DivType t1 t2), CanDiv t1 t1, CanDiv t1 t2, CanDiv Integer t1, CanDiv Integer (DivType Integer t1)) => T t1 -> T t2 -> Spec

HSpec properties that each implementation of CanDiv should satisfy.

specCanDivNotMixed :: (Show t, Show (DivType Integer (DivType Integer t)), Show (DivType t t), Show (MulType t (DivType t t)), Arbitrary t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType (DivType Integer (DivType Integer t)) t), CanTestCertainly (EqCompareType (DivType t t) t), CanTestCertainly (EqCompareType (DivType t t) (MulType t (DivType t t))), HasEqAsymmetric (DivType Integer (DivType Integer t)) t, HasEqAsymmetric (DivType t t) t, HasEqAsymmetric (DivType t t) (MulType t (DivType t t)), CanTestZero t, CanTestZero (DivType Integer t), CanMulAsymmetric t (DivType t t), CanDiv t t, CanDiv Integer t, CanDiv Integer (DivType Integer t)) => T t -> Spec

HSpec properties that each implementation of CanDiv should satisfy.