Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

AERN2.Real.Arithmetic

Contents

Orphan instances

Description

Arithmetic operations on Cauchy Real numbers, except those that are defined for more general sequences

Synopsis

pi :: CauchyReal
piA :: QAArrow to => CauchyRealA to

Documentation

pi :: CauchyReal #

To get pi in an arbitrary arrow, use piA.

piA :: QAArrow to => CauchyRealA to #

Orphan instances

Floating CauchyRealCN #
Instance details Methods pi :: CauchyRealCN # exp :: CauchyRealCN -> CauchyRealCN # log :: CauchyRealCN -> CauchyRealCN # sqrt :: CauchyRealCN -> CauchyRealCN # (**) :: CauchyRealCN -> CauchyRealCN -> CauchyRealCN # logBase :: CauchyRealCN -> CauchyRealCN -> CauchyRealCN # sin :: CauchyRealCN -> CauchyRealCN # cos :: CauchyRealCN -> CauchyRealCN # tan :: CauchyRealCN -> CauchyRealCN # asin :: CauchyRealCN -> CauchyRealCN # acos :: CauchyRealCN -> CauchyRealCN # atan :: CauchyRealCN -> CauchyRealCN # sinh :: CauchyRealCN -> CauchyRealCN # cosh :: CauchyRealCN -> CauchyRealCN # tanh :: CauchyRealCN -> CauchyRealCN # asinh :: CauchyRealCN -> CauchyRealCN # acosh :: CauchyRealCN -> CauchyRealCN # atanh :: CauchyRealCN -> CauchyRealCN # log1p :: CauchyRealCN -> CauchyRealCN # expm1 :: CauchyRealCN -> CauchyRealCN # log1pexp :: CauchyRealCN -> CauchyRealCN # log1mexp :: CauchyRealCN -> CauchyRealCN #
Floating CauchyReal #
Instance details Methods pi :: CauchyReal # exp :: CauchyReal -> CauchyReal # log :: CauchyReal -> CauchyReal # sqrt :: CauchyReal -> CauchyReal # (**) :: CauchyReal -> CauchyReal -> CauchyReal # logBase :: CauchyReal -> CauchyReal -> CauchyReal # sin :: CauchyReal -> CauchyReal # cos :: CauchyReal -> CauchyReal # tan :: CauchyReal -> CauchyReal # asin :: CauchyReal -> CauchyReal # acos :: CauchyReal -> CauchyReal # atan :: CauchyReal -> CauchyReal # sinh :: CauchyReal -> CauchyReal # cosh :: CauchyReal -> CauchyReal # tanh :: CauchyReal -> CauchyReal # asinh :: CauchyReal -> CauchyReal # acosh :: CauchyReal -> CauchyReal # atanh :: CauchyReal -> CauchyReal # log1p :: CauchyReal -> CauchyReal # expm1 :: CauchyReal -> CauchyReal # log1pexp :: CauchyReal -> CauchyReal # log1mexp :: CauchyReal -> CauchyReal #
CanSqrt Int #
Instance details Associated Types type SqrtType Int :: * # Methods sqrt :: Int -> SqrtType Int #
CanSqrt Integer #
Instance details Associated Types type SqrtType Integer :: * # Methods sqrt :: Integer -> SqrtType Integer #
CanSqrt Rational #
Instance details Associated Types type SqrtType Rational :: * # Methods sqrt :: Rational -> SqrtType Rational #
CanSqrt Dyadic #
Instance details Associated Types type SqrtType Dyadic :: * # Methods sqrt :: Dyadic -> SqrtType Dyadic #
CanExp Int #
Instance details Associated Types type ExpType Int :: * # Methods exp :: Int -> ExpType Int #
CanExp Integer #
Instance details Associated Types type ExpType Integer :: * # Methods exp :: Integer -> ExpType Integer #
CanExp Rational #
Instance details Associated Types type ExpType Rational :: * # Methods exp :: Rational -> ExpType Rational #
CanExp Dyadic #
Instance details Associated Types type ExpType Dyadic :: * # Methods exp :: Dyadic -> ExpType Dyadic #
CanLog Int #
Instance details Associated Types type LogType Int :: * # Methods log :: Int -> LogType Int #
CanLog Integer #
Instance details Associated Types type LogType Integer :: * # Methods log :: Integer -> LogType Integer #
CanLog Rational #
Instance details Associated Types type LogType Rational :: * # Methods log :: Rational -> LogType Rational #
CanLog Dyadic #
Instance details Associated Types type LogType Dyadic :: * # Methods log :: Dyadic -> LogType Dyadic #
CanSinCos Int #
Instance details Associated Types type SinCosType Int :: * # Methods cos :: Int -> SinCosType Int # sin :: Int -> SinCosType Int #
CanSinCos Integer #
Instance details Associated Types type SinCosType Integer :: * # Methods cos :: Integer -> SinCosType Integer # sin :: Integer -> SinCosType Integer #
CanSinCos Rational #
Instance details Associated Types type SinCosType Rational :: * # Methods cos :: Rational -> SinCosType Rational # sin :: Rational -> SinCosType Rational #
CanSinCos Dyadic #
Instance details Associated Types type SinCosType Dyadic :: * # Methods cos :: Dyadic -> SinCosType Dyadic # sin :: Dyadic -> SinCosType Dyadic #
Convertible CauchyReal Double #
Instance details Methods safeConvert :: CauchyReal -> ConvertResult Double #
CanDiv Double CauchyReal #
Instance details Associated Types type DivTypeNoCN Double CauchyReal :: * # type DivType Double CauchyReal :: * # Methods divideNoCN :: Double -> CauchyReal -> DivTypeNoCN Double CauchyReal # divide :: Double -> CauchyReal -> DivType Double CauchyReal #
CanDiv CauchyReal Double #
Instance details Associated Types type DivTypeNoCN CauchyReal Double :: * # type DivType CauchyReal Double :: * # Methods divideNoCN :: CauchyReal -> Double -> DivTypeNoCN CauchyReal Double # divide :: CauchyReal -> Double -> DivType CauchyReal Double #
CanMulAsymmetric Double CauchyReal #
Instance details Associated Types type MulType Double CauchyReal :: * # Methods mul :: Double -> CauchyReal -> MulType Double CauchyReal #
CanMulAsymmetric CauchyReal Double #
Instance details Associated Types type MulType CauchyReal Double :: * # Methods mul :: CauchyReal -> Double -> MulType CauchyReal Double #
CanPow Double CauchyReal #
Instance details Associated Types type PowTypeNoCN Double CauchyReal :: * # type PowType Double CauchyReal :: * # Methods powNoCN :: Double -> CauchyReal -> PowTypeNoCN Double CauchyReal # pow :: Double -> CauchyReal -> PowType Double CauchyReal #
CanPow Int Rational #
Instance details Associated Types type PowTypeNoCN Int Rational :: * # type PowType Int Rational :: * # Methods powNoCN :: Int -> Rational -> PowTypeNoCN Int Rational # pow :: Int -> Rational -> PowType Int Rational #
CanPow Int Dyadic #
Instance details Associated Types type PowTypeNoCN Int Dyadic :: * # type PowType Int Dyadic :: * # Methods powNoCN :: Int -> Dyadic -> PowTypeNoCN Int Dyadic # pow :: Int -> Dyadic -> PowType Int Dyadic #
CanPow Integer Rational #
Instance details Associated Types type PowTypeNoCN Integer Rational :: * # type PowType Integer Rational :: * # Methods powNoCN :: Integer -> Rational -> PowTypeNoCN Integer Rational # pow :: Integer -> Rational -> PowType Integer Rational #
CanPow Integer Dyadic #
Instance details Associated Types type PowTypeNoCN Integer Dyadic :: * # type PowType Integer Dyadic :: * # Methods powNoCN :: Integer -> Dyadic -> PowTypeNoCN Integer Dyadic # pow :: Integer -> Dyadic -> PowType Integer Dyadic #
CanPow Rational Rational #
Instance details Associated Types type PowTypeNoCN Rational Rational :: * # type PowType Rational Rational :: * # Methods powNoCN :: Rational -> Rational -> PowTypeNoCN Rational Rational # pow :: Rational -> Rational -> PowType Rational Rational #
CanPow Rational Dyadic #
Instance details Associated Types type PowTypeNoCN Rational Dyadic :: * # type PowType Rational Dyadic :: * # Methods powNoCN :: Rational -> Dyadic -> PowTypeNoCN Rational Dyadic # pow :: Rational -> Dyadic -> PowType Rational Dyadic #
CanPow Dyadic Rational #
Instance details Associated Types type PowTypeNoCN Dyadic Rational :: * # type PowType Dyadic Rational :: * # Methods powNoCN :: Dyadic -> Rational -> PowTypeNoCN Dyadic Rational # pow :: Dyadic -> Rational -> PowType Dyadic Rational #
CanPow Dyadic Dyadic #
Instance details Associated Types type PowTypeNoCN Dyadic Dyadic :: * # type PowType Dyadic Dyadic :: * # Methods powNoCN :: Dyadic -> Dyadic -> PowTypeNoCN Dyadic Dyadic # pow :: Dyadic -> Dyadic -> PowType Dyadic Dyadic #
CanPow CauchyReal Double #
Instance details Associated Types type PowTypeNoCN CauchyReal Double :: * # type PowType CauchyReal Double :: * # Methods powNoCN :: CauchyReal -> Double -> PowTypeNoCN CauchyReal Double # pow :: CauchyReal -> Double -> PowType CauchyReal Double #
CanAddAsymmetric Double CauchyReal #
Instance details Associated Types type AddType Double CauchyReal :: * # Methods add :: Double -> CauchyReal -> AddType Double CauchyReal #
CanAddAsymmetric CauchyReal Double #
Instance details Associated Types type AddType CauchyReal Double :: * # Methods add :: CauchyReal -> Double -> AddType CauchyReal Double #
CanSub Double CauchyReal #
Instance details Associated Types type SubType Double CauchyReal :: * # Methods sub :: Double -> CauchyReal -> SubType Double CauchyReal #
CanSub CauchyReal Double #
Instance details Associated Types type SubType CauchyReal Double :: * # Methods sub :: CauchyReal -> Double -> SubType CauchyReal Double #
QAArrow to => Field (CauchyRealA to) #
Instance details
QAArrow to => OrderedField (CauchyRealA to) #
Instance details
QAArrow to => Ring (CauchyRealA to) #
Instance details
QAArrow to => OrderedRing (CauchyRealA to) #
Instance details
CanMulAsymmetric t (CauchyRealA to) => CanMulAsymmetric (Complex t) (CauchyRealA to) #
Instance details Associated Types type MulType (Complex t) (CauchyRealA to) :: * # Methods mul :: Complex t -> CauchyRealA to -> MulType (Complex t) (CauchyRealA to) #
CanMulAsymmetric (CauchyRealA to) t => CanMulAsymmetric (CauchyRealA to) (Complex t) #
Instance details Associated Types type MulType (CauchyRealA to) (Complex t) :: * # Methods mul :: CauchyRealA to -> Complex t -> MulType (CauchyRealA to) (Complex t) #
(QAArrow to, CanAddAsymmetric t (CauchyRealA to)) => CanAddAsymmetric (Complex t) (CauchyRealA to) #
Instance details Associated Types type AddType (Complex t) (CauchyRealA to) :: * # Methods add :: Complex t -> CauchyRealA to -> AddType (Complex t) (CauchyRealA to) #
(QAArrow to, CanAddAsymmetric (CauchyRealA to) t) => CanAddAsymmetric (CauchyRealA to) (Complex t) #
Instance details Associated Types type AddType (CauchyRealA to) (Complex t) :: * # Methods add :: CauchyRealA to -> Complex t -> AddType (CauchyRealA to) (Complex t) #
(QAArrow to, CanAdd t (CauchyRealA to)) => CanSub (Complex t) (CauchyRealA to) #
Instance details Associated Types type SubType (Complex t) (CauchyRealA to) :: * # Methods sub :: Complex t -> CauchyRealA to -> SubType (Complex t) (CauchyRealA to) #
(QAArrow to, CanAdd (CauchyRealA to) t, CanNegSameType t) => CanSub (CauchyRealA to) (Complex t) #
Instance details Associated Types type SubType (CauchyRealA to) (Complex t) :: * # Methods sub :: CauchyRealA to -> Complex t -> SubType (CauchyRealA to) (Complex t) #