Numeric.MixedTypes.Complex

Instances for Data.Complex.

Documentation

tComplex :: T t -> T (Complex t)

Orphan instances

ConvertibleExactly Int t => ConvertibleExactly Int (Complex t)

Methods

safeConvertExactly :: Int -> ConvertResult (Complex t)

ConvertibleExactly Integer t => ConvertibleExactly Integer (Complex t)

Methods

safeConvertExactly :: Integer -> ConvertResult (Complex t)

ConvertibleExactly Rational t => ConvertibleExactly Rational (Complex t)

Methods

safeConvertExactly :: Rational -> ConvertResult (Complex t)

HasEqAsymmetric Double b => HasEqAsymmetric Double (Complex b)

Associated Types

type EqCompareType Double (Complex b)

Methods

equalTo :: Double -> Complex b -> EqCompareType Double (Complex b)

notEqualTo :: Double -> Complex b -> EqCompareType Double (Complex b)

HasEqAsymmetric Int b => HasEqAsymmetric Int (Complex b)

Associated Types

type EqCompareType Int (Complex b)

Methods

equalTo :: Int -> Complex b -> EqCompareType Int (Complex b)

notEqualTo :: Int -> Complex b -> EqCompareType Int (Complex b)

HasEqAsymmetric Integer b => HasEqAsymmetric Integer (Complex b)

Associated Types

type EqCompareType Integer (Complex b)

Methods

equalTo :: Integer -> Complex b -> EqCompareType Integer (Complex b)

notEqualTo :: Integer -> Complex b -> EqCompareType Integer (Complex b)

HasEqAsymmetric Rational b => HasEqAsymmetric Rational (Complex b)

Associated Types

type EqCompareType Rational (Complex b)

Methods

equalTo :: Rational -> Complex b -> EqCompareType Rational (Complex b)

notEqualTo :: Rational -> Complex b -> EqCompareType Rational (Complex b)

CanSub Double b => CanSub Double (Complex b)

Associated Types

type SubType Double (Complex b)

Methods

sub :: Double -> Complex b -> SubType Double (Complex b)

CanSub Int b => CanSub Int (Complex b)

Associated Types

type SubType Int (Complex b)

Methods

sub :: Int -> Complex b -> SubType Int (Complex b)

CanSub Integer b => CanSub Integer (Complex b)

Associated Types

type SubType Integer (Complex b)

Methods

sub :: Integer -> Complex b -> SubType Integer (Complex b)

CanSub Rational b => CanSub Rational (Complex b)

Associated Types

type SubType Rational (Complex b)

Methods

sub :: Rational -> Complex b -> SubType Rational (Complex b)

CanAddAsymmetric Double b => CanAddAsymmetric Double (Complex b)

Associated Types

type AddType Double (Complex b)

Methods

add :: Double -> Complex b -> AddType Double (Complex b)

CanAddAsymmetric Int b => CanAddAsymmetric Int (Complex b)

Associated Types

type AddType Int (Complex b)

Methods

add :: Int -> Complex b -> AddType Int (Complex b)

CanAddAsymmetric Integer b => CanAddAsymmetric Integer (Complex b)

Associated Types

type AddType Integer (Complex b)

Methods

add :: Integer -> Complex b -> AddType Integer (Complex b)

CanAddAsymmetric Rational b => CanAddAsymmetric Rational (Complex b)

Associated Types

type AddType Rational (Complex b)

Methods

add :: Rational -> Complex b -> AddType Rational (Complex b)

CanMulAsymmetric Double b => CanMulAsymmetric Double (Complex b)

Associated Types

type MulType Double (Complex b)

Methods

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

CanMulAsymmetric Int b => CanMulAsymmetric Int (Complex b)

Associated Types

type MulType Int (Complex b)

Methods

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

CanMulAsymmetric Integer b => CanMulAsymmetric Integer (Complex b)

Associated Types

type MulType Integer (Complex b)

Methods

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

CanMulAsymmetric Rational b => CanMulAsymmetric Rational (Complex b)

Associated Types

type MulType Rational (Complex b)

Methods

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

(CanMulAsymmetric Double b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Double b) (MulType b b)) => CanDiv Double (Complex b)

Associated Types

type DivType Double (Complex b)

Methods

divide :: Double -> Complex b -> DivType Double (Complex b)

(CanMulAsymmetric Int b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Int b) (MulType b b)) => CanDiv Int (Complex b)

Associated Types

type DivType Int (Complex b)

Methods

divide :: Int -> Complex b -> DivType Int (Complex b)

(CanMulAsymmetric Integer b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Integer b) (MulType b b)) => CanDiv Integer (Complex b)

Associated Types

type DivType Integer (Complex b)

Methods

divide :: Integer -> Complex b -> DivType Integer (Complex b)

(CanMulAsymmetric Rational b, CanMulAsymmetric b b, CanAddSameType (MulType b b), CanDiv (MulType Rational b) (MulType b b)) => CanDiv Rational (Complex b)

Associated Types

type DivType Rational (Complex b)

Methods

divide :: Rational -> Complex b -> DivType Rational (Complex b)

CanNeg t => CanNeg (Complex t)

Associated Types

type NegType (Complex t)

Methods

negate :: Complex t -> NegType (Complex t)

(CanTestInteger t, CanTestZero t) => CanTestInteger (Complex t)

Methods

certainlyNotInteger :: Complex t -> Bool

certainlyInteger :: Complex t -> Bool

certainlyIntegerGetIt :: Complex t -> Maybe Integer

(CanMulAsymmetric t t, CanAddSameType (MulType t t), CanSqrt (MulType t t)) => CanAbs (Complex t)

Associated Types

type AbsType (Complex t)

Methods

abs :: Complex t -> AbsType (Complex t)

(CanExp t, CanSinCos t, CanMulAsymmetric (ExpType t) (SinCosType t)) => CanExp (Complex t)

Associated Types

type ExpType (Complex t)

Methods

exp :: Complex t -> ExpType (Complex t)

HasEqAsymmetric a Integer => HasEqAsymmetric (Complex a) Integer

Associated Types

type EqCompareType (Complex a) Integer

Methods

equalTo :: Complex a -> Integer -> EqCompareType (Complex a) Integer

notEqualTo :: Complex a -> Integer -> EqCompareType (Complex a) Integer

HasEqAsymmetric a Int => HasEqAsymmetric (Complex a) Int

Associated Types

type EqCompareType (Complex a) Int

Methods

equalTo :: Complex a -> Int -> EqCompareType (Complex a) Int

notEqualTo :: Complex a -> Int -> EqCompareType (Complex a) Int

HasEqAsymmetric a Rational => HasEqAsymmetric (Complex a) Rational

Associated Types

type EqCompareType (Complex a) Rational

Methods

equalTo :: Complex a -> Rational -> EqCompareType (Complex a) Rational

notEqualTo :: Complex a -> Rational -> EqCompareType (Complex a) Rational

HasEqAsymmetric a Double => HasEqAsymmetric (Complex a) Double

Associated Types

type EqCompareType (Complex a) Double

Methods

equalTo :: Complex a -> Double -> EqCompareType (Complex a) Double

notEqualTo :: Complex a -> Double -> EqCompareType (Complex a) Double

CanSub a Integer => CanSub (Complex a) Integer

Associated Types

type SubType (Complex a) Integer

Methods

sub :: Complex a -> Integer -> SubType (Complex a) Integer

CanSub a Int => CanSub (Complex a) Int

Associated Types

type SubType (Complex a) Int

Methods

sub :: Complex a -> Int -> SubType (Complex a) Int

CanSub a Rational => CanSub (Complex a) Rational

Associated Types

type SubType (Complex a) Rational

Methods

sub :: Complex a -> Rational -> SubType (Complex a) Rational

CanSub a Double => CanSub (Complex a) Double

Associated Types

type SubType (Complex a) Double

Methods

sub :: Complex a -> Double -> SubType (Complex a) Double

CanAddAsymmetric a Integer => CanAddAsymmetric (Complex a) Integer

Associated Types

type AddType (Complex a) Integer

Methods

add :: Complex a -> Integer -> AddType (Complex a) Integer

CanAddAsymmetric a Int => CanAddAsymmetric (Complex a) Int

Associated Types

type AddType (Complex a) Int

Methods

add :: Complex a -> Int -> AddType (Complex a) Int

CanAddAsymmetric a Rational => CanAddAsymmetric (Complex a) Rational

Associated Types

type AddType (Complex a) Rational

Methods

add :: Complex a -> Rational -> AddType (Complex a) Rational

CanAddAsymmetric a Double => CanAddAsymmetric (Complex a) Double

Associated Types

type AddType (Complex a) Double

Methods

add :: Complex a -> Double -> AddType (Complex a) Double

CanMulAsymmetric a Integer => CanMulAsymmetric (Complex a) Integer

Associated Types

type MulType (Complex a) Integer

Methods

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

CanMulAsymmetric a Int => CanMulAsymmetric (Complex a) Int

Associated Types

type MulType (Complex a) Int

Methods

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

CanMulAsymmetric a Rational => CanMulAsymmetric (Complex a) Rational

Associated Types

type MulType (Complex a) Rational

Methods

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

CanMulAsymmetric a Double => CanMulAsymmetric (Complex a) Double

Associated Types

type MulType (Complex a) Double

Methods

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

CanDiv a Integer => CanDiv (Complex a) Integer

Associated Types

type DivType (Complex a) Integer

Methods

divide :: Complex a -> Integer -> DivType (Complex a) Integer

CanDiv a Int => CanDiv (Complex a) Int

Associated Types

type DivType (Complex a) Int

Methods

divide :: Complex a -> Int -> DivType (Complex a) Int

CanDiv a Rational => CanDiv (Complex a) Rational

Associated Types

type DivType (Complex a) Rational

Methods

divide :: Complex a -> Rational -> DivType (Complex a) Rational

CanDiv a Double => CanDiv (Complex a) Double

Associated Types

type DivType (Complex a) Double

Methods

divide :: Complex a -> Double -> DivType (Complex a) Double

ConvertibleExactly t1 t2 => ConvertibleExactly (Complex t1) (Complex t2)

Methods

safeConvertExactly :: Complex t1 -> ConvertResult (Complex t2)

HasEqAsymmetric a b => HasEqAsymmetric (Complex a) (Complex b)

Associated Types

type EqCompareType (Complex a) (Complex b)

Methods

equalTo :: Complex a -> Complex b -> EqCompareType (Complex a) (Complex b)

notEqualTo :: Complex a -> Complex b -> EqCompareType (Complex a) (Complex b)

CanSub a b => CanSub (Complex a) (Complex b)

Associated Types

type SubType (Complex a) (Complex b)

Methods

sub :: Complex a -> Complex b -> SubType (Complex a) (Complex b)

CanAddAsymmetric a b => CanAddAsymmetric (Complex a) (Complex b)

Associated Types

type AddType (Complex a) (Complex b)

Methods

add :: Complex a -> Complex b -> AddType (Complex a) (Complex b)

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

Associated Types

type MulType (Complex a) (Complex b)

Methods

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

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

Associated Types

type DivType (Complex a) (Complex b)

Methods

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