Numeric.MixedTypes.Ring

Ring

type CanAddSubMulBy t s = (CanAddThis t s, CanSubThis t s, CanSub s t, SubType s t ~ t, CanMulBy t s)

class (RingPre t, CanEnsureCN t, RingPre (EnsureCN t)) => Ring t

Instances

Ring Integer

Defined in Numeric.MixedTypes.Ring

Ring Rational

Defined in Numeric.MixedTypes.Ring

Ring (CN Integer)

Defined in Numeric.MixedTypes.Ring

Ring (CN Rational)

Defined in Numeric.MixedTypes.Ring

class (Ring t, HasEq t t, HasEq (EnsureCN t) t, HasEq t (EnsureCN t), HasEq t Int, HasEq t Integer, HasEq (EnsureCN t) Int, HasEq (EnsureCN t) Integer, HasOrder t t, HasOrder (EnsureCN t) t, HasOrder t (EnsureCN t), HasOrder t Int, HasOrder t Integer, HasOrder (EnsureCN t) Int, HasOrder (EnsureCN t) Integer) => OrderedRing t

Instances

OrderedRing Integer

Defined in Numeric.MixedTypes.Ring

OrderedRing Rational

Defined in Numeric.MixedTypes.Ring

OrderedRing (CN Integer)

Defined in Numeric.MixedTypes.Ring

OrderedRing (CN Rational)

Defined in Numeric.MixedTypes.Ring

class (Ring t, HasEqCertainly t t, HasEqCertainly (EnsureCN t) t, HasEqCertainly t (EnsureCN t), HasEqCertainly t Int, HasEq t Integer, HasEqCertainly (EnsureCN t) Int, HasEq (EnsureCN t) Integer, HasOrderCertainly t t, HasOrderCertainly (EnsureCN t) t, HasOrderCertainly t (EnsureCN t), HasOrderCertainly t Int, HasOrderCertainly t Integer, HasOrderCertainly (EnsureCN t) Int, HasOrderCertainly (EnsureCN t) Integer, CanTestPosNeg t) => OrderedCertainlyRing t

Instances

OrderedCertainlyRing Integer

Defined in Numeric.MixedTypes.Ring

OrderedCertainlyRing Rational

Defined in Numeric.MixedTypes.Ring

OrderedCertainlyRing (CN Integer)

Defined in Numeric.MixedTypes.Ring

OrderedCertainlyRing (CN Rational)

Defined in Numeric.MixedTypes.Ring

Multiplication

type CanMul t1 t2 = (CanMulAsymmetric t1 t2, CanMulAsymmetric t2 t1, MulType t1 t2 ~ MulType t2 t1)

class CanMulAsymmetric t1 t2 where

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

Minimal complete definition

Nothing

Associated Types

type MulType t1 t2

type MulType t1 t2 = t1

Methods

mul :: t1 -> t2 -> MulType t1 t2

default mul :: (MulType t1 t2 ~ t1, t1 ~ t2, Num t1) => t1 -> t2 -> MulType t1 t2

Instances

CanMulAsymmetric Double Double

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Double Double

Methods

mul :: Double -> Double -> MulType Double Double

CanMulAsymmetric Double Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Double Int

Methods

mul :: Double -> Int -> MulType Double Int

CanMulAsymmetric Double Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Double Integer

Methods

mul :: Double -> Integer -> MulType Double Integer

CanMulAsymmetric Double Rational

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Double Rational

Methods

mul :: Double -> Rational -> MulType Double Rational

CanMulAsymmetric Int Double

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Int Double

Methods

mul :: Int -> Double -> MulType Int Double

CanMulAsymmetric Int Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Int Int

Methods

mul :: Int -> Int -> MulType Int Int

CanMulAsymmetric Int Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Int Integer

Methods

mul :: Int -> Integer -> MulType Int Integer

CanMulAsymmetric Int Rational

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Int Rational

Methods

mul :: Int -> Rational -> MulType Int Rational

CanMulAsymmetric Integer Double

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Integer Double

Methods

mul :: Integer -> Double -> MulType Integer Double

CanMulAsymmetric Integer Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Integer Int

Methods

mul :: Integer -> Int -> MulType Integer Int

CanMulAsymmetric Integer Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Integer Integer

Methods

mul :: Integer -> Integer -> MulType Integer Integer

CanMulAsymmetric Integer Rational

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Integer Rational

Methods

mul :: Integer -> Rational -> MulType Integer Rational

CanMulAsymmetric Rational Double

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Rational Double

Methods

mul :: Rational -> Double -> MulType Rational Double

CanMulAsymmetric Rational Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Rational Int

Methods

mul :: Rational -> Int -> MulType Rational Int

CanMulAsymmetric Rational Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Rational Integer

Methods

mul :: Rational -> Integer -> MulType Rational Integer

CanMulAsymmetric Rational Rational

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Rational Rational

Methods

mul :: Rational -> Rational -> MulType Rational Rational

CanMulAsymmetric Double b => CanMulAsymmetric Double (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType Double (Complex b)

Methods

mul :: Double -> Complex b -> MulType Double (Complex b)

CanMulAsymmetric Int b => CanMulAsymmetric Int (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType Int (Complex b)

Methods

mul :: Int -> Complex b -> MulType Int (Complex b)

CanMulAsymmetric Integer b => CanMulAsymmetric Integer (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType Integer (Complex b)

Methods

mul :: Integer -> Complex b -> MulType Integer (Complex b)

CanMulAsymmetric Rational b => CanMulAsymmetric Rational (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType Rational (Complex b)

Methods

mul :: Rational -> Complex b -> MulType Rational (Complex b)

(CanMulAsymmetric Double b, CanEnsureCE es b, CanEnsureCE es (MulType Double b), SuitableForCE es) => CanMulAsymmetric Double (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Double (CollectErrors es b)

Methods

mul :: Double -> CollectErrors es b -> MulType Double (CollectErrors es b)

(CanMulAsymmetric Int b, CanEnsureCE es b, CanEnsureCE es (MulType Int b), SuitableForCE es) => CanMulAsymmetric Int (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Int (CollectErrors es b)

Methods

mul :: Int -> CollectErrors es b -> MulType Int (CollectErrors es b)

(CanMulAsymmetric Integer b, CanEnsureCE es b, CanEnsureCE es (MulType Integer b), SuitableForCE es) => CanMulAsymmetric Integer (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Integer (CollectErrors es b)

Methods

mul :: Integer -> CollectErrors es b -> MulType Integer (CollectErrors es b)

(CanMulAsymmetric Rational b, CanEnsureCE es b, CanEnsureCE es (MulType Rational b), SuitableForCE es) => CanMulAsymmetric Rational (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType Rational (CollectErrors es b)

Methods

mul :: Rational -> CollectErrors es b -> MulType Rational (CollectErrors es b)

CanMulAsymmetric a Integer => CanMulAsymmetric (Complex a) Integer

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) Integer

Methods

mul :: Complex a -> Integer -> MulType (Complex a) Integer

CanMulAsymmetric a Int => CanMulAsymmetric (Complex a) Int

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) Int

Methods

mul :: Complex a -> Int -> MulType (Complex a) Int

CanMulAsymmetric a Rational => CanMulAsymmetric (Complex a) Rational

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) Rational

Methods

mul :: Complex a -> Rational -> MulType (Complex a) Rational

CanMulAsymmetric a Double => CanMulAsymmetric (Complex a) Double

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) Double

Methods

mul :: Complex a -> Double -> MulType (Complex a) Double

CanMulAsymmetric a b => CanMulAsymmetric [a] [b]

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType [a] [b]

Methods

mul :: [a] -> [b] -> MulType [a] [b]

CanMulAsymmetric a b => CanMulAsymmetric (Maybe a) (Maybe b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType (Maybe a) (Maybe b)

Methods

mul :: Maybe a -> Maybe b -> MulType (Maybe a) (Maybe b)

(CanMulAsymmetric a b, CanAddSameType (MulType a b), CanSubSameType (MulType a b)) => CanMulAsymmetric (Complex a) (Complex b)

Defined in Numeric.MixedTypes.Complex

Associated Types

type MulType (Complex a) (Complex b)

Methods

mul :: Complex a -> Complex b -> MulType (Complex a) (Complex b)

(CanMulAsymmetric a Integer, CanEnsureCE es a, CanEnsureCE es (MulType a Integer), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType (CollectErrors es a) Integer

Methods

mul :: CollectErrors es a -> Integer -> MulType (CollectErrors es a) Integer

(CanMulAsymmetric a Int, CanEnsureCE es a, CanEnsureCE es (MulType a Int), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType (CollectErrors es a) Int

Methods

mul :: CollectErrors es a -> Int -> MulType (CollectErrors es a) Int

(CanMulAsymmetric a Rational, CanEnsureCE es a, CanEnsureCE es (MulType a Rational), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) Rational

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType (CollectErrors es a) Rational

Methods

mul :: CollectErrors es a -> Rational -> MulType (CollectErrors es a) Rational

(CanMulAsymmetric a Double, CanEnsureCE es a, CanEnsureCE es (MulType a Double), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) Double

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType (CollectErrors es a) Double

Methods

mul :: CollectErrors es a -> Double -> MulType (CollectErrors es a) Double

(CanMulAsymmetric a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (MulType a b), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type MulType (CollectErrors es a) (CollectErrors es b)

Methods

mul :: CollectErrors es a -> CollectErrors es b -> MulType (CollectErrors es a) (CollectErrors es b)

type CanMulBy t1 t2 = (CanMul t1 t2, MulType t1 t2 ~ t1)

type CanMulSameType t = CanMulBy t t

(*) :: CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2 infixl 7

product :: (CanMulSameType t, ConvertibleExactly Integer t) => [t] -> t

Tests

specCanMul :: (Show t1, Show t2, Show t3, Show (MulType t1 t2), Show (MulType t2 t1), Show (MulType t1 (MulType t2 t3)), Show (MulType (MulType t1 t2) t3), Show (MulType t1 (AddType t2 t3)), Show (AddType (MulType t1 t2) (MulType t1 t3)), Arbitrary t1, Arbitrary t2, Arbitrary t3, ConvertibleExactly Integer t2, CanTestCertainly (EqCompareType (MulType t1 t2) t1), CanTestCertainly (EqCompareType (MulType t1 t2) (MulType t2 t1)), CanTestCertainly (EqCompareType (MulType t1 (MulType t2 t3)) (MulType (MulType t1 t2) t3)), CanTestCertainly (EqCompareType (MulType t1 (AddType t2 t3)) (AddType (MulType t1 t2) (MulType t1 t3))), HasEqAsymmetric (MulType t1 t2) t1, HasEqAsymmetric (MulType t1 t2) (MulType t2 t1), HasEqAsymmetric (MulType t1 (MulType t2 t3)) (MulType (MulType t1 t2) t3), HasEqAsymmetric (MulType t1 (AddType t2 t3)) (AddType (MulType t1 t2) (MulType t1 t3)), CanAddAsymmetric t2 t3, CanAddAsymmetric (MulType t1 t2) (MulType t1 t3), CanMulAsymmetric t1 t2, CanMulAsymmetric t1 t3, CanMulAsymmetric t1 (MulType t2 t3), CanMulAsymmetric t1 (AddType t2 t3), CanMulAsymmetric t2 t1, CanMulAsymmetric t2 t3, CanMulAsymmetric (MulType t1 t2) t3) => T t1 -> T t2 -> T t3 -> Spec

HSpec properties that each implementation of CanMul should satisfy.

specCanMulNotMixed :: (Show t, Show (MulType t t), Show (MulType t (MulType t t)), Show (MulType (MulType t t) t), Show (MulType t (AddType t t)), Show (AddType (MulType t t) (MulType t t)), Arbitrary t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType (MulType t t) t), CanTestCertainly (EqCompareType (MulType t t) (MulType t t)), CanTestCertainly (EqCompareType (MulType t (MulType t t)) (MulType (MulType t t) t)), CanTestCertainly (EqCompareType (MulType t (AddType t t)) (AddType (MulType t t) (MulType t t))), HasEqAsymmetric (MulType t t) t, HasEqAsymmetric (MulType t t) (MulType t t), HasEqAsymmetric (MulType t (MulType t t)) (MulType (MulType t t) t), HasEqAsymmetric (MulType t (AddType t t)) (AddType (MulType t t) (MulType t t)), CanAddAsymmetric t t, CanAddAsymmetric (MulType t t) (MulType t t), CanMulAsymmetric t t, CanMulAsymmetric t (MulType t t), CanMulAsymmetric t (AddType t t), CanMulAsymmetric (MulType t t) t) => T t -> Spec

HSpec properties that each implementation of CanMul should satisfy.

specCanMulSameType :: (Show t, ConvertibleExactly Integer t, CanTestCertainly (EqCompareType t t), HasEqAsymmetric t t, CanMulAsymmetric t t, MulType t t ~ t) => T t -> Spec

HSpec properties that each implementation of CanMulSameType should satisfy.

Exponentiation

class CanPow b e where

A replacement for Prelude's binary ^ and ^^. If Num t1 and Integral t2, then one can use the default implementation to mirror Prelude's ^.

Minimal complete definition

powNoCN

Associated Types

type PowTypeNoCN b e

type PowTypeNoCN b e = b

type PowType b e

type PowType b e = EnsureCN (PowTypeNoCN b e)

Methods

powNoCN :: b -> e -> PowTypeNoCN b e

pow :: b -> e -> PowType b e

default pow :: (HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, CanTestInteger e, CanEnsureCN (PowTypeNoCN b e), PowType b e ~ EnsureCN (PowTypeNoCN b e)) => b -> e -> PowType b e

Instances

CanPow Double Double

Defined in Numeric.MixedTypes.Elementary

Associated Types

type PowTypeNoCN Double Double

type PowType Double Double

Methods

powNoCN :: Double -> Double -> PowTypeNoCN Double Double

pow :: Double -> Double -> PowType Double Double

CanPow Double Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Double Int

type PowType Double Int

Methods

powNoCN :: Double -> Int -> PowTypeNoCN Double Int

pow :: Double -> Int -> PowType Double Int

CanPow Double Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Double Integer

type PowType Double Integer

Methods

powNoCN :: Double -> Integer -> PowTypeNoCN Double Integer

pow :: Double -> Integer -> PowType Double Integer

CanPow Double Rational

Defined in Numeric.MixedTypes.Elementary

Associated Types

type PowTypeNoCN Double Rational

type PowType Double Rational

Methods

powNoCN :: Double -> Rational -> PowTypeNoCN Double Rational

pow :: Double -> Rational -> PowType Double Rational

CanPow Int Double

Defined in Numeric.MixedTypes.Elementary

Associated Types

type PowTypeNoCN Int Double

type PowType Int Double

Methods

powNoCN :: Int -> Double -> PowTypeNoCN Int Double

pow :: Int -> Double -> PowType Int Double

CanPow Int Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Int Int

type PowType Int Int

Methods

powNoCN :: Int -> Int -> PowTypeNoCN Int Int

pow :: Int -> Int -> PowType Int Int

CanPow Int Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Int Integer

type PowType Int Integer

Methods

powNoCN :: Int -> Integer -> PowTypeNoCN Int Integer

pow :: Int -> Integer -> PowType Int Integer

CanPow Integer Double

Defined in Numeric.MixedTypes.Elementary

Associated Types

type PowTypeNoCN Integer Double

type PowType Integer Double

Methods

powNoCN :: Integer -> Double -> PowTypeNoCN Integer Double

pow :: Integer -> Double -> PowType Integer Double

CanPow Integer Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Integer Int

type PowType Integer Int

Methods

powNoCN :: Integer -> Int -> PowTypeNoCN Integer Int

pow :: Integer -> Int -> PowType Integer Int

CanPow Integer Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Integer Integer

type PowType Integer Integer

Methods

powNoCN :: Integer -> Integer -> PowTypeNoCN Integer Integer

pow :: Integer -> Integer -> PowType Integer Integer

CanPow Rational Double

Defined in Numeric.MixedTypes.Elementary

Associated Types

type PowTypeNoCN Rational Double

type PowType Rational Double

Methods

powNoCN :: Rational -> Double -> PowTypeNoCN Rational Double

pow :: Rational -> Double -> PowType Rational Double

CanPow Rational Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Rational Int

type PowType Rational Int

Methods

powNoCN :: Rational -> Int -> PowTypeNoCN Rational Int

pow :: Rational -> Int -> PowType Rational Int

CanPow Rational Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Rational Integer

type PowType Rational Integer

Methods

powNoCN :: Rational -> Integer -> PowTypeNoCN Rational Integer

pow :: Rational -> Integer -> PowType Rational Integer

(CanPow Double b, CanEnsureCE es b, CanEnsureCE es (PowType Double b), CanEnsureCE es (PowTypeNoCN Double b), SuitableForCE es) => CanPow Double (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Double (CollectErrors es b)

type PowType Double (CollectErrors es b)

Methods

powNoCN :: Double -> CollectErrors es b -> PowTypeNoCN Double (CollectErrors es b)

pow :: Double -> CollectErrors es b -> PowType Double (CollectErrors es b)

(CanPow Int b, CanEnsureCE es b, CanEnsureCE es (PowType Int b), CanEnsureCE es (PowTypeNoCN Int b), SuitableForCE es) => CanPow Int (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Int (CollectErrors es b)

type PowType Int (CollectErrors es b)

Methods

powNoCN :: Int -> CollectErrors es b -> PowTypeNoCN Int (CollectErrors es b)

pow :: Int -> CollectErrors es b -> PowType Int (CollectErrors es b)

(CanPow Integer b, CanEnsureCE es b, CanEnsureCE es (PowType Integer b), CanEnsureCE es (PowTypeNoCN Integer b), SuitableForCE es) => CanPow Integer (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Integer (CollectErrors es b)

type PowType Integer (CollectErrors es b)

Methods

powNoCN :: Integer -> CollectErrors es b -> PowTypeNoCN Integer (CollectErrors es b)

pow :: Integer -> CollectErrors es b -> PowType Integer (CollectErrors es b)

(CanPow Rational b, CanEnsureCE es b, CanEnsureCE es (PowType Rational b), CanEnsureCE es (PowTypeNoCN Rational b), SuitableForCE es) => CanPow Rational (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN Rational (CollectErrors es b)

type PowType Rational (CollectErrors es b)

Methods

powNoCN :: Rational -> CollectErrors es b -> PowTypeNoCN Rational (CollectErrors es b)

pow :: Rational -> CollectErrors es b -> PowType Rational (CollectErrors es b)

CanPow a b => CanPow (Maybe a) (Maybe b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN (Maybe a) (Maybe b)

type PowType (Maybe a) (Maybe b)

Methods

powNoCN :: Maybe a -> Maybe b -> PowTypeNoCN (Maybe a) (Maybe b)

pow :: Maybe a -> Maybe b -> PowType (Maybe a) (Maybe b)

(CanPow a Integer, CanEnsureCE es a, CanEnsureCE es (PowType a Integer), CanEnsureCE es (PowTypeNoCN a Integer), SuitableForCE es) => CanPow (CollectErrors es a) Integer

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN (CollectErrors es a) Integer

type PowType (CollectErrors es a) Integer

Methods

powNoCN :: CollectErrors es a -> Integer -> PowTypeNoCN (CollectErrors es a) Integer

pow :: CollectErrors es a -> Integer -> PowType (CollectErrors es a) Integer

(CanPow a Int, CanEnsureCE es a, CanEnsureCE es (PowType a Int), CanEnsureCE es (PowTypeNoCN a Int), SuitableForCE es) => CanPow (CollectErrors es a) Int

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN (CollectErrors es a) Int

type PowType (CollectErrors es a) Int

Methods

powNoCN :: CollectErrors es a -> Int -> PowTypeNoCN (CollectErrors es a) Int

pow :: CollectErrors es a -> Int -> PowType (CollectErrors es a) Int

(CanPow a Rational, CanEnsureCE es a, CanEnsureCE es (PowType a Rational), CanEnsureCE es (PowTypeNoCN a Rational), SuitableForCE es) => CanPow (CollectErrors es a) Rational

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN (CollectErrors es a) Rational

type PowType (CollectErrors es a) Rational

Methods

powNoCN :: CollectErrors es a -> Rational -> PowTypeNoCN (CollectErrors es a) Rational

pow :: CollectErrors es a -> Rational -> PowType (CollectErrors es a) Rational

(CanPow a Double, CanEnsureCE es a, CanEnsureCE es (PowType a Double), CanEnsureCE es (PowTypeNoCN a Double), SuitableForCE es) => CanPow (CollectErrors es a) Double

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN (CollectErrors es a) Double

type PowType (CollectErrors es a) Double

Methods

powNoCN :: CollectErrors es a -> Double -> PowTypeNoCN (CollectErrors es a) Double

pow :: CollectErrors es a -> Double -> PowType (CollectErrors es a) Double

(CanPow a b, CanEnsureCE es a, CanEnsureCE es b, CanEnsureCE es (PowTypeNoCN a b), CanEnsureCE es (PowType a b), SuitableForCE es) => CanPow (CollectErrors es a) (CollectErrors es b)

Defined in Numeric.MixedTypes.Ring

Associated Types

type PowTypeNoCN (CollectErrors es a) (CollectErrors es b)

type PowType (CollectErrors es a) (CollectErrors es b)

Methods

powNoCN :: CollectErrors es a -> CollectErrors es b -> PowTypeNoCN (CollectErrors es a) (CollectErrors es b)

pow :: CollectErrors es a -> CollectErrors es b -> PowType (CollectErrors es a) (CollectErrors es b)

type CanPowBy t1 t2 = (CanPow t1 t2, PowType t1 t2 ~ t1, PowTypeNoCN t1 t2 ~ t1)

type CanPowCNBy t1 t2 = (CanPow t1 t2, PowType t1 t2 ~ EnsureCN t1, PowTypeNoCN t1 t2 ~ t1, CanEnsureCN t1, CanPow (EnsureCN t1) t2, PowType (EnsureCN t1) t2 ~ EnsureCN t1, PowTypeNoCN (EnsureCN t1) t2 ~ EnsureCN t1)

(^) :: CanPow t1 t2 => t1 -> t2 -> PowType t1 t2 infixl 8

(^!) :: CanPow t1 t2 => t1 -> t2 -> PowTypeNoCN t1 t2 infixl 8

Like ^ but throwing an exception if the power is undefined.

powUsingMul :: (CanBeInteger e, CanMulSameType t) => t -> t -> e -> t

integerPowCN :: (HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, HasEqCertainly e Integer, CanEnsureCN r) => (b -> e -> r) -> b -> e -> EnsureCN r

Tests

specCanPow :: (Show t1, Show t2, Show (PowType t1 t2), Show (MulType t1 (PowType t1 t2)), Show (PowType t1 (AddType t2 Integer)), Arbitrary t1, Arbitrary t2, ConvertibleExactly Integer t1, ConvertibleExactly Integer t2, CanTestCertainly (EqCompareType (PowType t1 t2) t1), CanTestCertainly (EqCompareType (MulType t1 (PowType t1 t2)) (PowType t1 (AddType t2 Integer))), HasEqAsymmetric (PowType t1 t2) t1, HasEqAsymmetric (MulType t1 (PowType t1 t2)) (PowType t1 (AddType t2 Integer)), CanTestPosNeg t2, CanAddAsymmetric t2 Integer, CanPow t1 t2, CanPow t1 (AddType t2 Integer), CanMulAsymmetric t1 (PowType t1 t2)) => T t1 -> T t2 -> Spec

HSpec properties that each implementation of CanPow should satisfy.