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 b0 => HasEqAsymmetric Double (Complex b0)

Associated Types

type EqCompareType Double (Complex b0) :: *

Methods

equalTo :: Double -> Complex b0 -> EqCompareType Double (Complex b0)

notEqualTo :: Double -> Complex b0 -> EqCompareType Double (Complex b0)

HasEqAsymmetric Int b0 => HasEqAsymmetric Int (Complex b0)

Associated Types

type EqCompareType Int (Complex b0) :: *

Methods

equalTo :: Int -> Complex b0 -> EqCompareType Int (Complex b0)

notEqualTo :: Int -> Complex b0 -> EqCompareType Int (Complex b0)

HasEqAsymmetric Integer b0 => HasEqAsymmetric Integer (Complex b0)

Associated Types

type EqCompareType Integer (Complex b0) :: *

Methods

equalTo :: Integer -> Complex b0 -> EqCompareType Integer (Complex b0)

notEqualTo :: Integer -> Complex b0 -> EqCompareType Integer (Complex b0)

HasEqAsymmetric Rational b0 => HasEqAsymmetric Rational (Complex b0)

Associated Types

type EqCompareType Rational (Complex b0) :: *

Methods

equalTo :: Rational -> Complex b0 -> EqCompareType Rational (Complex b0)

notEqualTo :: Rational -> Complex b0 -> EqCompareType Rational (Complex b0)

CanSub Double b0 => CanSub Double (Complex b0)

Associated Types

type SubType Double (Complex b0) :: *

Methods

sub :: Double -> Complex b0 -> SubType Double (Complex b0)

CanSub Int b0 => CanSub Int (Complex b0)

Associated Types

type SubType Int (Complex b0) :: *

Methods

sub :: Int -> Complex b0 -> SubType Int (Complex b0)

CanSub Integer b0 => CanSub Integer (Complex b0)

Associated Types

type SubType Integer (Complex b0) :: *

Methods

sub :: Integer -> Complex b0 -> SubType Integer (Complex b0)

CanSub Rational b0 => CanSub Rational (Complex b0)

Associated Types

type SubType Rational (Complex b0) :: *

Methods

sub :: Rational -> Complex b0 -> SubType Rational (Complex b0)

CanAddAsymmetric Double b0 => CanAddAsymmetric Double (Complex b0)

Associated Types

type AddType Double (Complex b0) :: *

Methods

add :: Double -> Complex b0 -> AddType Double (Complex b0)

CanAddAsymmetric Int b0 => CanAddAsymmetric Int (Complex b0)

Associated Types

type AddType Int (Complex b0) :: *

Methods

add :: Int -> Complex b0 -> AddType Int (Complex b0)

CanAddAsymmetric Integer b0 => CanAddAsymmetric Integer (Complex b0)

Associated Types

type AddType Integer (Complex b0) :: *

Methods

add :: Integer -> Complex b0 -> AddType Integer (Complex b0)

CanAddAsymmetric Rational b0 => CanAddAsymmetric Rational (Complex b0)

Associated Types

type AddType Rational (Complex b0) :: *

Methods

add :: Rational -> Complex b0 -> AddType Rational (Complex b0)

CanMulAsymmetric Double b0 => CanMulAsymmetric Double (Complex b0)

Associated Types

type MulType Double (Complex b0) :: *

Methods

mul :: Double -> Complex b0 -> MulType Double (Complex b0)

CanMulAsymmetric Int b0 => CanMulAsymmetric Int (Complex b0)

Associated Types

type MulType Int (Complex b0) :: *

Methods

mul :: Int -> Complex b0 -> MulType Int (Complex b0)

CanMulAsymmetric Integer b0 => CanMulAsymmetric Integer (Complex b0)

Associated Types

type MulType Integer (Complex b0) :: *

Methods

mul :: Integer -> Complex b0 -> MulType Integer (Complex b0)

CanMulAsymmetric Rational b0 => CanMulAsymmetric Rational (Complex b0)

Associated Types

type MulType Rational (Complex b0) :: *

Methods

mul :: Rational -> Complex b0 -> MulType Rational (Complex b0)

(CanMulAsymmetric Double b0, CanMulAsymmetric b0 b0, CanAddSameType (MulType b0 b0), CanDiv (MulType Double b0) (MulType b0 b0)) => CanDiv Double (Complex b0)

Associated Types

type DivTypeNoCN Double (Complex b0) :: *

type DivType Double (Complex b0) :: *

Methods

divideNoCN :: Double -> Complex b0 -> DivTypeNoCN Double (Complex b0)

divide :: Double -> Complex b0 -> DivType Double (Complex b0)

(CanMulAsymmetric Int b0, CanMulAsymmetric b0 b0, CanAddSameType (MulType b0 b0), CanDiv (MulType Int b0) (MulType b0 b0)) => CanDiv Int (Complex b0)

Associated Types

type DivTypeNoCN Int (Complex b0) :: *

type DivType Int (Complex b0) :: *

Methods

divideNoCN :: Int -> Complex b0 -> DivTypeNoCN Int (Complex b0)

divide :: Int -> Complex b0 -> DivType Int (Complex b0)

(CanMulAsymmetric Integer b0, CanMulAsymmetric b0 b0, CanAddSameType (MulType b0 b0), CanDiv (MulType Integer b0) (MulType b0 b0)) => CanDiv Integer (Complex b0)

Associated Types

type DivTypeNoCN Integer (Complex b0) :: *

type DivType Integer (Complex b0) :: *

Methods

divideNoCN :: Integer -> Complex b0 -> DivTypeNoCN Integer (Complex b0)

divide :: Integer -> Complex b0 -> DivType Integer (Complex b0)

(CanMulAsymmetric Rational b0, CanMulAsymmetric b0 b0, CanAddSameType (MulType b0 b0), CanDiv (MulType Rational b0) (MulType b0 b0)) => CanDiv Rational (Complex b0)

Associated Types

type DivTypeNoCN Rational (Complex b0) :: *

type DivType Rational (Complex b0) :: *

Methods

divideNoCN :: Rational -> Complex b0 -> DivTypeNoCN Rational (Complex b0)

divide :: Rational -> Complex b0 -> DivType Rational (Complex b0)

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 a0 Double => HasEqAsymmetric (Complex a0) Double

Associated Types

type EqCompareType (Complex a0) Double :: *

Methods

equalTo :: Complex a0 -> Double -> EqCompareType (Complex a0) Double

notEqualTo :: Complex a0 -> Double -> EqCompareType (Complex a0) Double

HasEqAsymmetric a0 Rational => HasEqAsymmetric (Complex a0) Rational

Associated Types

type EqCompareType (Complex a0) Rational :: *

Methods

equalTo :: Complex a0 -> Rational -> EqCompareType (Complex a0) Rational

notEqualTo :: Complex a0 -> Rational -> EqCompareType (Complex a0) Rational

HasEqAsymmetric a0 Int => HasEqAsymmetric (Complex a0) Int

Associated Types

type EqCompareType (Complex a0) Int :: *

Methods

equalTo :: Complex a0 -> Int -> EqCompareType (Complex a0) Int

notEqualTo :: Complex a0 -> Int -> EqCompareType (Complex a0) Int

HasEqAsymmetric a0 Integer => HasEqAsymmetric (Complex a0) Integer

Associated Types

type EqCompareType (Complex a0) Integer :: *

Methods

equalTo :: Complex a0 -> Integer -> EqCompareType (Complex a0) Integer

notEqualTo :: Complex a0 -> Integer -> EqCompareType (Complex a0) Integer

CanSub a0 Double => CanSub (Complex a0) Double

Associated Types

type SubType (Complex a0) Double :: *

Methods

sub :: Complex a0 -> Double -> SubType (Complex a0) Double

CanSub a0 Rational => CanSub (Complex a0) Rational

Associated Types

type SubType (Complex a0) Rational :: *

Methods

sub :: Complex a0 -> Rational -> SubType (Complex a0) Rational

CanSub a0 Int => CanSub (Complex a0) Int

Associated Types

type SubType (Complex a0) Int :: *

Methods

sub :: Complex a0 -> Int -> SubType (Complex a0) Int

CanSub a0 Integer => CanSub (Complex a0) Integer

Associated Types

type SubType (Complex a0) Integer :: *

Methods

sub :: Complex a0 -> Integer -> SubType (Complex a0) Integer

CanAddAsymmetric a0 Double => CanAddAsymmetric (Complex a0) Double

Associated Types

type AddType (Complex a0) Double :: *

Methods

add :: Complex a0 -> Double -> AddType (Complex a0) Double

CanAddAsymmetric a0 Rational => CanAddAsymmetric (Complex a0) Rational

Associated Types

type AddType (Complex a0) Rational :: *

Methods

add :: Complex a0 -> Rational -> AddType (Complex a0) Rational

CanAddAsymmetric a0 Int => CanAddAsymmetric (Complex a0) Int

Associated Types

type AddType (Complex a0) Int :: *

Methods

add :: Complex a0 -> Int -> AddType (Complex a0) Int

CanAddAsymmetric a0 Integer => CanAddAsymmetric (Complex a0) Integer

Associated Types

type AddType (Complex a0) Integer :: *

Methods

add :: Complex a0 -> Integer -> AddType (Complex a0) Integer

CanMulAsymmetric a0 Double => CanMulAsymmetric (Complex a0) Double

Associated Types

type MulType (Complex a0) Double :: *

Methods

mul :: Complex a0 -> Double -> MulType (Complex a0) Double

CanMulAsymmetric a0 Rational => CanMulAsymmetric (Complex a0) Rational

Associated Types

type MulType (Complex a0) Rational :: *

Methods

mul :: Complex a0 -> Rational -> MulType (Complex a0) Rational

CanMulAsymmetric a0 Int => CanMulAsymmetric (Complex a0) Int

Associated Types

type MulType (Complex a0) Int :: *

Methods

mul :: Complex a0 -> Int -> MulType (Complex a0) Int

CanMulAsymmetric a0 Integer => CanMulAsymmetric (Complex a0) Integer

Associated Types

type MulType (Complex a0) Integer :: *

Methods

mul :: Complex a0 -> Integer -> MulType (Complex a0) Integer

CanDiv a0 Double => CanDiv (Complex a0) Double

Associated Types

type DivTypeNoCN (Complex a0) Double :: *

type DivType (Complex a0) Double :: *

Methods

divideNoCN :: Complex a0 -> Double -> DivTypeNoCN (Complex a0) Double

divide :: Complex a0 -> Double -> DivType (Complex a0) Double

CanDiv a0 Rational => CanDiv (Complex a0) Rational

Associated Types

type DivTypeNoCN (Complex a0) Rational :: *

type DivType (Complex a0) Rational :: *

Methods

divideNoCN :: Complex a0 -> Rational -> DivTypeNoCN (Complex a0) Rational

divide :: Complex a0 -> Rational -> DivType (Complex a0) Rational

CanDiv a0 Int => CanDiv (Complex a0) Int

Associated Types

type DivTypeNoCN (Complex a0) Int :: *

type DivType (Complex a0) Int :: *

Methods

divideNoCN :: Complex a0 -> Int -> DivTypeNoCN (Complex a0) Int

divide :: Complex a0 -> Int -> DivType (Complex a0) Int

CanDiv a0 Integer => CanDiv (Complex a0) Integer

Associated Types

type DivTypeNoCN (Complex a0) Integer :: *

type DivType (Complex a0) Integer :: *

Methods

divideNoCN :: Complex a0 -> Integer -> DivTypeNoCN (Complex a0) Integer

divide :: Complex a0 -> Integer -> DivType (Complex a0) Integer

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 DivTypeNoCN (Complex a) (Complex b) :: *

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

Methods

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

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